CRUST AND UPPER MANTLE STRUCTURE
OF
THE NORTHEASTERN UNITED STATES
by
Steven R. Taylor
B.S., Ohio University, Athens, Ohio
(1975)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHY
at the
0
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
May, 1980
Signature of Author.................
Department of Earth
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1980
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CRUST AND UPPER MANTLE STRUCTURE
OF
THE NORTHEASTERN UNITED STATES
by
Steven R. Taylor
Submitted to the Department of Earth and Planetary Sciences
on May 9, 1980, in partial fulfillment of the requirements
for the degree of Doctor of Philosophy
ABSTRACT
Recognition that mountain belts are places where oceans
have closed
implies that continental
structure differs
across them.
Using the northeastern
United States (NEUS)
seismic network, it is shown that this applies to the
northern Appalachians by investigating the crustal structure
of the Precambrian Grenville Province in New York state and
the New England Paleozoic Appalachian Province.
The crust
and upper mantle structure of the NEUS
is
studied
by
combining teleseismic and regional body wave observations
with surface wave dispersion measurements.
The velocity models suggest that structures down to
possibly 200 km and greater can be correlated with surficial
geologic and tectonic features and that the two orogenic
belts show marked differences in
crustal
structure.
This
has the important implication that major orogenic belts have
effects that reach well into the lithosphere which are
stable for extended periods of time, perhaps as long as 1
b.y.
Regional travel times recorded across the NEUS seismic
network
indicate
that
the northern Appalachians are
characterized by a well-defined two layer crust, with a
relatively high velocity lower layer. The upper crustal
layer, approximately 15 km thick with P and S velocities of
6.1 and 3.6 km/s, respectively, overlies a high velocity
lower crust with P and S velocities of 7.0 and 4.1 km/s.
The average crustal thickness is approximately 40 km. The
crust of the Grenville Province is vertically homogeneous
with nearly constant P and S velocities of 6.6 and 3.7 km/s,
respectively, and an average crustal thickness of 37 km.
Analysis of Rayleigh wave phase and group velocities
yields structural models that are relatively consistent with
the models derived from regional travel times. A method for
calculating interstation phase and group velocities from the
interstation transfer function using Wiener deconvolution is
2
presented.
The Rayleigh wave phase and group velocities
along different paths are inverted simultaneously using a
maximum-likelihood technique.
Phase and group velocities
are also calculated across the MIT short-period network in
southeastern
New
England
by
estimating
the
frequency-wavenumber power spectra.
Lateral variations in structure are studied
using time
term analysis and teleseismic P wave residuals.
A region of
thick or low-velocity crust trends northeast across eastern
New York, western Massachusetts, southeast Vermont, central
New Hampshire, and central Maine. In eastern New York this
zone correlates with Bouguer gravity lows and with the
Taconic klippen; a thick pile of thrusts emplaced during the
mid-Ordovician Taconic orogeny.
The crustal thickening
beneath central New England correlates well with Bouguer
gravity
lows and is found in the region of highest
topography indicating an isostatically compensated highland
area.
The suture between the Grenville and Appalachian Province
in the NEUS probably occurs along a north-northeast trending
belt extending from northwestern Vermont to southwestern
Connecticut.
High
crustal
velocities and/or crustal
thinning, a linear gravity high, a serpentinite belt,
Precambrian uplifts, and the Taconic thrusts are found along
much of this belt which shows many similarities to the Ivera
zone in northern Italy.
There is also the possibility of a second suture located
in the eastern section of the study area separating the
central orogenic belt from an eastern block (Avalonia).
Refraction models, and Pn and teleseismic P wave residuals
indicate that the crust of the eastern block is probably
thinner than that of the central belt and may be missing the
high
velocity
lower
crustal
layer.
In
eastern
Massachusetts, these two regions are separated by prominent
fault zones across which no formations can be traced.
Three-dimensional inversion of
teleseismic
P
wave
residuals indicates that a relatively low velocity anomaly
extending to depths in excess of 200 km and dipping to the
northwest shows a spatial correlation with the Bronson Hill
- Boundary Mountains Anticlinorium in central New Hampshire
and Maine.
These structures occupy the sites of a complex
series of island arc sequences last active in Early Devonian
time prior to the Acadian orogeny. This low-velocity region
may represent subducted oceanic lithosphere which
has
undergone post-orogenic radioactive heating. Alternatively,
the oceanic lithosphere may have been totally subducted
resulting in lower velocity material filling the vacated
Benioff zone.
The observed differences in crustal structure between the
Grenville and Appalachian Provinces are probably the result
in
variations of petrology, chemistry, water content,
temperature, and tectonic evolution. Comparison of seismic
velocities with resistivity measurements suggests that the
lower crust of the Grenville Province may be composed of
rocks with hydrous mineral phases resulting in lowered
velocities and a higher Poisson's ratio. Alternatively, the
rocks of the lower crust beneath the Grenville Province may
be similar to those found on the surface while higher
velocity, mafic mineralogies are prevalent in the lower
crust of the Appalachians.
This is consistent with the
hypothesis that the Grenville crust underwent substantial
reactivation,
thickened, and became vertically uniform
during the Grenville orogeny. In contrast, the rocks of the
Appalachian belt probably were associated with a cycle of
oceanic opening and closure which suggests an ensimatic
origin of the lower crust in this region.
Thesis Advisor: M. Nafi Toksoz
Professor of Geophysics
ACKNOWLEDGEMENTS
ones
The old adage "giving the tie off
to
applies
my
advisor
M.
Toksoz
Nafi
neck"
gave
who
tremendous amount of help and support over the
literally
me
a
His
years.
insight for identifying interesting geophysical problems and
defining
ways to solve them made things much easier for me.
I will remain indebted to Nafi.
Sykes
Lynn
and
Golisano,
Mary
Aggarwal,
Yash
Lamont-Doherty Geological Observatory freely provided
used
data
period
in
many
aspects
and
College
Ed Chiburis of Weston Observatory at Boston
of
short
Many
of this thesis.
geological discussions with B. C. Burchfiel, Pat Barosh, and
Frank Spear are also greatly appreciated.
My fellow partners-in-crime kept my spirits up and
me
all
in
aspects of my work.
aided
My fuzzy-faced office-mate
Michael Clair Fehler demonstrated to me that
a
can
person
finish a thesis at M.I.T. without becoming a babbling idiot.
MCF
is a real star, and although he specialized in the more
sensual aspects of geophysics such as the study of jerky and
wet cracks, and hot dry rocks, he would always take time
to
listen
my
problems, then say something like "You don't
know that? Its simply the
then
set
me
straight.
correspondence
I'll
over-the-glasses looks, his funny
and
his
stink
to
executive command.
man of many talents, can tell you
principle."
always
miss
accent,
his
his
and
stern
binoculars,
Arthur C. H. Cheng, the
about
dominant
diagonal
5
matrices and the lie of Rick Middleton's hockey stick in the
same
breath (unless he's reading the sports page...in which
case he won't tell you
stinks
and
can't
anything.)
I
George
Zandt
tell the difference between a phone line
glitch and a deep earthquake
velocity),
Although
(both
have
a
high
apparent
hope that our continued search for mysterious
blocks in the lithosphere and resurgent domes causes
cross
paths.
Clifford
H.
Thurber,
my
office-mate, sits over there at his desk
frustrate
me
with
his
efficency.
us
to
theoretical-type
and
continues
to
His programs work the
first time, he write lots of papers on every different topic
in geophysics,
and
attitude on life.
he
continues
to
maintain
a
healthy
Never once did he give me a hard time for
stealing cookies out of his desk drawer.
Norm Burr, Bill Ellsworth, and Randy
major
influence
during
Richardson
my formative years at M.I.T.
introduced me to the wonders of computer
and
most
me
hacking,
importantly to Hilltop Steak House.
took me under his wing and helped with
told
"Yes,
Steve
were
there
is
a
Without intending to, Randy convinced
3-D
to
a
Norm
LLL,
Bill sort of
inversions
and
U Lambda V-transpose".
me
to
let
somebody
else figure out the state of stress in the lithosphere.
In later years, I had
along
the
way
Albert Hsui,
Mike
John
Sean Solomon,
Chaplin,
recommend
with
fun
Rob
drinking
interesting
discussions
Nabelek, Jay Pulli, Jim Muller,
Wai Ying Chung,
Comer,
and
and
Gerardo
and Mark Willis.
giggling
with
Suarez,
I also highly
Steve
Roecker,
especially on a mountain.
Of
course,
students,
I
Roger
shan't
Buck,
forget
input
into
stellar
seismology
Ken Tubman, Rob Stewart, Dan Davis,
Lynn Hall, and all the others.
much
my
Ken
Tubman
also
provided
the surface wave analysis and good old RB
kept my ego pumped up.
These
guys
are
all
going
to
be
superstars.
There are also the
fifth
floor.
Sara
"real"
people
scattered
Brydges
seemed
to be doing me favors
everytime I turned around
else,
and
in
addition
helped me keep up on local gossip.
to
about
everything
George Keough, Al
Taylor, and Dave Johnston provided much assistance with
maintenance
and
operation
of
the
the
M.I.T seismic network.
Then there's always the other two crazies at the end of
hall,
the
the
Judy Roos and Sharyn Belk.
Of course, none of this would have been possible
without
the love, help, and support from both sets of my parents, my
sister-ugly
who
sent
me
funny
rocks
from
the Canadian
Rockies, and the rest of the Goff family.
Pino's Pizza (End your quest, at Pino's you've found
the
best) supplied me with my weekly grease quota.
And
without
getting
mushy,
I
thank
Heather
for
everything.
This research was supported
Commission
by
the
Nuclear
Regulatory
contract NRC-04-76-209 and the Advanced Research
Projects Agency,
monitored
by
the
Air
Force
office
Scientific Research under contract F44620-75-C-0064.
of
TABLE OF CONTENTS
PAGE
Abstract
1
Acknowledgements
4
Chapter 1.
Introduction
11
Chapter 2.
Geologic and Geophysical Setting
16
2.1
Geologic Setting
16
2.2
Geophysical Setting
19
2.2.1
Gravity and Magnetics
20
2.2.2
Heat Flow and Resistivity
22
24
Figures
Crustal Structure from Regional
Chapter 3.
Travel Times
3.1
Structure from Measured Quarry Blasts
3.2
Average Structure Using P and S Arrivals
31
32
from Regional Earthquakes
3.2.1
Data
34
3.2.2
Analysis of Travel Time Curves
36
3.2.3
Error Analysis
38
3.2.4
Results
Lateral Structure from Time Term Analysis
3.3
of the Pn Branch
40
3.3.1
Method
41
3.3.2
Results and Interpretation
43
Comparison With Other Refraction Models in
3.4
Eastern North America
46
48
Tables
Figures
Chapter 4.
Structure Derived from Surface Waves
4.1
Introduction
4.2
Crust and Upper Mantle Structure from Mea-
69
69
surement of Interstation Phase and Group
Velocities
4.2.1
Data
70
70
9
PAGE
4.2.2
Interstation Transfer Function
Using Wiener Deconvolution
4.2.3
Measurement of Interstation Phase
Velocities
4.2.4
74
Measurement of Interstation Group
Velocities
76
4.2.5
Error Analysis
81
4.2.6
Description of Rayleigh Wave Phase
and Group Velocities
4.3
72
85
Estimation of Frequency-Wavenumber Power
Spectrum in Southeastern New England
4.4
87
4.3.1
Data
89
4.3.2
Interpretation and Discussion
91
Simultaneous Inversion of Rayleigh Wave
Phase and Group Velocities Using a
Maximum-Likelihood Technique
4.4.1
93
Information Derived from Fundamental
Mode Rayleigh Wave Phase and Group
Velocities
4.4.2
Inversion Results
Tables
102
Figures
105
Chapter 5.
Crust and Upper Mantle Structure from
P Waves
148
5.1
Travel Time Residuals
150
5.2
Three-Dimensional Inversion
160
Teleseismic
Tables
170
Figures
173
Chapter 6.
Variations of Crust and Upper Mantle
Structure in the Appalachian Orogenic
Belt:
6.1
Implications for Tectonic Evolution
Summary of Results Presented in Previous
Chapters
6.2
190
190
Contrasts Between Grenville and Appalachian
Provinces in the NEUS
194
6.2.1
Compositional Differences
195
6.2.2
Contrasts in Tectonic Evolution
198
PAGE
6.3
Contrasts Between Northern and Southern
Appalachians
6.4
209
Tectonic Evolution of the Northern
Appalachians
212
Table
219
Figures
220
References
226
Appendix A.
Generalized and Stochastic Inversion
Appendix B.
Non-Linear Inversion of Travel Time Data
240
for Cross-Over Distances and Apparent
Velocities
246
Appendix
Time Term Analysis
251
Appendix
Computation of Frequency-Wavenumber
Power Spectra
Figures
Appendix E.
267
Calculation of Phase and Group Velocity
Partial Derivatives
Appendix F.
270
Maximum-Likelihood Inversion of Phase and
Group Velocity
Appendix G.
257
273
Interstation Transfer Function Using
Wiener Deconvolution
Figures
Biographical Note
277
283
287
CHAPTER 1
INTRODUCTION
With
the
network
in
northeastern
operation
United
since
States
1975,
it
and
upper
mantle
of the Precambrian Grenville Province in New York
state and the New England
Paleozoic
The
this thesis is
region under study in
segment of
extends
seismic
became possible to
investigate for the first time the crust
structure
(NEUS)
an
at
impressive
least
3,000
Appalachian
Paleozoic
km
actually one small
mountain
from
Province.
chain
that
the southeastern United
States through New England and into Newfoundland.
The tectonic history of ancient mountain belts is usually
interpreted in terms of the reigning evolutionary models for
neo-tectonic belts such as the Himalayas, the Alps,
Zagros.
However,
the
geology
and
mountain belts is often known in
difficult
to
formulate
evolutionary model because
encountered.
cores
of
great
even
of
geophysics
a
the
detail
simple
numerous
or
of
and
the
older
it
first
is
order
complications
Ancient orogenic belts represent deeply eroded
more recent mountain chains and detailed geologic
and geophysical studies of these older
Appalachians
should
provide
belts
important
such
as
the
constraints
for
interpreting the younger belts.
Many of the geologic, tectonic, and geophysical
problems
associated
with the northern Appalachians were discussed at
the Zen-Zietz Penrose Conference of the
of
America
in
1972,
(1973).
During
detailed
seismic
geologic
and
and
the
Geological
Society
are summarized by Zietz and Zen
conference,
it
became
clear
that
work would be necessary to aid in solving
tectonic
problems.
A
detailed
seismic
refraction survey was judged to be too expensive.
"Without it,
however,
calculations
based
on
gravity data are too unconstrained to lead to much
more
than
inconclusive
speculation.
Lynn Sykes
suggested that some of the desired information
velocity
structure
less cost by a
observations
might
long-term
using
be
obtained at vastly
program
of
although
the convergence
through
of
earthquake
arrays of geophones linked by
telephone; this suggestion seemed to
interest,
on
in
much
the core area, because of
phyical
metamorphism
arouse
properties
and
(largely
intrusion)
supracrustal rocks and the basement,
that remote physical measurements
of
the
one may doubt
could
lead
to
reasonable discrimination of these rocks.
Cross-sections extending to
crust
and
preferably
potentially
geologists
base
of
the
lower, are, nonetheless, a
profitable
and
the
meeting
geophysicists
ground
because
for
these
sections help to define the geometric problems
a
foldbelt.
Geologists
can
use
of
structural,
13
lithologic, and metamorphic data obtained
surface
to
predict
geologic
kilometers below the surface
physical
conditions
of
and
and
to
some
types
of
give
of
reconstruct
the past, including such
estimates
Geophysicists can
the
conditions several
things as the structure and volume
eroded
at
of
crustal
important
downward
rocks
shortening.
assistance
projection
near-surface environment and
now
can
in
provide
to
the
almost
the only information available for deeper parts of
the crust and mantle."
The
above
quote
taken
from
Zietz
and
Zen
(1973)
summarizes some of the goals of this thesis; i.e. to collect
body
and surface wave data from a regional seismic network,
derive a structural model, and interpret the model in
terms
of geologic and other geophysical information.
Chapter 2 is mainly a literature review
geologic
setting
of
New
England
summarizing
and
other
the
relevant
geophysical observations such as seismic, gravity, magnetic,
heat flow, and electrical measurements.
In Chapter
blasts
are
3,
refraction
first
profiles
presented
and
from
timed
contrasts
quarry
between
the
Precambrian Grenville Province in New
York
Paleozoic
explored using travel
times
from
network.
Appalachian
regional
Lateral
Province
are
earthquakes
variations
recorded
State
by
and
the
the
NEUS
in structure across the NEUS
are then analyzed by a time term analysis of the
Pn
branch
of
the
travel
time
curve.
The last section in Chapter 3
compares the derived velocity models with other models
from
both the northern and southern Appalachians.
Surface wave dispersion
Chapter
4
for
a
measurements
number
northeastern North America.
velocities
are
measured
function which is
Rayleigh
across
wave
the
from
presented
different
Interstation
calculated
the
paths
phase
interstation
using
Wiener
in
across
and
group
transfer
deconvolution.
phase and group velocities are also measured
MIT
short-period
frequency-wavenumber
observed
of
are
phase
power
and
seismic
spectra.
group
network
from
the
For
each
path, the
velocities
are
inverted
simultaneously using a maximum-likelihood technique in order
to derive a shear velocity with depth profile.
In Chapter
across
the
5,
NEUS
teleseismic
P
wave
residuals
recorded
seismic network are analyzed to determine
lateral variations
in
beneath the region.
crust
and
upper
mantle
structure
The residuals are compared with gravity
and the time term observations and a three-dimensional model
for
the
crust
and
upper
technique of Aki et al.,
In Chapter 6, the
first summarized.
between
in
mantle
is
presented using the
(1977).
results
from
previous
chapters
are
Then the crust and upper mantle structure
the Grenville and Appalachian Provinces is compared
terms
of
variations
in
composition
and
tectonic
evolution.
Contrasts in geologic and geophysical structures are then
15
made between the northern and
southern
COCORP
Blue
findings
across
the
Appalachians.
Ridge
and
The
Piedmont in
Georgia, North Carolina, and Tennessee have solved
numerous
long-standing geologic and tectonic problems in the southern
Appalachians and are included in the discussion.
Finally, a first order plate tectonic model
England
Appalachians
is
presented
geologic and geophysical constraints.
which
of
the
satisfies
New
many
16
CHAPTER 2
GEOLOGIC AND GEOPHYSICAL SETTING
In this chapter, the geologic setting of the northeastern
United States
tectonic
is
reviewed
a
simple
model
for
evolution will be presented in Chapter 6.
structures
only regional, large-scale
discussions
are
geophysical
studies
the
in
techniques
seismic
using
the
chapters,
Then,
general.
Because
analyzed
following
quite
kept
are
its
previous
seismic, gravity, magnetic,
utilizing
and electrical techniques are reviewed.
heat flow,
2.1
and
GEOLOGIC SETTING
The northern
complex
extremely
have
Appalachians
undergone
geological development.
long
a
and
Table 6.1 lists
major orogenic episodes in the Appalachians and the
maximum
manifestation in the area of influence (from Rodgers, 1970).
and
Dating
been
complicated
northern
by
numerous
Appalachians
tectonic units (Bird and
western
belt
correlation
stratigraphic
can
be
Dewey,
orogenic
between regions has
episodes.
The
three
major
divided
into
1970;
Naylor,
1975):
a
and an eastern belt possibly representing the
margins of two once convergent continental masses surround a
central
orogenic
belt
underlain by rocks of
eugeoclinal
western
unit
is
mainly
Province
Grenville
and
Berkshires,
Hudson
the
overlying the Grenville basement
Unconformably
Highlands.
of
Precambrian
the
Mountains,
such as the Green
mainly
in the Adirondacks and outlying massifs
exposed
are
which
The
2.1).
(Figure
lithologies
composed
grades
is an Eocambrian to Cambrian platform sequence which
a
into
upward
were
Paleontological evidence suggests that they
contemporaneously with the shelf sediments (Zen,
through Quebec
contains
of
Gulf
the
Synclinorium
previously
discussed
from Connecticut
traced
St.
broad
of
Lawrence.
CVS
The
a thick, highly metamorphosed eugeoclinal sequence
into
divided
to
be
can
and
massifs
Precambrian
the
of
east
the
(CVS) is found to
Valley
Connecticut
The
warps.
deposited
1972).
The central orogenic belt consists of a number
structural
of
graywackes.
and
sandstones,
shales,
deep-water
primarily
consist
which
klippe
above are the Taconic
Found
clastic sequence.
Ordovician
Lower
two
members
Ordovician unconformity.
separated
a
by
major
Middle
A linear serpentinite belt follows
the western flanks of the CVS.
East of CVS lies the
consists
which
a
of
Bronson
chain
of
Hill
Anticlinorium
elliptical gneissic domes
(Oliverian Plutonic series in New Hampshire).
can
be
Hampshire
traced
and
from
is
Connecticut
probably
through
continuous
Mountains Anticlinorium in Maine.
(BHA)
with
The structure
New
northern
the Boundary
Mantling the domes
is
a
of
series
mafic
metavolcanics
associated
with
felsic
metavolcanics and metasediments (Ammonoosuc Volcanics in New
Hampshire) of Middle Ordovician age or older (440
of
m.y.;
Unconformably overlying the Ammonoosucs is a
Naylor, 1975).
series
30
Silurian
to Lower Devonian highly metamorphosed
clastics with some carbonates
and volcanics.
(MS)
Eastward of the BHA lies the Merrimack Synclinorium
major
a
is
which
Maine
extending from eastern Connecticut through
New
It
Brunswick.
Ordovician
to
metamorphosed
(Devonian
Lower
to
into
and
the site of thick accumulations of
is
metasediments
Devonian
Formation)
can
typically
These metasediments
grade.
sillimanite
Littleton
feature
tectonic
northeast-trending
be
with
correlated
The MS also contains
Devonian strata at the top of the BHA.
large volumes of intrusives belonging to the Middle Devonian
New
Hampshire
Plutonic
Series
the
and
Mesozoic
White
Mountain Magma series.
On the eastern flank of the MS a major northeast-trending
thrust belt (Clinton-Newbury, Bloody Bluff,
Faults)
extends
from
and
Lake
Char
southern Connecticut through eastern
Massachusetts (Skehan, 1969).
with the formations in the
Magnetic anomalies associated
thrust
belt
suggest
that
the
faults continue offshore in an east-northeast direction into
the
Gulf of Maine (Weston Geophysical,
1976) and possibly into New Brunswick
eastern
1976; Alvord et al.,
(Nelson,
1976).
In
Massachusetts the northwest dipping thrusts greatly
offset metamorphic isograds and no stratigraphic
units
can
be
across
traced
them
Barosh,
(P.
personal
commun.).
Deformation and metamorphism in the MS probably delineate
of the Middle Devonian Acadian
intensity
maximum
of
zone
a
orogeny (Rodgers, 1970).
described thrust belt.
the
of
rocks
with
These units are probably correlative
Zone
Avalon
metasedimentary
and scattered age dating have made geologic
enigmatic
(Naylor,
1975;
Zarrow
greater
than
650
from
et al.,
interpretations
1978).
according to Naylor (1975), no rocks have been
age
age
Unfossiliferous strata
to Carboniferous.
Precambrian
rocks
metavolcanic
and
metamorphosed mainly to chlorite grade ranging in
late
Nelson,
1970;
The region in eastern Massachusetts is characterized
plutonic,
by
and
Newfoundland
in
Dewey,
southeastern New Brunswick (Bird and
1976).
above
exposed to the east of the
The Eastern Basement is
However,
assigned
an
m.y. which is significantly younger
than the Grenville age rocks ( 1,100 m.y.)
in
the
western
belt.
GEOPHYSICAL SETTING
2.2
To date, very little
seismological
work
pertaining
to
crust and mantle structure has been done in the northeastern
United
States.
Early
studies involving analysis of local
earthquake data and timed quarry
Leet
(1941),
Linehan (1962),
blasts
include
Katz (1955),
those
by
and Nakamura and
Howell (1964).
More recently, some refraction work has been
published by Chiburis and Graham (1978), Aggarwal in Schnerk
et al.,
(1976),
and
Taylor
and
Toksoz
(1979a).
These
studies
along with other refraction models from neighboring
regions are summarized in Table 3.5 and discussed in section
3.4.
Some observations have been made on teleseismic
recorded
in
the
measured dT/d&
stations
and
by
the
five
Fletcher
et
study
the
Although
Boston
original
al.,
by
College
who observed
(1978),
the
teleseismic P wave residuals across
Canada.
waves
by Wu and Allen (1972) who directly
NEUS
across
P
U.S.
eastern
and
et al., (1978)
Fletcher
their
involves readings from only a few nuclear explosions,
observations are quite similar to those discussed in Chapter
Early
5.
arrivals
are
observed
Grenville Province relative to
for
those
in
stations
the
in
the
Appalachians
especially for sources from the northwest.
Surface wave studies in the NEUS are limited to those
by
Brune and Dorman (1963), Dorman and Ewing (1962),
and Taylor
and
refraction
Toksoz
(1979b)
and
are
consistent
with
results and are discussed in Chapter 4.
2.2.1
GRAVITY AND MAGNETICS
Gravity
correlations
and
with
magnetic
geologic
anomalies
show
very
good
features in the eastern United
States.
Their prominent features will be described in
section
and
will
eastern U.S.
into the tectonic framework of the
fit
their
Detailed
6.
Chapter
in
discussed
be
this
gravity and areomagnetic maps are available over much of the
A generalized Bouguer gravity map after Kane et al.,
NEUS.
the
for
2.2b
U.S.
eastern
in
and
shown in Figure 2.2a for the NEUS
is
(1972)
Figure
(Diment et al., (1972)).
The
prominant features observed in the regional gravity field in
the NEUS are a low over the Taconic klippen in
the
over
low
a
York,
Vermont
and
gravity
high
western
is
Massachusetts,
found
western
in
western
western
Connecticut,
Quebec
into
and
Vermont,
in
trending
north-northeast
A
Maine.
CVS
the
over
low
Hampshire, and a northeast-trending
New
northern New
in
Mountains
White
eastern
and is
associated with the Precambrian uplifts and the serpentinite
There is also a gravity high found
belt.
(1972), more detailed maps show a
et al.,
regional
As noted by Kane
and along the Atlantic coast.
Adirondacks
trends
where
broad
discontinuity
northeast-striking
elements of eastern and northern New England
the
from
in
gravity
separated
are
more northernly-trending anomalies of western New
along
England
northern
the
in
a
line
extending
from
Rhode
Island
to
north-central Vermont.
Excellent areomagnetic data is available over much of the
NEUS.
to
much
Because a dipolar field falls of as r-3
r'A
as
opposed
for the gravity data, the magnetic anomalies are of
higher
wavenumber
and
show
a
very
impressive
correlation
with
surface
geologic
Areomagnetic data has been
structural
and
features (Figure 2.3).
crutial
for
mapping
important
stratigraphic contacts where they are often
obscured by glacial sediments or water (Alvord et al., 1976;
Weston
Geophys.
observed
on
Res.
the
Inc.,
Prominant
features
areomagnetic maps are the Clinton-Newbury
and Bloody Bluff Fault zone
eastern
1976).
Connecticut,
in
rocks
eastern
Massachusetts
and
of the White Mountain Plutonic
series, diabase dikes associated with Triassic rifting,
Oliverian
domes
and
gneiss domes of the BHA.
Cambrian-Ordovician rocks
such
as
the
the
In general,
Nashoba
Formation
the Clinton-Newbury and Bloody Bluff Fault Zone have
within
a stronger magnetic signiture than Silurian-Devonian rocks.
2.2.2
HEAT FLOW AND RESISTIVITY.
Heat flow measurements
subject
such
to
as
radiogenic
heat
summarizes
early
2.4).
for
the
NEUS
are
few
and
are
many effects which are difficult to correct for
climatic
corrections
in
variations,
thermal
production.
heat
for
More recent measurements
radioactivity
Diment
flow
Pleistocene
al.,
(1972)
measurements
and
makes
which
variations
include
is
(Figure
corrections
were made by Jaupart (1979).
trending
and
et
climatic
indicates that central New England
north-northeast
conductivity,
Figure 2.4
characterized
zone of high heat flow.
by
a
Although
many of these measurements are taken from highly radioactive
plutons, Jaupart (1979) concludes that these trends
after
persist
corrections for radioactivity which suggests that the
anomalies
may
be
caused
by
differences
in
mantle
temperature.
Resistivity measurements
of
a
highly
Mountains
conductive
lower
approximately
15
(Kasameyer, 1974).
in
the
km
underlies
thick
a
upper
1979),
slightly
crust
Using geomagnetic
Adirondack
New
England
conductive,
in
New
sounding,
crust.
caused
However,
by
Merrimack
highly
the
resistivity
Bailey
et
at
the
base
of
the
anomaly they observe may actually be
conductive
Synclinorium
such
contain abundant graphite
formations
found
in
the
as the Brimfield Schist which
and
iron
sulfides
(T.
Madden,
comm.).
In the next three chapters, body wave data from
teleseismic
events
and
measurements will be presented.
will
England
which they attributed to a 200 degree
thermal anomaly and low
and
while
(1978) found evidence for high telluric current flow in
central
pers.
crust
in New York state (Connerney et al.,
a resistive lower crust
al.,
in the NEUS suggest the presense
be
jointly
interpreted
surface
wave
In Chapter 6,
with
the
regional
dispersion
the
results
geologic
geophysical information summarized in this chapter.
and
24
FIGURE CAPTIONS
Figure 2.1a
Generalized geologic map of northeastern
United States. Modified from King (1969).
Figure 2.1b
Major tectonic structure in northeastern
United States. Shaded regions correspond to
sillimanite-grade metamorphic zones.
Figure 2.2a
Bouguer gravity in
northeastern
United
States.
Areas
with
positive
gravity
anomalies are shaded.
Modified from Kane et
al. (1972).
Figure 2.2b
Bouguer gravity in eastern
from Diment et al. (1972).
Figure 2.3
Areomagnetic map of New
interval is 100 gammas.
Figure 2.4
Heat flow corrected for Pleistocene climatic
variations; from Diment et al., (1972).
United
England.
States;
Contour
EXPLANATION
Thrust fault, barbs on upper block
"""
Normal fault, hachures on downthrown side
STRATIFIED ROCKS
D
Cenozoic glacial deposits
Triassic red beds
Carboniferous
Silurian - Devonian eugeoclinal rocks
Cambrian - Ordovician foreland rocks
Cambrian - Ordovician deformed miogeoclinal rocks
Cambrian - Ordovician eugeoclinal rocks
W
Precambrian rocks of the eastern block
Precambrian uplifts, Grenville basement
Precambrian Grenville basement
jG.NEOUS ROCKS
1
74
72
70
68
D
Mesozoic White Mountain Plutonic Series
Devonian New Hampshire Plutonic Series
Cambrian
-
Ordovician serpentinites, ultramafics
Precambrian anorthosites
Figure 2.la
74
72
70
68
Figure 2.lb
27
74
72
70
68
Figure 2. 2a
900
800
70*
500-
400
400-
300
C
3Q0*
90*
80*
Figure 2.2b
Figure 2.3
5900
S)oor
700
300
Figure 2.4
31
CHAPTER 3
CRUSTAL STRUCTURE FROM REGIONAL TRAVEL TIMES
Analysis
of
travel
earthquakes
in
the
limited in scope
indicating
(1941)
have
yielded
complicated
using
small network.
York
quarry
United
States have been
inconsistent
early
and
results,
results
in
Leet
New
data from regional earthquakes recorded on a
Katz (1955) published refraction results
State
from
work
has
in
interpretation of a few timed quarry
blasts recorded along linear arrays.
refraction
blasts
structure in the region.
and Linehan (1962) published
England
New
from
northeastern
and
the
times
been
More
recently,
some
reported by Chiburis and Graham
(1978), Aggarwal (in Schnerk et al.,
1976), and
Taylor
and
blasts
are
Toksoz (1979).
In this chapter, results from
presented
seismic
using
data
network.
velocity
from
Average
structure
using
timed
quarry
portable stations and the NEUS
compressional
and
shear
regional earthquakes are derived
using data from the NEUS network, and lateral variations
structure
the
Pn
wave
in
are studied by performing a time term analysis of
travel
contrasted
time
branch.
Finally,
the
results
are
with other travel time studies in other portions
of the Appalachians and eastern North America.
3.1
STRUCTURE FROM MEASURED QUARRY BLASTS
Ten quarry blasts have been
Canada
and
stations.
timed
in
New
England
and
recorded on both portable and permanent seismic
The blasts and stations used are shown in
Figure
3.1, and the origin times, and blast locations are listed in
Table
3.1.
About
half
of
the
blasts
were
southern New England, and the rest in the
asbestoes
mines
in Quebec.
located in
large,
open
pit
Three shots were also recorded
in Vermont.
Instruments used both for collecting origin times and
portable
stations
recording on
recording
FM
consisted
smoked
paper
signals
on
of
Sprengnether
drums,
and
USGS
cassette tapes.
as
MEQ-800's
J-302
VCO's
Drum recordings
were made with a speed of 240 mm/min where reading precision
for sharp arrivals has a standard error of about
The
cassette
sec.
recordings could be discrimminated and played
back at very high speeds (3 cm/s
precision
0.05
or
greater)
and
is on the order of a few milliseconds.
readings, accuracy was limited by the drift of
reading
For these
the
crystal
oscillator clock, whose timing corrections were less than 20
ms/day, and the impulsiveness of the signal.
The
quarry
approximately
and
roadcut
5,000-20,000
blasts
kg.
ranged
Shot
in
size
configurations were
generally an array of 40-200 drillholes, each 15-20
and
8-10
cm
in diameter.
from
m
deep
The delay time along the string
was up to 0.5 sec and the explosive was usually a mixture of
33
ammonium-nitrate and fuel oil.
The 5,000 Kg shots generally
produced clear arrivals out to 150 km
this
distance
are
and
readings
beyond
and are limited to only the larger
few
blasts.
A composite refraction profile and compressional
model is
shown in Figure 3.2 and listed in Table
velocity
3.2.
One
of the most notable features discovered upon analysis of the
travel
times
uppermost
is
the
crustal
extreme
regional variability of the
layer.
Velocities
in
eastern
Massachusetts range from less than 5 km/s to 5.8 km/s, and a
6.0
km/s 'upper
Because
the
layer
blasts
was
identified
produced
few
in southern Maine.
impulsive
arrivals
at
distances greater than 150 km, the crustal thickness and the
velocities
However,
of
it
the
does
characterized
by
lower
appear
layers are not well constrained.
that
the
lower
crust
is
velocities greater than 7.0 km/s and that
the cross-over distance for the Pn branch
is
greater
than
160 km, indicating crustal thicknesses in excess of 35 km.
3.2
AVERAGE STRUCTURE USING P AND S ARRIVALS FROM REGIONAL
EARTHQUAKES
Refraction models derived
useful
from
timed
blasts
are
very
in determining crustal structure and as discussed in
the previous section indicate a high
complexity
in
the
NEUS.
However,
degree
of
structural
there are a number of
34
difficulties in working solely with the
surveys.
First,
the
data
seismic
collection
expensive, and time-consuming.
refraction
can be difficult,
A number of refraction lines
were set up by the author only to find that the blast either
occurred much earlier than expected or was delayed,
too
small
to
produce usable recordings.
Second,
importantly, most of the blasts were too small
impulsive
crustal
Pn
arrivals
thickness.
profiles
was
also
which
are
by
certain crutial distance intervals.
to
was
and more
generate
essential in estimating
Interpretation
complicated
or
of
the
refraction
the paucity of data at
In constrast, a
wealth
of information can be derived by analyzing readings from the
large
number of earthquakes recorded and cataloged over the
past four or five years since the NEUS seismic
initiated.
Although
the
network
earthquake-generated
was
dataset
contains errors which are due to effects of mislocations and
errors in origin times, it represents a much
collection
of
surveys using
earthquake
more
complete
arrival-time information than the refraction
explosive
dataset
sources.
In
this
section,
the
and the method of analysis is discussed
along with a description of the results.
3.2.1
DATA
A dataset of 1545 P-wave and 546 S-wave readings from
regional
170
earthquakes with eqicentral distances up to 600 km
was selected from earthquake bulletins of the
network
(Chiburis et al., 1975-1979).
seismic
The earthquakes used
The magnitude
are shown in Figure 3.4.
NEUS
range
was
between
1.5 and 3.8, and small magnitude events and swarms with poor
epicentral
control
well-constrained
Adirondacks
were
focal
were
eliminated.
depths
deleted
of
from
A
about
few
events with
10
km
the dataset.
in
These events
were characterized by "depth" hyperbolae (Figure 3.5a)
readings
at
nearby
stations
which
would
carrections
were
made.
as
discussed
unless
Some relatively deep events
(d>10 km) were located by the Canadian
However,
from
cause positive
errors in velocity estimates of upper crustal layers
depth
the
network
in
Quebec.
below, the effects that these focal
depths have on the travel times to the distant NEUS stations
is small.
Because most events are shallow (less than 10 km)
a surface focus was assumed, and travel times were
computed
with respect to published epicenters and origin times.
Travel
time
event-station
plots
were
combinations
constructed
and
for
various
it became readily apparent
that significant differences in travel time
curves
existed
between stations lying above Grenville basement and stations
lying
in
the
belt and the
New
England Appalachians.
Precambrian
uplifts
were
The serpentinite
used
stations into the two regions (Figure 2.1a).
time
above
plots
using
Grenville
separately
and
P
and
to
separate
Reduced travel
and S travel times for stations lying
Appalachian
shown
in
basement
Figures
3.6
are
and
plotted
3.7.
The
Appalachian and Grenville stations show similar travel times
past
epicentral
overlays
of
significant
regions.
travel
distances
the
travel
crustal
For
time
about
time
is
less
200
curves
differences
distances
curve
of
However,
demonstrate
exist
than
km.
between
that
the
two
200 km, the Grenville
remarkably
linear,
while
the
Appalachian curve shows lower velocities out to at least 100
km
where
arrival
times
on
the
separate
plots begin to
rapidly converge.
Although readings made
from
the
enlarged
develocorder
films generally have a standard error of 0.1 sec,
the
travel
origin
time
time,
scatter in
plots arise from errors in hypocenter and
misidentification
of
phases,
and
lateral
complexities in structure.
ANALYSIS OF TRAVEL TIME CURVES
3.2.2
A
number
interpretation
3.6.
of
different
of
are
available
was
analysis.
region
in
However, the distribution of
events
the NEUS is not suitable for this type of
Many of the events
being
velocity
considered following the technique described
by Aki and Lee (1976).
stations
for
the travel time profiles shown in Figure
A simultaneous inversion for hypocenters and
structure
and
techniques
used
occur
outside
of
the
modeled and were originally located using the
Canadian Seismic Network.
There is
also
a
lack
of
deep
events
and the resolution of deeper crustal layers would be
very poor.
A Wiechert-Herglotz or tau inversion was also considered.
However, because of the scatter in the data these
techniques
were
judged
to
be too eloquent.
On the other
extreme, identifying and fitting straight line
travel
inversion
segments
to
time branches is very subjective and may not achieve
a best solution in a least squares sense.
A more systematic,
technique
of
yet
Mitchell
Appendix.B for details).
simple
approach
following
the
and Hashim (1977) was selected (see
Given a set of travel time data, a
nonlinear least squares method is used to solve for apparent
velocities, critical distances, and corresponding
times
for a plane layered earth model.
system of equations
critical
distance
containing
divided
The method solves a
nonlinear
by
intercept
terms
refractor
involving
velocity
(see
Appendix B and Figure 3.3).
Because a
distances,
least
their
squares
technique
corresponding
is
times,
used,
critical
and
apparent
velocities are perturbed about a trial model.
model
was
selected
by
corresponding times from
expanded
time
scales.
estimating
reduced
The
initial
critical distances and
travel
time
plots
with
Trial apparent velocities were then
calculated by taking the inverse slope of
a
least
squares
line fit to the data along the selected distance interval.
38
ERROR ANALYSIS
3.2.3
The travel time data generally had a
of about 0.7 sec.
standard
deviation
This scatter is probably caused mostly by
errors in epicentral location, focal depth, and origin time.
Reading
errors, phase misidentification, and differences in
travel time with azimuth caused
structure
and
anisotropy
by
are
lateral
variations
in
probably
also
important
events
are
probably
factors.
Epicentral
locations
accurate to within 5 km.
for
most
Location errors of 5 km will cause
travel time errors of less than one second.
Effects of errors in earthquake depth on travel times was
also investigated.
Adirondacks
With the exception of one
in
the
and La Malbaie, Quebec, most earthquakes in the
study area have foci of less than 10
1977).
area
Recently,
accurate
km
(Sbar
of
location
Sykes,
aftershocks near
Bath, Maine indicated depths of less than 7 km
Chiburis, 1980).
and
(Graham
and
For a homogeneous upper crust, the partial
derivatives
of travel time with respect to depth, z, can be
approximated
by
DT
where VO is
distance.
the
These
crustal
(3.1%)
velocity,
x
is
the
partial derivatives for various depths are
plotted as a function of distance in Figure 3.5b
6.5
km/s.
For
epicentral
for
VO
=
depth errors of 5 km, the errors in travel
time will be less than 1 second and will be
negligible
for
distances greater than about 40 km.
It is possible that the velocity model used
the
earthquakes
interpretation.
times used in
velocity
introduces
the
model
the
NEUS
NEUS
were
(Chiburis
stations
calculated
et
al.,
located
by
demonstrated
constructing
an
1975-1979).
The
combining
readings
variations
in
small differences in
curves
shown
array
can
in
Figure
fairly accurate
be
obtained
by
a series of station bisectors based on
relative arrival times with no
Although
same
by Anderson (1979),
epicenter locations within
simply
the
model should not have a significant effect on
the appearence of the travel time
As
using
lateral
velocity such as eastern North America,
3.6.
the
In a region with reasonably dense
station coverage and without strong
velocity
into
with the Canadian network using a
different velocity model.
the
bias
locating
Most of the earthquake locations and origin
earthquakes in Canada were
from
some
in
information
on
velocities.
most of the earthquakes are located using the same
velocity model, the differences
in
travel
times
observed
between Appalachian and Grenville stations (Figure 3.6, 3.7)
gives
further
support
that
the
location
velocity model
introduces little bias into the final interpretation.
3.2.4
RESULTS
40
The final velocity
Appalachian
and
models,
Grenville
and
P
fit
to
the
data
for
and S travel time curves are
shown out to 300 km in Figure 3.7.
The critical
distances,
corresponding times, apparent velocities, layer thicknesses,
and
model
discussed
errors
in
interpretation
are
section
of
listed
3.4,
the
in
the
3.3.
results
As will be
obtained
from
travel time profiles are consistent
with previous refraction models
and
the two orogenic belts.
between
Table
show
large
contrasts
The crust of the Grenville
Province appears to be very homogeneous with nearly constant
P
and- S
wave
velocities
respectively,
with
In
the
contrast,
slightly
thicker
an
of
about
and
3.7
km/s,
average crustal thickness of 37 km.
Appalachians
are
(approximately
40
well-defined layers.
6.6
The upper crust
characterized
km)
in
crust
the
by
with
a
two
Appalachians
shows relatively low P and S velocities of about 6.1 and 3.6
km/s,
respectively, to about 15 km where an abrupt increase
to 7.0 km/s and 4.1 km/s occurs.
Both regions show
similar
Pn velocities of 8.0 km/s for the Grenville and 8.1 km/s for
the Appalachians.
3.3
LATERAL STRUCTURE FROM TIME TERM
ANALYSIS
OF
THE
Pn
BRANCH
The least squares technique
section
represents
an
discussed
in
the
previous
average crustal model for two large
regions and cannot adequately portray lateral variations
crustal
structure.
To
study
these lateral variations in
crustal structure, a time term analysis was applied
Pn
branch
of
the
travel
in
time
curve
for
to
the
all
stations
North
America
simultaneously (D > 200 km).
Previous time
term
studies
include
those by James et al.
States,
Berry
and
West
in
eastern
(1968)
(1966)
in the Middle Atlantic
from
the
Lake
Superior
refraction experiment, and Berry and Fuchs (1973) in eastern
Canada.
3.3.1
METHOD
The time term method (Scheiddegger
Willmore
and
and
Willmore,
1957;
Bancroft, 1960) is based on the fact that the
travel time, Tij, between a source i and station
j
can
be
represented by the sum of a source and receiver term and the
distance, Dij, divided by the average refractor velocity (in
this case the Pn velocity) Vpn (Figure 3.8)
Because the sum of the source and receiver terms equal
constant
(the
zero-distance
intercept
time branch), there are infinitely many
system
is singular (see Appendix C).
inverse operator for the system was
a
time of the travel
solutions
and
the
Thus, the generalized
computed
and
the
one
zero
eigenvalue
resulting
from
the non-uniqueness of the
source and receiver term was truncated (Wiggins, 1972).
A
of
derivation
dip
of
number
of
the
crutial
is
made
in
the
First, it is assumed that the
equation 3.2.
refractor
are
assumptions
small.
Without
an
adequate
azimuthal distribution of sources, problems similar to those
of
an
unreversed seismic refraction profile can result and
there can
be
refractor
velocity.
However,
3.4, there is a reasonably good
events.
in
errors
systematic
the
time
and
terms
can be seen from Figure
as
azimuthal
distribution
of
Also, in an older, stable geologic province such as
that in the NEUS, the regional dips of the Moho are expected
to
Similar errors can occur if there exist large
be small.
As discussed
regional variations in the refractor velocity.
in the previous section,
although
the
and
Grenville
England Appalachians show regional differences in
New
the crust,
the Pn velocities appear to be quite similar.
It is
are
also assumed that effects
of
anisotropy
velocity
small and that a large velocity gradient does not exist
travel
time
branch
is small).
1975).
defined
into
involving
distance
be
(1973)
Fuchs
anisotropy
terms
sines
and
the time term equation (McCollom and Crosson,
Berry and
gradients can
Pn
Velocity anisotropy can be
examined by including azimuthal terms
cosines
the
of
in the upper mantle (i.e. the second derivative
in
Grenville
the
modeled
found
by
only
Province.
incorporating
into equation 3.2.
poorly
weak,
Velocity
higher
order
However, as can be seen
from Figure 3.6, the Pn travel time branch is fairly linear,
and the coefficients of the
higher
order
terms
would
be
small.
RESULTS AND INTERPRETATION
3.3.2
Earthquakes were selected from those of Figure 3.4
yielded
three
or more Pn arrivals in the distance range of
In all, 71 events, 61 stations and 343 readings
200-600 km.
were used.
For each event, epicentral distances and moveout
times from the nearest station
station
which
time
terms,
j
were
Relative
calculated.
were computed by subtracting off
the mean time term from each station time term, Ki
,
using
where N is the number of stations.
The calculated Pn velocity is 8.04 km/s and the
station
relative
time terms, standard errors, and number of readings
are listed in Table 3.4 and shown in Figure 3.9 for stations
with four or more readings.
As will be discussed in Chapter 5, the station time terms
have fewer readings and therefore are less constrained
than
the
average relative teleseismic P-wave residuals, although
the
two
sets
correlation.
are
observed
of
residuals
do
show
a
relatively
good
A trend of positive time terms (late arrivals)
in
part
of
eastern
New
York,
western
Massachusetts, southeast Vermont, central New Hampshire, and
central Maine.
terms
(early
arrivals)
are
northeastern New York and northwestern Vermont
in
observed
Negative time
and also along much of the coastline.
As discussed in Appendix C, for a layer over a half-space
time
model, the station
thickness,
velocity,
terms
and
functions
are
upper
mantle
velocity.
unless some constraints can be placed on
time terms can be interpreted
station
crustal
of
the
Thus,
problem,
the
a number of different
ways.
Because
constant
the
and
Pn
velocities
the
average
appear
crustal
to
be
relatively
velocities are similar
across the NEUS, it was decided to model the time terms as a
function of
terms
crustal
thickness.
time
absolute
Inverting
for crustal thickness requires the direct measurement
of the source terms, Sj, at a given site
origin time
resulting
and
travel
measuring
the
j, by
intercept
time vs. distance plot.
recording the
time
from
the
It would then be
necessary to record a Pn arrival at the same site, calculate
the resulting "station
Because
all
of
term",
for
and
equate
=
Sj
Rj.
the station terms are relative, this would
assign absolute values to
invert
Rj,
absolute
them,
crustal
which
could
be
used
to
thickness assuming a crustal
velocity function.
Only relative time terms were calculated in
so
the
this
study,
crust and upper mantle parameters from this and the
previous section could be used to obtain, at best,
a
first
order
approximation
of
crustal
thickness variations.
obtain the crustal thickness values
from
the
relative
time
at
each
station
To
site
terms, a single layer over a half
space model is used where the crustal thickness is
and
where Vpn = 8.04, Va
stations
=
6.6,
hO
38
=
km
for
and 39 km for Appalachian stations.
Grenville
Note that the
estimate of the average crustal velocity is slightly high so
the crustal thickness variations are probably the maximum to
in
The crustal thickness map is shown
be expected.
Figure
3.10.
As indicated by observing the relative station time terms
in Figure 3.9, the crustal thickness appears to be
greatest
(and/or
velocities are lowest) in a northeast trending belt
running
from
Hampshire,
eastern
and
into
York,'
New
Maine.
This belt shows a remarkable
correlation with the belt of Bouguer gravity lows
Figure
2.2.
velocities)
Crustal
is
thinning
found
in
New
central
through
(and/or
northwestern
shown
high
in
crustal
Vermont
and
northeastern New York and along the Atlantic coast.
The
thickness
crustal
simplified
model
approximation.
and
map
is
represents
based
at
best
an
on
a
overly
first order
Many factors contribute to erroneous crustal
thickness estimations many of which are described in
detail
46
by Bath (1978).
3.4
COMPARISON WITH
OTHER
REFRACTION
EASTERN
IN
MODELS
NORTH AMERICA
Results
suggests
from
that
observations
of
regional
travel
significant differences in crustal structure
exist between the Grenville and Appalachian
this
section,
Provinces.
In
the models presented in this chapter will be
compared with other refraction models
North
times
America.
measured
in
eastern
The tectonic implications of the structural
differences will be examined in Chapter 6.
Refraction
Appalachians
Table 3.5.
of
a
layers.
models
and
the
the
northern
and
relatively
southern
Grenville Province are contrasted in
The northern Appalachians appear to be
composed
40 km crust with two well-defined
thick,
The lower crust is characterized by relatively high
velocities of 7 km/s.
models
for
of
Leet
This is
(1941)
consistent
with
and Steinhart et al.,
refraction
(1962) in the
NEUS, R.L.Street (pers. comm.) in central New Hampshire, and
Dainty et al. (1966) in Newfoundland.
by
Chiburis
and
Two models
presented
Graham (1978) in southeastern New England
and Nakamura and Howell (1964)
in
eastern
Maine
suggests
a
missing high velocity lower layer
along the Atlantic coast.
The region where the Chiburis and
crustal
thinning
and
Graham (1978) model was compiled
is
located
in
a
region
characterized
by a zone of negative time terms and apparent
crustal thinning (Figures
these
surveys
may
3.9
and
3.10).
Interestingly,
have sampled rocks of the eastern Block
(or Avalon zone) discussed in Chapter 2.
Refraction models from the Grenville Province
be
along
similar
fairly
appear
to
its length from the southeastern
In eastern Canada the high velocity
U.S. to eastern Canada.
lower crustal layer is absent or weakly developed (Dainty et
It also appears that the
al., 1966; Berry and Fuchs, 1973).
Grenville crust thickens from about 36
edge
at
km
its
eastern
about 45 km at its western edge in the vicinity of
to
In New York state, the Grenville crust
the Grenville Front.
appears to be uniform, about 36 km
ranging
6.4
from
6.6
to
km/s
with
thick,
velocities
1955; Aggarwal
(Katz,
in
Schnerk et al., 1976).
Further south, west of
the
Blue
Ridge,
the
Grenville
crust appears to have two layers but the lower crustal layer
is
about
6.7
km/s
which
is
low relative to the northern
Appalachians (Steinhart and Meyer, 1961).
layer
upper
miogeoclinal
The
could
composed
the
of
that
Appalachians
are
more
appear
like
to
high
thick
allochthonous
show
velocity
the Grenville models than
those of the northern Appalachians because of
the
km
rocks.
southern
structures
by
The 14
the
lack
of
velocity lower crustal layer (Long, 1979; Warren,
1968; Bollinger et al.,
1980).
This
has
very
implications that will be discussed in Chapter 6.
important
Table 3.1
Blast Locations and Origin Times
Date
Location
Lat.
8/25/76
Keating Quarry
42,539
Lon g.
O.T.
71. 689
21:24:51.53
10/4/76
i
21:36:20.0
4/7/77
i"
21:29:42.2
"
8/30/76
Benevento Sand & Gravel
42.588
71. 138
19:28:08.25
5/3/77
Cook Concrete
43.698
70. 262
17:30:47.65
6/17/77
East Barret, Vt.
1-91 roadcut blast
44.323
72. 041
19:25:08.1
6/22/79
National Mines, Que.
46.140
71.225
19:44:02.61
6/27/79
John Mansville Mines, Que
45.771
71,949
19:47:42.24
8/1/79
Vermont Asbestoes
44.76
72.53
18:31:50.75
8/14/79
"
"o
i
18:47:11.25
TABLE 3.2
Refraction Model From Timed Quarry Blasts
(Km)
DEPTH
VP
0. --
22.1
6.0
22.1
-
7.1
Moho
44.6
8.1
(Km/s)
Table 3.3
Vo=6.4 km/s
Travel Time Models
Grenville
Appalachians
P
P
S
S
# events
128
96
82
58
Til
0.1
0.2
0.4
0.4
Ti
2.9
6.2
0.8
0.8
6.9
11.4
5.9
12.5
ti
22. 011.0
39. 4±1. 6
17. 6±6.1
16. 8±4 .1
t2
30.0
57.3
34.2
60.3
Xcl
133.6+6.5
139.3±5.6
112.4+40.0
59.2±14.9
Xc 2
189.3+7.9
214. 4±9. 0
223. 011.5
220.0±10.9
V1 .
6.1
3.6
6.6
3.7
V2
7.0
4.2
6.6
3.7
V3
8.2
4.7
8.0
4.6
ZO
Zi
2.2
2.1
3.1
1.9
10.9±0.5
14.9±0.6
0.7±0.2
0.3±0.7
Z2
26.7±1.1
24.8±1.0
32.01.7
35.6±1.6
Ztotal
39.8
41.8
35.8
37.8
0.72
0.60
0.87
Ti
2
3
data Std. Dev. 0.73
(See Figure 3.3 for symbol definitions)
Table 3. 4
Station Time Terms, Errors, and Number of Readings
Vpn
=
8. 04
Station
AGM
APT
BCT
BML
BNH
CBM
coV
D3A
DANY
DNH
ECT
EMM
ESJ
FLET
FLR
GFN
GLO
HDM
HKM
HNH
HRV
JKM
LNX
MARL
MDV
MIM
MPVT
NSC
ONH
PNH
PNY
PTN
QUA
TBR
TMT
TRM
UCT
WES
WFM
WND
WNH
WNY
WPNY
WPR
km/s
71 events
Relative Time Term
-0.1
-0.2
-0.2
0.1
0.4
-0.3
-0.2
-0.1
-0.2
-0.2
0.4
-0.6
-0.2
-0.4
-0.1
0.2
-0.5
-0.4
0.0
0.0
-0.2
0.6
1.1
0.2
-0.1
-0.4
-0.2
-0.4
0.1
0.5
0.1
0.5
0.4
-0.1
0.3
0.3
-0.3
-0.5
-0.2
0.8
0.2
-0.1
0.6
0.0
343 readings
No. Readings
5
2
12
12
18
8
3
11
2
8
20
34
1
2
2
4
5
4
1
5
5
4
4
5
4
26
3
6
3
5
4
3
8
5
5
9
11
9
6
3
8
3
2
5
Std. Error
.05
.08
.03
.06
.03
.04
.06
.04
.08
.04
.02
. 03
.10
.08
.08
.06
.05
.06
.10
.05
.05
. 06
.06
. 05
.06
.03
.06
.05
.07
.05
.06
.06
.04
.05
.04
. 04
.04
.04
.05
.06
.05
. 06
.08
.05
Table 3.5
Generalized Refraction Models in Eastern North America
Canadian Appalachians
Cont. Margin
Appalachians
Grenville
Berry and Fuchs
(1973)
(km/s)
Depth (km)
V,
0.-20.
20.-40.
Moho
6.3
6.6-6.9
8.06
Dainty et al.
(1966)
0.~-37.
Moho
6.25
8.18
Dainty et al.
(1966)
Dainty et al.
Depth
vi
Depth
Vp_
0.-15.
15.-25.
25.-42.
Moho
5.9
6.3
7.2
8.1
0.-9.
9.-35.
Moho
5.4
6.25
8.0
Northeastern United States
Grenville
Katz
(1954)
0.-35.
Moho
6.4
8.14
Aggarwal in
(Schnerk et al.
0.-4.0
4.0-35.0
Moho
6.1
6.6
8.1
1976)
Appalachians
Cont. Margin
Street
Nakamura and
Howell (1964)
(1976)
0.-2.5
2.5-26.0
26.0-42.1
Moho
5.76
6.40
7.47
8.13
Taylor and Toksoz
(1979)
0.-7.3
7.3-26.1
26.1-39.0
Moho
Leet (1941)
0.-16.0
16.0-29.0
29.0-36.0
Moho
5.7
6.3
7.3
8.13
0.-30.
Moho
Chiburus and
Graham (1978)
0.-3.0
3.0-13.0
13.-31.0
Moho
6.13
6.77
7.17
8.43
Steinhart et al. (1962)
(Gulf of Me. to Me. interior)
0.-20.0
20.0-40.0
40.0
6.0
7.0
8.0
6.0
8.1
5.6
6.1
6.6
8.1
(1966
Table 3.5
(continued)
Southern Appalachians
Grenville
Appalachians
Steinhart and Meyer
(1961)
Bollinger et al.
Depth
(kin)
0.-13.7
13.7-45.3
Moho
VP
(km/s)
6.20
6.73
8.06
0.-15.0
15.0-39.0
Moho
(1980)
5.63
6.53
8.18
Long
V,
(1980)
(km/s)
6.09
6.50
8.18
(1968)
0.-20.0
20.0-38.0
Moho
6.1
6.7
8.0
Bollinger et al.
0.-10.0
10.0-49.0
Moho
(kin)
Warren
Warren (1968)
0.-23.0
23.0-40.0
Moho
Depth
(east of Blue Ridge)
6.0
6.7
8.1
(1979)+
0.-5.0
5.0-35.0
Moho
6.3
6.5
8.1
*
Crust thins to 31 km to the east beneath central Piedmont
+
Crust varies from 30-37 km thickness
FIGURE CAPTIONS
Figure 3.1
Blasts, portable and permanent stations used
in refraction surveys.
Figure 3.2
Travel times from blasts and model fit.
Figure 3.3
Terminology used for two-layer
half-space model (see Appendix B).
Figure 3.4
Events used in travel time analysis.
Figure 3.5a
Travel times from Grenville earthquakes.
Solid lines correspond to travel times from
depths of 5 and 10 km.
Figure 3.5b
time with
Partial
derivatives of travel
depth for layer over a half space model.
Figure 3.6a
Reduced P-wave travel times to
Appalachian stations.
Figure 3.6b
Same as Figure 3.6a for Grenville
Figure 3.6c
S-wave travel
times
stations.
Appalachian
Figure 3.6d
Same as Figure 3.6c for Grenville
Figure 3.7
Same as Figure 3.6 to 300 km
models and model fit.
with
velocity
Figure 3.8
Terminology used for time
discussion (see Appendix C).
term
analysis
Figure 3.9
Map of relative station
seconds.
Figure 3.10
Crustal thickness from relative time terms.
to
Pn
over
600
600
time
km
a
for
stations.
km
for
stations.
terms
in
46
44
42
(QUARRY BLASTS)
TRAVEL TIME
40-
0
20
0
200
lee
DISTANCE
(KM)
300
400
T
-
-
-
-
---
-
-
-
-
-.
.
V3
-
T
xc
V0
xc2
V,
V3
Figure 3.3
West Longitude, degrees
800
780
760
740
720
700
680
660
640
480
470
460
450
z
0
rt
I
rt
rt
440
430
(
(D
42*
(D
(D
410
400
390
380
Figure 3.4
15
10
-5
0
20
40
60
80
100
(KL:)
Figure
3.5a
d t/d z
05 ----.
.
-
-. Z=15
,. km
10 '-
los
O.DN-
I
0
20
IV
0s10
40
DISTANCE
0
(kin)
Figure 3.5b
T - X/8
APPALACHIAN
30
P UAUES
-
20
10
-10
0
100
200
DISTANCE
300
400
500
600
(km)
Figure 3.6a
T
-
GRENVILLE
X/8
P WAUES
30
20
10
0
-10
0
100
200
DISTANCE
300
400
500
600
(km)
Figure 3. 6b
T - X/4.6
APPALACHIAN
S WAVES
30
20
10
0
-10
0
100
200
DISTANCE
300
400
500
600
(km)
Figure 3.6c
T - X/4.6
GRENUILLE
S UAUES
30
20
10
0
-10
0
100
200
DISTANCE
300
400
500
600
(km)
Figure 3. 6d
P
APPALACHIANS
0
GRENVILLE
5
S
0
P
T
-
X/80
100
200
300
100
200
300
100
200
300
100
200
300
T - X/80
T- X/46
DISTANCE
(km)
VELOCITY (km/s)
Figure 3.7
4a
4S
14R
Figure 3.8
46
44
42
74
72
70
68
Figure 3.9
48
A
44
40
74
70
66
Figure 3.10
Chapter 4.
STRUCTURE DERIVED FROM SURFACE WAVES
4.1
INTRODUCTION
In order to study average properties
upper
NEUS,
the
in
mantle
of
surface
crust
the
and
dispersion
wave
information is collected using a variety of techniques along
a
number
different
of
in
investigations
paths.
America include those by
North
eastern
Dorman
Brune and Dorman (1963) in the Canadian Shield,
Ewing
and
New York State, Long and Mathur (1972) in
in
(1962)
wave
surface
Previous
(1979)
the southern Appalachians, and Mitchell and Herrmann
for the eastern United States.
inversion
In this chapter we discuss the measurement and
of
surface
phase
wave
Because the surface wave
structure
and
group velocities in the NEUS.
dispersion
reflects
average
the
a given path, the stations and events used
along
are selected such that the paths are confined mainly to
either
the
Grenville
or
one
Appalachian
tectonic
region,
Province.
For crust and upper mantle structure, long period
(15-50 sec) phase and group velocities
are
computed
from
the
windowed
of
Rayleigh
interstation
functions which are estimated using a least squares
filtering
technique.
waves
transfer
inverse
The transfer function gives the phase
delay of
the
interstation
medium
from
which
the
phase
velocities are calculated.
The multiple filtering technique
is
transfer
then
applied
to
the
function
to calculate
interstation group velocities.
Rayleigh wave phase
ranging
from
15-40
and
sec
group
are
velocities
calculated
in
for
periods
southern New
England by measuring the frequency-wavenumber power spectrum
across
the
Rayleigh
M.I.T.
short-period
wave
phase
and
group
The
network.
seismic
are
velocities
simultaneously using a maximum-likelihood technique.
last section, the shear wave velocity structure is
inverted
In the
compared
between different regions.
CRUST AND UPPER MANTLE STRUCTURE
4.2
FROM
MEASUREMENT
OF
INTERSTATION PHASE AND GROUP VELOCITIES
4.2.1
DATA
In this section we describe the measurement
wave
phase
of
Rayleigh
and group velocities between Canadian and WWSSN
station pairs.
The long-period seismograph records from St.
Johns, Newfoundland (STJ); Montreal, Quebec (MNT);
Ottawa,
Quebec (OTT); Weston, MA (WES); and Ogdensburg, NJ (OGD) are
used
in
this
of
part
the
analysis.
Great circle paths
between a variety of station pairs are chosen
different
regions
in
the
Appalachians
which
sample
and the Grenville
The parameters for the 10 events used and station
Province.
pairs are listed in Table 4.1 and shown in Figure 4.1.
Most
station pairs lie within 1 degree of the same
from
the
source.
and
OGD-MNT
Grenville basement is sampled between OGD-OTT
using
from
events
South
are sampled between OTT-WES and
the
A2).
Structure parallel the
northern
the
MNT-WES
using
earthquakes
from
Sicily
simplicity,
the
path
and
Crete
path (MNTOTT-WES) path A2; and
the
path
km
later
spatial
and
small
relatively
section,
of
the
tradeoff
except
resolution,
the
errors
spatial
involved
As will be
good.
and
are
However
temporal
phase and group
the
in
the
those
for
spacings
resolution is
between
of
Most
G.
station
the
eastern
the
STJ-WES and OGD which are 1500-1900 km.
a
For
Appalachians
in
path
interstation separations are 400-500
discussed in
the
the other Appalachian
the
(MNT,OTT-OGD)
Province
Al).
(Path
to
parallel
(STJ-WES,OGD) will be called path Al;
Grenville
of
fabric
tectonic
the
is sampled between STJ-WES-OGD using
Appalachians
earthquakes
because
and
Kuriles, Alaska, and the Mid-Atlantic Ridge (Path
from
between
America
The central New England Appalachians
G).
(Path
Carribbean
azimuth
velocities are fairly large.
frequency
domain.
approximately 5
enlarged
copies
records
seismic
the
Analysis of
km/s
Group
and
2.5
is
performed
windows
velocity
km/s
were
in
the
between
digitized
from
of photographic film at an uneven sampling
rate of about 1 sample/s, interpolated
using
the
weighted
average slope technique of Wiggins (1976) and resampled at 2
A
samples/s.
perpendicular to the swing of the
base-line
order to prevent distortion
galvanometer was selected in
as
waveforms
by
described
digitized seismograms were 20%
cosine
The
Linde (1971).
and
James
tapered,
of
detrended,
corrected for instrument response using the formulas of
and
Examples
Hagiwara (1958) as corrected by Brune (1962).
seismograms
of
and their corrected amplitude and phase spectra
are shown in Figure 4.2.
4.2.2
INTERSTATION
TRANSFER
FUNCTION
USING
WIENER
DECONVOLUTION
Using
the
interstation
are more
details
paths
phase
as
than
velocities
Figure
phase
4.1,
identical
are
group
required
to
we
calculate
Group velocities
velocities
gradients.
velocity
models can produce
phase
in
and group velocities.
sensitive
such
shown
to
structural
However, a suite of
velocity
curves,
discrimminate
and
between
these.
Both phase and group velocities are measured between long
period station pairs by choosing stations lying on the
azimuth
from
an earthquake.
velocities are measured by
difference
between
Typically, interstation phase
calculating
station
same
pairs.
Fourier
phase
Interstation
group
the
velocities can be calculated by measuring the group
arrival
73
times
at
each station either directly from the seismograms
or by narrow bandpass filtering each seismogram and dividing
the time difference into the station separation.
Landisman
et
al.,
cross-correlogram
(1969)
suggest
approximates
the
that
the
windowed
interstation
impulse
response and can be used to measure both interstation
and
group
velocities.
Although this is a useful technique
for phase velocities, test cases
show
phase
performed
in
Appendix
G
that measurement of interstation group velocities from
the cross-correlogram can lead to errors of almost
10%
for
station separations of 500 km
A more accurate technique is to estimate the interstation
transfer
function
using
a
Wiener
or
least
squares
deconvolution (see Appendix G for details).
Given two seismograms positioned
circle
path
from
a
source,
we
interstation transfer function (also
impulse
response
or
Green's
along
want
the
to
known
function).
same
great
estimate
as
the
medium
The phase of the
transfer function gives the phase delay of the system
will
be
which
used to calculate the interstation phase velocity.
The shape of
provides
the
the
transfer
information
on
function
the
in
the
time
domain
dispersiveness of the system
which will be used to estimate interstation group velocity.
The convolution of the input at station
the
1
which
system and produces the output at station 2 is
drives
given by
the frequency domain representation
v(J~
~
IFM
~
F (
41
where the subscripts 1,2 and m refer to station
2,
and
the
1,
interstation medium, respectively.
deconvolve the output by dividing (4.1)
by
station
We wish to
the
input
and
computing the transfer function
This
simple
particularly
deconvolution
in
the
can
presense
be
very
of spectral holes for which
frequencies the filter parameters (transfer
be indeterminant.
to
find
(Wiener,
1966; Peacock and Treitel,
The cross-correlation
isw
are
Levinson
= F,
actually
the
recursion
Appendix G).
Thus,
1949;
Treitel
and
1969).
function gives
-
r I t.'M e
which
will
coefficients and we have chosen a least
squares or Wiener deconvolution
2
function)
Various deconvolution schemes can be used
the filter
Robinson,
unstable,
; OL 4)/-
2 e-
normal
I4'
equations
solved
using
in the least squares deconvolution (see
by comparison of equations 4.2 with 4.3,
we see that the cross-correlogram gives the phase
delay
of
the interstation medium but not necessarily the group delay.
4.2.3
In
MEASUREMENT OF INTERSTATION PHASE VELOCITIES
this
interstation
section,
phase
we
discuss
velocities.
the
measurement
Assuming
of
identical
instruments (or
applied)
one
that
an
instrument
correction
and that the focal phase,,(W),
azimuth,
the
observed
Fourier
is
has
been
a constant along
phase at each station
along a great circle path is
station 2:
40 (j))
§4s)
station 1:
where:
ti - digitizing
epicentral
distance
start
to
time
at
station i;
()-
station
i;
-
xi
instrumental phase
shift.
Subtracting gives the phase difference
Rearranging
terms
gives
the
following
formula
for
measuring
the
interstation phase velocity
Phase velocities were first
computed
by
phase differences between the two stations.
be
seen
from
Figure
unstable,
particularly
difficult
to
small, the
unwrap.
proper
4.2,
at
the phase spectrum can be very
frequencies,
higher
the
Because
integer
However, as can
N
is
and
was
station separation is
obvious
but
the
phase
velocities are very sensitive to small errors in the phase.
From equation 4.2, it can be seen that the phase spectrum
of the interstation transfer function gives the phase
delay
of
the system and can be used to measure interstation phase
velocities.
The transfer function contains
information
on
digitizing start times and the phase velocities are computed
using
(T)x
where
is the phase of the transfer function and
tO
is
the first lag time.
To
reduce
spectrum,
the
the
effect
transfer
correlation is high.
transfer
of
function
noise
in
the
spectrum
recomputed.
The
of
the
windowed
resulting
spectrum is much smoother and the phase velocities are
stable.
phase
function can be windowed where the
The phase
is
random
Landisman et al.,
phase
more
(1969) suggest that the length of
the windowed cross-correlogram (or transfer function in this
case)
be
approximately five times the value of the longest
period desired.
4.2.3
MEASUREMENT OF INTERSTATION GROUP VELOCITIES
Because
controlled
the
dispersion
in
the
transfer
function
is
by the properties of the interstation medium, it
can be used to measure interstation group velocities.
Group
velocities can be accurately measured using narrow band-pass
filtering (multiple filtering;
The
Dziewonski et
al.
(1969)).
method is particularly useful when a signal is not well
dispersed such as in the
vicinity
of
a
stationary
phase
where visual measurements are impossible.
The seismic signal is
with
at
first
detrended,
tapered,
least 2N zeros (where N is the number of samples),
Fourier transformed, and corrected for instrument
The
signal
represents
response.
is then narrow bandpass filtered about a center
frequency WO
.
It is assumed
the
real
part
imaginary part is the
signal
padded
(Oppenheim
that
of
Hilbert
and
a
the
bandpassed
complex waveform and the
transform
Schafer,
trace
of
1975).
the
filtered
Depending on the
dispersive characteristics of the medium, the group
arrival
time is approximately equal to the time of maximum amplitude
of the envelope of the complex filtered signal (Cara, 1973).
It
should
be
noted
that
the
phase velocity can also be
computed from the instantaneous phase at
maximum
amplitude
(Taner
et
al.,
the
1979).
time
the
envelope
function
are
plotted
the
This process is
repeated for a series of center frequencies and
of
of
as
the
values
a function of
frequency vs. time or group velocity.
The original signal, f(x,t), is convolved with a
filter,hO(t),
symmetric
about
a
giving a filtered trace fO(x,t).
center
In the
bandpass
frequency
frequency
W.o
,
domain,
the convolution is given by
where, x - epicentral distance,&CJ -
center
frequency,CJC-
cutoff frequency,
discussed by Dziewonski et al.
gives
the
optimum
half
tradeoff
(1969),
between
bandwidth,
and
W.
.
a
Gaussian
time
and
-
As
filter
frequency
resolution.
The spectrum of the filter is defined to be
A constant Q filter is often used where the
is
bandwidth,&Q
proportional to the center frequency, Q
;
AND
a_C= z
or
ND~ ca.
IA
,&(j10c-4J
Thus, the frequency cutoffs are given by
C =(It BA N))4Qo
and the filter bandwidth increases
On
a
group
scale
log-period
velocity
Representations
of
the
Schafer,
function
the
filters
are
have
equal
width.
found
by
calculating
the
of the bandpassed signals (Oppenheim and
1975; Taner et al.,
analysis,,
frequency.
signal power as a function of frequency
and time or group velocity
envelope
center
gives constant resolution of
this
because
with
1979).
In
complex
waveform
signal, fr(t), is represented as
bandpassed
the real part of a complex function of time;
5(t=
where
and
phase
i
~t+
z Ate(49
Aenvelope
(f)
function
r(40)((()Ir()
=instantaneous
The real and imaginary parts of s(t) are
tranform
by
their
Once fi(t) is calculated from the ideal
Hilbert transforms.
Hilbert
related
of
(by
fr(t)
the phase by 90
shifting
degrees), the envelope function of the bandpassed signal can
be calculated from equation 4.9.
bandpassed
An
of
example
a
narrow
and its envelope function after inverse
signal
Fourier transforming is shown in Figure 4.3.
the
To the first order, the maximum of
of
envelope
the
signal corresponds to the arrival time of the wave
filtered
group about the center frequency (Dziewonski
et
al.,1972).
This is derived by truncating the Taylor series expansion of
and
k( 0)
F(W))
However, as discussed by Cara
expansions into equation 4.6.
(1973) and Dziewonski et al.
not
valid
necessarily
1
are
always
not
this
(1972),
for
approximation
showing
frequencies
dispersion or in the vicinity of a
and
order and inserting the
first
the
past
stationary
small.
Thus,
a
expansion of k(W) is necessary to adaquately
dispersion
Numerical
curves.
et al,
1972).
are
are
selected
of
phase
where
third
order
describe
around
the
basis
of
the
the
1-2%
Gaussian
first
dispersion characteristics of the region under study
1973; Inston et al.,
most
However, errors can be minimized
if the relative bandwidth, and the damping of
filter
strong
experiments have shown that
the errors caused by the above assumption
(Dziewonski
is
order
(Cara,
1971).
Many of the problems associated with the dispersiveness of
the system can be
reduced
by
computing
the
interstation
80
transfer
function.
As
discussed
in
section
4.2.2, the
dispersion observed on the transfer function is
of
the
station
separation
interstation medium.
generally
transfer
much
less
calculated
group
than
the
Thus,
velocities
of
the
distance,
group
taking
station.
the
the
because
the
errors
in
by the assumptions of
Attempts were
velocities
difference
However,
systematic
caused
filtering technique on each of
small
epicentral
the
terms are reduced.
'2.
interstation
and
properties
function exhibits less dispersion than each of the
stations.
the
the
function
Because the interstation separation is
individual
small
and
a
by
made
to
find
using the multiple
individual
seismograms
in group arrival times at each
the
interstation
distance
is
relative to the epicentral distance, a small error in
the absolute travel time resulted in large errors
velocity.
This
technique
computation time than
also
analysis
of
requires
the
in
group
much
more
windowed
transfer
function.
Figure 4.4 shows examples of
contoured
plots
of
group
velocity vs. frequency derived by performing narrow bandpass
filtering
and
numbers
description
and in
the windowed transfer functions.
on
correspond
to
signal
power
of Figure 4.4 for details).
section 4.2.4, the
transfer
The letters
in
db
(see
As discussed above
function
shows
little
dispersion over distances of 500 km and the group velocities
can
often be very unstable, particularly in the vicinity of
spectral holes.
Velocities
were
generally
determined
by
picking the maximum of the envelope function.
However, in a
number of cases we ignored small frequency ranges which gave
unreasonable group velocities.
4.2.4
ERROR ANALYSIS
To determine whether differences in
group
velocities
on
the
phase
in various regions are significant,
necessary to identify the
effects
observed
sources of
measurements.
errors
it
necessary to determine the effects of measurement
the
model
derived
reasons,
is
their
will be
error
on
from inversion of the dispersion curves
(see section 4.4).
of
it
and
Subsequently,
and
Measurement errors result for
including
instrument
and
noise in the data, and assumptions and
a
number
processing errors,
techniques
used
in
calculating phase and group velocities.
Digitizing errors
were
checked
by
comparing
generated plots with the original seismograms.
in
section
4.2.1,
systematic
spectral
digitizing
table
swing of
the
instrument
with
the
corrections
to
prevent
errors,
was
the
oriented
galvanometers.
response
polarity
for
using
waveform
vertical
parallel
Corrections
computer
As discussed
distortion
axis
of
and
the
to the estimated
were
made
for
the formulas of Hagiwara (1958)
correction
of
Brune
(1962).
Timing
WWSSN stations are generally less than 0.1
second which is only a small fraction of the travel time for
82
a given phase between two stations.
a
Epicenter mislocation may be
error
Because the events used were all relatively large
stations.
ISC
(Table 4.1) the
25
are
locations
accurate
probably
to
Interstation distance is the factor used in
km.
by
caused
a
azimuth
and
determination,
velocity
group
the phase and
errors
of
source
to the calculation of relative distance between two
related
within
small
mislocation of 25 km at a
tangential
distance of 5000 km to the nearest station will be much less
than
At interstation distances of
one degree.
500
km
an
azimuth error of one degree causes a relative distance error
of
0.1
approximately
resulting in velocity errors of
km
less than 1%.
For most events used,
the stations were within
refraction
and
multipath
that
results from section 4.3 show
than
20
can
sec)
have
apparent
transmission are small,
shorter
(less
periods
azimuths of possibly 10
difficult
These effects are
degrees from the true azimuth.
to
degree
Although it is assumed effects of
of the great circle path.
lateral
1
for using a two-station technique and can cause
correct
phase or group velocities to
be
too
by
high
up
to
.05
However, few of the seismograms used in this study
km/sec.
show serious effects of beating resulting from multipathing.
Signal generated noise in the form of body wave
or
higher
mode
fundamental
windows
were
mode
waves
surface
wavetrain.
selected
to
can
For
include
contaminate the
also
this
arrivals
study,
higher
digitized
mode arrivals.
However, for most events, if higher modes were present, they
showed little correlation
between
stations
and
were
not
evident on the filtered transfer functions.
Errors in phase velocity can be determined by
the
errors
estimating
in the phase spectrum of the transfer function.
For period T, the percentage error in phase velocity
caused
by a phase error,A4 , is
Ax
_
A
where
is the wavelength and
distance.
The
phase
errors
ax
is
the
interstation
are related to the signal to
noise ratio (Clay and Hinich, 1970) by
where
and
spectra
of
are
the
values
for
the
amplitude
the noise and signal for frequency f.
Then the
phase velocity errors for frequency f become
c.
-
trAX
\s6f)~
By calculating the interstation phase
windowed
transfer
velocities
from
the
function, the uncorrelated noise between
the two records is reduced, thus decreasing the magnitude of
the errors.
In
general,
spectrum
the
smoothness
of
the
unwrapped
phase
indicates the accuracy in phase determination.
By
comparing Figure 4.2 with Figure 4.5 it can be seen that the
phase spectra of the windowed transfer
more
stable
than
that
functions
are
of the individual stations.
much
For a
number of events, the phase spectra were smoothed by fitting
a polynomial to
examples
the
unwrapped
Figure
4.6
be
The signal to
noise
ratio
be
can
improved by increasing the number of measurements.
At the expense of spatial resolution, phase velocity
can
shows
of a polynomial fit to the unwrapped phase and the
calculated phase velocity.
also
phase.
reduced
by
increasing
ratio (equation 4.12).
wavelength
to
errors
the distance to wavelength
For many paths in
this
study,
the
distance ratio varied from 1/10 to 1/2 which
is quite large.
However, a number
achieved
velocity
phase
of
other
measurements
studies
accurate
have
to
2% or
better with similar wavelength to distance ratios (McEvilly,
1964; McCowan et al.,
Figures
4.7
1978).
a,b,c
show
measured
phase
and
group
velocities for three different paths; 4.7a - between STJ and
WES
and OGD parallel to the trend of the Appalachians (Path
Al);
4.7 b - paths between
mainly
confined
OTT,
and
WES
OGD
and
MNT,
OTT
most Grenville Province (Path G).
deviations.
Also
which
sample
period
4.4).
Table
4.2
summarizes
can
usually
be
seen
that
determined
(approximately
the
to
2.5 - 5%).
(see
the phase and group
velocities and standard deviations shown in Figure
it
and
shown in Figures 4.8 are phase
and group velocities calculated from structural models
section
are
Figure 4.8 shows
the phase and group velocities averaged at each
standard
which
to the New England Appalachians (Path A2);
and 4.7c - paths between
eastern
MNT,
4.8
and
phase and group velocities are
within
0.05
to
0.15
km/s
Errors were set to 0.10 and 0.20
85
km/s for phase and group velocity respectively, for
periods
with insufficient data.
In general, the group velocity errors are slightly larger
than
the
phase
consistent
velocity
with
errors
(Table
4.2).
This
is
the discussion by Knopoff and Chang (1977)
who show under the
phase
errors
condition
of
random
and
uncorrelated
that the group velocity errors will be larger
than the phase velocity errors.
As discussed in section 4.2.3, systematic errors in group
velocity may arise from approximations made in the
filtering
analysis.
The
group
velocity
correlated between neighboring periods if
very close.
errors
the
multiple
may
samples
be
are
Using a constant Q filter, the percentage error
in group velocity is approximately (Der et al.,1970)
a,q-- U(
-
4 13)
which implies errors of 15% for the
period
range
used
in
this study.
4.2.6
DESCRIPTION
OF
RAYLEIGH
WAVE
PHASE
AND
GROUP
VELOCITIES
A summary of the interstation phase and group velocities,
and a comparison with other dispersion
eastern
North
measured
in
America is shown in Figures 4.8 and 4.9.
As
can be seen from Figure
three
paths
curves
are
subtle
4.8
and
the
for
differences
many
between
periods
are
the
not
significant under consideration of the standard errors.
The group velocities for path Al and G are quite
while
similar
the phase velocities along Al are generally less than
those along G.
As discussed by Pilant and Knopoff (1970), a
suite of different earth models can
produce
velocity
phase
curves
with
different
similar
group
velocities.
In
contrast, paths A2 and Al show similar phase velocity curves
but the group velocities differ for periods less than
about
26 seconds.
For most periods, the phase velocities
paths
fall
in
along
all
three
between those of the Canadian Shield (Brune
and Dorman, 1963) and the New York state - Pennsylvania area
(Dorman and Ewing,
regions
are
1962).
The
group
velocities
in
all
similar except the velocities measured in this
study show a steeper increase between periods of 20
and
35
seconds indicating greater dispersion.
Although the differences in phase
for
the
three
paths
and
group
velocities
are not large, the dispersion curves
will be inverted separately in a later section to show
the
models
are
consistent
that
with the body wave travel time
studies discussed in Chapters 3 and 5.
Addition of Love wave dispersion data
help
increase
(Wiggins,
1972).
the
resolution
However,
errors
theoretically
can
of a surface wave inversion
in
compiling
Love
wave
velocities may be caused by the contamination of fundamental
modes
with
horizontal
higher modes and in digitizing and rotating two
seismograms
to
the
radial
and
transverse
directions.
Thus,
the errors in calculating the Love wave
dispersion over the short continental paths
than
those
may
involved with the Rayleigh waves.
to
discrimminate
larger
Inclusion of
Love wave dispersion curves probably would not
ability
be
enhance
the
between different crustal models
for this experiment.
4.3
ESTIMATION OF FREQUENCY-WAVENUMBER
POWER
SPECTRUM
IN
The interstation phase and group velocities
measured
in
SOUTHEASTERN NEW ENGLAND
the
previous
because of
ratios.
mode
section
the
In
stations
subject
relatively
this
Rayleigh
are
large
to
significant errors
wavelength
waves
recorded
across
six
short
period
in southeastern New England are used to invert for
The
phase
and
velocities are measured from the frequency-wavenumber
(f-k) power
Because
distance
section, phase velocities of fundamental
crust and upper mantle velocity structure.
group
to
the
spectra
of
network
signals
diameter
traversing
is
small
the
network.
relative
to the
wavelengths being measured, the errors in the phase velocity
calculations would
station
be
large
technique.
In
using
the
contrast,
conventional
because
frequency-wavenumber method used in this study is
be
a
stacking
technique,
the
where N is the number of stations.
shown
errors are reduced by
two
the
to
1/N'
Thus, accurate phase and
group velocity measurements are possible
good
spatial resolution.
while
maintaining
Additionally, beamsteering allows
for the minimization of effects caused by multipathing which
are shown to be particularly severe for periods less than 20
seconds.
Early
studies
utilizing
a
time-domain
wavefront
correlation method were applied to surface waves propagating
across Japan (Aki, 1961) and across the United States (Ewing
and Press, 1959).
have
been
More recently, high resolution techniques
developed
frequency-wavenumber
designed
arrays
for
space
such
as
analyzing
using
LASA
seismic
data
and
from
al.
(1969),
Theoretical
of
Clay (1970),
Linville and Laster (1966),
in
specially
NORSAR.
development of the application and limitations
approach are outlined by Burg (1964),
signals
the
f-k
Lacoss et
Smith (1956),
and
Arnold (1978).
Applications of
surface
waves
the
include
and Lacoss, 1968)
and
f-k
technique
for
the
study
of
the analysis of microseisms (Toksoz
Rayleigh
propagation at LASA (Capon, 1970).
and
Love
wave
multipath
The method has also been
successful in separating out higher modes propagating across
Europe
(Nolet and Panza, 1976) and the United States (Cara,
1978).
Frequency-wavenumber power spectra have been used in
geothermal exploration to identify the
noise
propagating
from
sources
of
seismic
areas of hot spring activity (Liaw
and McEvilly, 1979; Donze and Laster, 1979).
The
technique
used
in
this
study
to
estimate
the
frequency-wavenumber
power spectra is discussed in Appendix
D.
4.3.1
DATA
Two earthquakes occurring on August
Rica
(10.05
N,
85.25
December 12, 1979 in
W,
23,
depth
Equador
in
Costa
km, Ms = 7.0) and
48
(1.584N,
1978
79.386W,
depth=33,
Ms=7.9) generated surface waves in the period range of 10 to
30
the
seconds
that were recorded very well by six stations of
Massachusetts
Institute
of
Technology
short
period
network (Figure 4.10).
The stations are all equipted with a
vertical
1
component,
hz
seismometer.
Signals
are
telemetered to M.I.T. and recorded on 16mm develcorder film.
For the Costa Rica event,
record
mode
with
group
Rayleigh
samples/sec,
a
six
minute
waves
was
digitized
each
the
at
approximately
and
resampled
at
2.5
used
fairly
4
km/s was digitized for the same six M.I.T. stations
for
bandpassed
4.11.
1
Equador earthquake, an eleven minute
section corresponding to a group velocity window of about
to
4
using the weighted average slope
technique described by Wiggins (1976)
For
of
velocities corresponding to fundamental
interpolated
sample/sec.
section
the
Costa
between
Rica
10
and
As can be seen from
coherent
event.
Filtered
seismograms
50 seconds are shown in Figure
Figure
4.11,
the
signals
are
across the array and show some evidence of
multipathing as indicated by the "beating" observed on
many
of the records.
also
were
noise ratics and
response,
array
inadequate
of low signal to
because
However,
digitized.
Rica
not
also complicated by P waves from an
was
event
was
it
Analysis for the
possible to separate out the higher modes.
Costa
waves
Rayleigh
Group arrivals thought to be higher mode
aftershock occurring 12 minutes after the main shock
(mb
5.5) which masked part of the higher mode wavetrain.
The amplitude and phase spectra for stations, uncorrected
The
4.11.
Figure
in
shown
are
for instrument response
signals are strongly peaked at approximately .055 hz (T = 18
As
seconds).
be
can
these
4.12,
Figure
from
seen
frequencies are about 104 magnification units down from
of
response
peak
response curves
absolute
Although the shape of the
each station.
the
for
MIT
similar,
are
stations
magnifications are not well known.
dividing
spectra
were
because
the
by
through
left
phase
frequencies well away
1958).
tapered.
The
windowed
normalized
The phase
the maximum amplitude.
uncorrected
for
from
the
Appendix D gives a
nearly
peak
seismograms
response
instrument
is
correction
detailed
constant
response
were
the
Therefore, the
measured amplitude spectra for each station were
by
the
also
for
(Hagiwara,
20%
description
cosine
of
sources of errors in the frequency-wavenumber analysis.
the
4.3.2
INTERPRETATION AND DISCUSSION
Using the Costa Rica earthquake, the
was
computed
using
the
Figure 4.11 and along the
clockwise
(measured
total
beam
from
is
shown
the
direction
6
decibel
.05
204
degrees
array
center.
The
power
and power
is
presented
steps below the maximum amplitudes measured.
hz (20 sec).
hz, the calculated phase
almost
of
in Figure 4.13 where the frequency units
Reasonable phase velocities were
below
spectra
representing the azimuth
are in hz, and wavenumber in km
in
power
minute signals shown in
north)
between the earthquake and
spectra
6
f-k
computed
for
frequencies
However, for frequencies above .05
velocities
increased
rapidly
to
3.9 km/sec possibly indicating group arrivals coming
in off-azimuth with high apparent velocities.
This was confirmed when the array
was
steered
sweep of azimuths between 190 and 225 degrees.
a-d,
show
across
a
Figures 4.14
the beamformed signal for frequencies decreasing
from .0645, .0596,.0547,.0508 hz
respectively
(T
=
15.5,
As can be seen from Figure 4.14,
16.8, 18.3, 19.7 seconds).
arrivals with frequencies above .05 hz come in as much as 15
degrees
off
azimuth
which
arrivals
explains
For frequencies
apparent phase velocities.
the
partially
around
the large
.05
hz
are incident from an azimuth of approximately
204 degrees.
To reduce the problem
of
the
lateral
refractions,
we
selected a 3.3 km/sec group velocity window with a length of
3
minutes which included arrivals preceeding the first beat
shown in Figure 4.11.
The recomputed f-k power spectrum
is
the phase velocities in Figure
shown
in
4.18.
From Figure 4.18, it appears that the shortened group
and
4.15
Figure
power
arriving
Lateral refraction of Rayleigh waves have been
discussed
the
of
much
excluded
window
velocity
off-azimuth.
authors including McGarr (1969),
many
by
von
Seggern
(1978).
discontinuities
causing
the
and
Sobel
of
Identification
lateral
and
the
refractions can be a
However, from
highly non-unique problem.
Capon (1970),
regionalized
the
phase velocity map for 20 second Rayleigh waves presented in
is
it
(1978),
Seggern
von
and
Sobel
possible that the
refracted
multipathed arrivals recorded in New England were
of
south
the United States and propagated northwards along
the continental margin.
direction
of
the
smooth
but
The calculated phase velocities
consistently
were
indicated that all periods were
approximately
frequencies
two
to
for
arriving
the
4.11
multipath
are
very
transmission
an
from
of
southeast
beamsteered
were
Beamsteering
high.
power
azimuth
the true
spectra
an azimuth range between 170-210
The seismograms from the Equador
degrees.
Figure
degrees
Figure 4.17 shows the
azimuth.
for
10
beam
the
on
spectra
Equador event (191 degrees) is
12/12/79
shown in Figure 4.16.
very
power
frequency-wavenumber
The
event
shown
in
coherent and show little effects of
as
evidenced
by
the
lack
of
modulation.
Thus, rather than using a group velocity window
to
multipathed arrivals, the phase velocities were
elimate
reduced by multiplying all periods by
both events are shown in Figure 4.18.
from
velocities
phase
The
cos(10.
periods above 30 seconds, the phase
velocities
were
For
still
These errors may be caused by the low signal to
quite high.
noise ratio at these longer periods.
were
Group velocities
The differentiation
the power spectra.
to
fit
polynomial
the
differentiating
by
obained
became unstable in both cases for periods less than about 20
seconds and greater than 32 seconds.
SIMULTANEOUS INVERSION OF RAYLEIGH WAVE PHASE AND GROUP
4.4
VELOCITIES USING A MAXIMUM-LIKELIHOOD
Once the phase and group velocity
paths
compiled
are
is
it
consuming
time
for
different
necessary to interpret them in
methods
Trial and error
terms of earth structure.
very
curves
TECHNIQUE
systematic and versatile approach is
minimizes
which
be
and give no information regarding the
uniqueness (resolution) or errors in the solution.
inversion
can
the
A
more
to perform a linearized
errors
in a least squares
sense.
an
Initially,
inverted
be
just
found
velocities,
inversion
routine
phase velocities.
that
they
accurately
often
was
that
Although structures could
reproduced
failed
programmed
to
match
observed
observed
phase
group
velocities.
The
inversion
scheme
was
then
expanded
to
invert phase and group velocities simultaneously.
As discussed in section 4.2.4, observation errors
between
phase
and
period.
Also,
calculation
partial
group
derivatives
integrals over the
necessary
to
velocities
of
thickness
weight
the
and as a function of
phase
involves
the
of
and
group
evaluation
a
solution
differ
layer.
velocity
of
energy
Thus,
it
is
in both data and model
space and a maximum-likelihood approach is used.
4.4.1
INFORMATION DERIVED FROM
FUNDAMENTAL
MODE
RAYLEIGH
WAVE PHASE AND GROUP VELOCITIES
In setting up the surface wave inversion,
it
is
necessary
to parameterize the problem and define what phase and
velocities
earth
the
structure.
presents
between
of
a
Inversion
non-unique
certain
thickness.
fundamental
However,
Rayleigh mode reveal about
of
problem
parameters
phase
as
of
results in a more non-unique problem
1970)
resulting
phase
and
from
group
integration,
two
the
velocities
because
such
inversion
group
of
alone
the trade-off
velocity
and
layer
group velocities alone
(Pilant
and
Knopoff,
derivative relationship between
velocity.
Because
structures
of
generating
a
constant
different
of
phase
velocity curves can produce identical group velocity curves.
Although phase
independent
and
group
variables,
velocities
they
are
not
completely
do provide slightly differing
sensitivities
to
different
structures
and
can
be
used
phase
and
simultaneously to increase resolution.
Much information on the
group
power
of
velocities can be obtained by examining their partial
derivatives.
and
resolving
group
velocity
Appendix E.
(1977)
The methods used for the calculation of
partial
derivatives
is
phase
outlined
Der and Landisman (1972) and Knopoff and
give
a
detailed
discussion
Chang
of the sensitivity of
phase and group velocities to various layer parameters as
function
of
period.
for
all
depths,
while
second-most important parameter.
the
compressional
a
For fundamental mode Rayleigh waves,
both phase and group velocities are most sensitive to
velocity
in
wave
the
density
However,
velocity
significant effect on dispersion.
for
also
has
shear
is
the
the
crust,
a
fairly
In general, the magnitude
of the phase velocity partials are smaller and smoother than
those for the group velocity.
equal
Thus,
it
appears
that
for
errors, group velocities have greater resolving power
than phase velocities.
With respect to shear velocity,
the
group velocity partials have a zero crossing while the phase
velocity
partials
do not.
This indicates that the effects
of a shear velocity increase at one depth can be compensated
for by a decrease at another depth with no resulting
in the group velocity curve.
structures
different
dispersion.
errors,
Numerical
group
can
This further confirms that two
produce
experiments
velocities
change
are
more
the same group velocity
show
that,
for
equal
sensitive to velocity
gradients or changes in major interface depths such
Moho
(Der
and
Landisman,
Under certain conditions,
inherently
as
the
1972; Knopoff and Chang, 1977).
the
group
velocity
errors
may
be larger than those of the phase velocity which
will degrade the resolving power of the group velocity
(see
section 4.2.4).
Shear wave velocity has a greater
group
velocities
than
density,
effect
on
phase
even though the effect of
density is not small (Burkhard and Jackson, 1976).
phase and group velocity partials with
have
a
zero-crossing
and
respect
However,
to
density
indicating the trade-off with depth.
Shear velocity and density are not independent variables and
are coupled by the equation A
shear
velocity
fundamental
mode
necessarily
(Wiggins,
and
density
phase
decrease
and
the
.
in
the
group
number
Thus,
inversion
velocities
of
degrees
is
using
does
of
not
freedom
1972; note his definition of number of degrees of
freedom is actually the number of non-zero
which
including both
not
eigenvalues,
p,
the statistical definition , m-p, where m is
the number of observations).
Ccmpressional
either
wave
velocities
have
little
effect
on
phase or group velocities except for shallow layers.
Thus, P-wave velocities can be
set
according
to
regional
refraction profiles (which was done in this study) or can be
adjusted
to
maintain
shear velocity is
a
reasonable Poisson's ratio as the
adjusted.
The phase and group velocities
are
inverted
for
shear
fixed.
density and P-wave velocity are held
while
only,
velocity
The simultaneous inversion for
not
does
density
paramenters are
the
improve
and
the
two
velocities
are
because
problem
P-wave
independent.
not
velocity
shear
known fairly well from regional travel time studies.
The effects of imprecisely known interface depths on
the
final solution are minimized by using a large number of thin
This makes adjoining layers dependent on each other
layers.
and
avoids
a diagonal resolution matrix.
The result gives
an average of the actual velocity model over a
depth
range
where the resolution in significant.
The details of the
are
Appendix
in
given
inversion
maximum-likelihood
The
F.
is
method
Aki
basically
(Wiggins,
stochastic inverse on a transformed system
scheme
a
1972;
and Richards,1980) where elements of the data space are
weighted according to the observation errors and
the
model
and
group
space is uniformly dimensionalized.
In summary, simultaneous
velocity
may
improves
resolve
velocity.
structures
phase
better
than
the
phase
group velocity is also useful in fixing the
slope of the phase velocity
constraints to the inversion.
4.4.2
of
the inversion because the group velocity
certain
The
inversion
INVERSION RESULTS
curve
and
may
provide
added
In this
the
from
results
section
of
inversions
the
dispersion
information from the three paths (Al, A2, G) are
presented.
It must again be emphasized that because of
relatively
large
errors
phase and group velocity
the
in
curves
measurements, the differences between the dispersion
subtle
are
and
the
However,
models are very non-unique.
models are calculated which are
the
body
the
with
consistent
wave data presented in chapters 3 and 5.
Initial models for the inversion were chosen on the basis
of
refraction
the
models
in
discussed
made using a large number of thin (4 km)
if
will
be
resolution
attainable
false
that
areas
Models
thick
layers
showing velocity gradients which may or
Also, a better fit to
model
the dispersion curves was attainable because the
parameters
and
of
using thin layers.
may not have been real were observed.
more
upper
impression
using thin layers were similar to those using
except
and
crust
too
For final runs, thicker
excessively high.
layers were used which eliminated the
velocity
this
In
layers.
the initial guess for the crustal thickness is
great, the final velocities for the lower
mantle
To
the effect of the initial model, primary runs were
minimize
case,
3.
Chapter
greater
flexibility.
had
For the period
range used, the resolution was optimal for the crust between
10-40 km, so 10 km thick layers were chosen for
and
20
km layers for the mantle.
the
crust,
Final models were chosen
on the basis of resolution, model covariance, RMS fit to the
dispersion and on the reliability of the solution.
If
the
99
final
solution gave abnormal structures such as excessively
large
crustal
velocities
low-velocity
zones
or
unreasonable
Sn
with large errors, different initial models were
used or the damping of the transformed system was increased.
The measurement errors shown in Figure 4.7 and listed
Table
4.2
were calculated by taking the standard deviation
of the phase velocities from the mean.
errors
The
phase
velocity
were doubled to give the group velocity errors which
decreased the weight of the group velocities
inversion.
errors
on
the
final
If there were only two or three data points, the
were set at 0.20 km/s for group velocities, and 0.10
km/s for phase velocities.
the
in
standard
velocities
deviations
and
0.2
km/s
Because path G has little
were
set
for
to
group
data,
0.1 km/s for phase
velocities
for
all
periods.
The final shear velocity models and errors for
paths
are
shown
in
Figure
the
4.19 and resolving kernals in
Figure 4.20.
The model errors are calculated by taking
square
of
root
matrix.
the
four
diagonal
elements
the
of the covariance
The fits to the observed phase and group velocities
are shown in Figures 4.8.
The solution for path Al converges
that
is
very
consistent
with
it is felt that this is the
models
because
phase
and
different
group
events.
path
a
model
most
reliable
of
the
was the longest and the measured
velocities
The
to
the Appalachian refraction
model.
the
rapidly
were
crust
is
most
consistent
characterized
by
for
two
100
well-defined layers with a high velocity lower layer and
is
approximately 40 km thick.
The shear velocity model for the Grenville path (path
also
is
characterized
by
approximately 35 km thick.
a
two
layer
However, the
crust
lower
that
crust
G)
is
does
not exhibit velocities that are as high as those found along
path
Al.
reasonable
Assuming
approximately
velocities
0.25,
the
Poissons
are only about 0.1 km/s higher than the 6.6 km/s
crust found from the refraction data.
the
from
compressional
crustal
lower
of
ratios
The two
layer
crust
inversion of the Grenville dispersion data is not
in agreement
with
models
an
have
the
refraction
average
results
although
both
shear velocity of about 3.7 km/s.
This may be explained by noting the location of path G which
crosses part of the Taconic thrust belt.
The thrust belt is
a thick pile of sediments and metasediments possibly
thick
et
(Diment
characterized
by
al.,
a
1972)
thick
which
low
would
velocity
10
km
probably
be
layer
overlying
Grenville basement.
The calculated phase and group velocities
and
G
are
different.
crust
relatively
for
paths
Al
even though the models are
similar
The model for path Al
has
a
slightly
thicker
with a higher velocity lower layer than the model for
path G and there is a trade-off between layer thickness
velocity.
This
demonstrates
and
the inability of the surface
waves to discriminate between different crustal models in an
older tectonic region where the velocity differences are not
101
great.
The dispersion curves for path A2 were more difficult
because
fit
to
and group velocities were inconsistent.
phase
The observed phase and group velocities appear to be too low
model.
The
model is similar to those expected from
final
the refraction results
and
shows
a
high
crustal layer with a 40 km thick crust.
more
of
path.
just
a
reasonable
any
to
fit
and high, respectively, for a good
velocity
gradient
velocity
lower
There appears to be
in the lower crust for this
Also shown in Figures 4.8 and 4.19 is a good fit
the
phase velocity curve and the corresponding model.
The model is
expected
very
consistent
that
with
which
would
across the region traversed by path A2.
probably has the thickest crust in the entire
study,
the
and
a
be
This area
region
under
45 km thick crust generates phase velocities
that fit the observed very well
while
maintaining
a
high
velocity lower crustal layer.
The
dispersion
frequency-wavenumber
power
spectra
England were inverted separately over
periods
than
for the -other paths.
in
a
southeastern
narrower
band
New
of
The results are similar
to the other Appalachian paths in that they
with a high velocity lower crust.
the
from
measured
curves
are
consistent
102
Table 4.1
Events and Stations Used in Surface Wave Analysis
Events
M,
Date
O.T.
Lat.
Long.
8/14/69
6/15/75
11/6/73
2/27/70
12/9/72
5/4/72
14:19: 01.
00:19: 34.
09:36: 05.
07: 07: 58.
06:44: 40.
21:40: 00.
43.1N
43. 667N
51. 6N
50.lN
15.2N
35. 124N
147. 5E
147. 801E
175.4W
179.6W
45.2W
23. 612E
t
"
1/15/68
"o
9/19/72
4/5/75
7/30/68
i
02:01:04.1
37. 78N
i
i
01:36:52.
09: 34: 36.
20:38:42.
19.5N
10. ON
6.930 S
Stations
MNT
WES
OTT
STJ
OGD
45. 503N
42. 385N
45. 393N
47.57 N
41. 067N
73. 623W
71.322W
75. 715W
52.73 W
74.617W
"
13. 03E
i
70.1W
69.8W
80. 455W
Sta. separation
Stas.
6.1
5.9
6.4
6.0
5.7
5.9
"I
6.1
"I
6.1
6.1
6.0
MNT-WES
"o
OTT-WES
392.5
"1
485.9
"
11
WES-OTT
STJ-WES
STJ-OGD
STJ-WES
STJ-OGD
OGD-OTT
"
OGD-MNT
it
1569.0
1880. U
1569.0
1880.0
488.7
i4
499.3
103
Table 4.2
Mean Phase and Group Velocities and Phase Velocity
Standard Errors
Path A2
C
Path G
Path Al
U
3.00
3.02
3.08
3.14
3.20
3.26
3.34
3.42
3.50
3.56
3.64
3.68
3.72
3.74
3.76
3.78
3.79
3.80
3.82
E
09
08
06
05
05
06
06
06
07
07
08
06
08
08
08
07
07
07
07
C
3.40
3.45
3.52
3.56
3.64
3.68
3.74
3.80
3.85
3.88
3.92
3.95
3.98
4.00
4.02
4.04
4.05
4.05
4.06
U
E
08
08
08
06
06
16
26
40
52
58
64
68
72
74
75
76
76
77
78
09
09
07
05
05
05
05
05
05
05
05
06
10
10
10
10
10
10
10
C
3.46
3.54
3.58
3.64
3.68
3.74
3.76
3.82
3.86
3.92
3.94
3.96
4.00
4.02
4.05
4.08
4.10
4.12
4.14
U
3.04
3.04
3.06
3.15
3.22
3.26
3.34
3.44
3.54
3.60
3.65
3.68
3.74
3.76
3.78
3.82
3.84
3.84
3.85
E
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
.10
104
Table 4.3
Final Velocity Models From Inversion of Phase and Group
Velocities
Path Al
Layer
Thickness, Depth
10.
10.
10.
10.
20.
20.
20.
0.
10.
20.
30.
40.
60.
80.
100.
Path A2
10.
10.
10.
10.
20.
20.
20.
10.
20.
30.
40.
60.
80.
100.
Path G
5.
10.
10.
10.
20.
20.
20.
0.
5.
15.
25.
35.
55.
75.
95.
(km)
Va
6.0
6.2
7.0
7.0
8.1
8.1
8.2
8.2
Density (g/cc)
105
FIGURE CAPTIONS
Figure 4.1
Stations and events used
analysis.
Figure 4.2
corrected
Seismograms and
8/14/69 and 12/9/72 events.
Figure 4.3
envelope
Narrow band-passed signals and
functions for frequencies of .04980 hz and
0.
(a) alpha =
.03979 hz, BAND=0.25;
(b) alpha = 20.; (c)
(boxcar function);
for
surface
wave
spectra
for
alpha = 50.
Figure 4.4
Examples of group velocities from multiple
filtering of interstation transfer function.
Character a represents lowest power; 9 increments.
(a)
highest power in dbinc
8/14/69 event; (b) 12/9/72 event; (c) 5/4/72
event.
Figure 4.5a
Transfer functions for 8/14/69, 12/9/72, and
5/4/72 events.
Figure 4.5b
Spectra of signals shown in
Figure 4.6a
fit
Unwrapped phase spectrum and polynomial
in
Figure
shown
to spectra of three events
4.5b.
Figure 4.6b
Interstation phase velocities
smoothed phase spectrum
from
events shown in Figure 4.6a.
Figure 4.7
Composite phase and group velocities for all
(c) Path
events; (a) Path Al; (b) Path A2;
G.
Figure 4.8
Averaged phase and group velocities and
calculated
with
deviations
standard
velocities from models shown in Figure 4.20.
(a) Path Al; (b) Path A2; (c) Path A2 with
45 km crust; (d) Path G.
Figure 4.9
Phase and group velocities from this study
compared with those of other studies in
eastern North America.
Figure 4.10
MIT stations
analysis.
Figure 4.11
Short-period seismograms and examples of
from 2 events used in F-K analysis.
spectra
used
in
Figure 4.5a.
calculated
for three
frequency-wavenumber
106
Seismograms are bandpassed filtered between
10 and 50 seconds. (a) 8/23/78 event; (b)
12/12/79 event.
Figure 4.12
Typical instrument response
period stations.
Figure 4.13
spectra
Frequency-wavenumber (F-K) power
from 8/23/78 event using total signal shown
Beam direction is 204
in Figure 4.11a.
(azimuth to the event).
north
degrees from
Shading in 6db steps below maximum power is
shown in the figure legend.
Figure 4.14
Beam-steered power spectrum for selected
.0596,
and
.0547,
frequencies of .0508,
.0645 hz along a range of azimuths from
8/23/78 event.
Actual azimuth to event is
204 degrees from array center. Same shading
as in Figure 4.13.
Figure 4.15
F-K power spectra using 3.3 km/s group
velocity window of three minute length along
beam direction of 204 degrees. Same shading
as in Figure 4.13.
Figure 4.16
F-K power spectra from 12/12/79 event using
signal shown in Figure 4.11b. Beam
total
degrees (azimuth to the
direction is 181
Symbol 0 corresponds to lowest
event).
to
highest in 6 db steps below
power; 5
maximum power.
Figure 4.17
selected
Beam-steered power spectra for
18.5
sec) and
=
.0542
hz
(T
frequencies of
a range of
30 sec) along
.0332 hz (T
Actual
event.
12/12/79
from
azimuths
azimuth to event is 181 degrees from array
center. Same contours as in Figure 4.16.
Figure 4.18
Phase and group velocities from F-K analysis
of 8/23/78 and 12/12/79 events across MIT
network.
Figure 4.19
Shear velocity with depth from simultaneous
inversion of phase and group velocities.
standard
Horizontal bars indicate model
errors for each layer. See Figure 4.8 for
calculated phase and group velocities from
these models. (a) Path Al; (b) Path A2; (c)
Path G.
Figure 4.20
Layer resolving kernels from simultaneous
inversion of phase and group velocities as a
for
MIT
short
107
function of depth. Arrow points to position
of layer. (a) Path Al; (b) Path A2; (c) Path
G.
STRTIONS FiND EVENTS
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20
10
0
(3)
(4)
50
(5)
60
70
(6)
80
90
(7)
DEPTH (km)
Figure
4
. 2 0a
(layer)
DEPTH (km)
(I)
5
RESOLVING KERNE L S
PA TH A2
(2)
15
(3)
25
(4)
35
(5)
50
(6)
70
(7)
90
,
I
10
I
(2)
I
20
I
(3)
I
30
I
(4)
,
.
.
40
50
(5)
60
70
(6)
80
90
(7)
DEPTH (km)
Figure 4.20b
(layer)
DEPTH (km)
RESOLVING
KERNELS
PATH G
.
2 )5
(2)
l0
(3)
20
(4)
30
(5)
45
(6)
65
(7)
85
(1)
10
(2)
20
(3)
30
(4)
40
50
(5)
60
70
(6)
DEPTH (km)
80
90
(7)
Figure 4.20c
148
CHAPTER 5
CRUST AND UPPER MANTLE STRUCTURE FROM TELESEISMIC P WAVES
This chapter
teleseismic
reports
P
on
wave
the
arrival
Northeastern Seismic Network.
P
wave
travel
beneath
and
an array.
in
the
recorded
by
of
the
teleseismic
crust
and
upper
1966; Nuttli
and
Bolt,
1969;
Iyer, 1976) at LASA (Sheppard, 1966; Iyer and
,
1969)
in
Arizona
1967), in Japan (Zandt, 1975; Hirahara, 1977), at
NORSAR (Aki et al.,
(Iyer,
study
Notable studies include those in
Healy, 1972; Greenfield and Sheppard,
(Johnson,
a
The inversion of
information
California (Bolt and Nuttli,
Steeples
times
of
time residuals is a commonly used method of
extracting velocity
mantle
results
1975;
1977),
Zandt,
in
Yellowstone
1978),
in
Hawaii
National
Park
(Ellsworth
and
Koyanagi, 1977)in New Madrid (Mitchell et al.,
southeastern United States (Volz,
1979),
1977), in the
and
beneath
the
Tarbela Array (Menke, 1977).
Many of the earlier studies consisted of determination of
residual patterns and development of qualitative
explain
the
observed
trends.
three-dimensional
structure
comprehensive analysis of
method
will
not
be
the
to
Recent models have utilized
the techniques developed by Aki et al.
the
models
(1977)
beneath
an
,
for
mapping
array.
three-dimensional
The
inversion
discussed in this chapter because the
149
details are covered in Aki et al.,
(1977), Zandt (1978),
and
Ellsworth (1977).
To date, very little
crust
and
upper
seismological
mantle
structure
northeastern United States.
and
Katz
Leet
work
has
pertaining
been
(1941),
done in the
Linehan
(1962),
(1955) published refraction results using a small
permanent array combined with some portable stations.
recently
relevant
studies
Schnerk
et
residuals
beneath
of
residuals
across
United
(Fletcher
et
Chapter 3 we
and
(1976).
teleseismic
Newfoundland (Stewart, 1978)
study of teleseismic P-wave
States
al.
include a surface wave analysis in
New York (Dorman and Ewing, 1962), analysis
PP
More
some refraction work has been reported by Chiburis
and Graham (1978) and Aggarwal in
Other
to
Canada
discussed
the
crustal
,
the
al.,
models
and a
eastern
1978).
derived
In
from
interpretation of regional travel time data.
In
this
teleseismic
chapter,
P-wave
a
three-dimensional
residuals
is
inversion
presented
using
collected from the Northeastern Seismic Network.
is
interpreted
in
conjuction
with
geological observations in an attempt
crust
ancient
and
upper
mantle
structure
orogenic
belts,
the
Provinces.
An
The
of
data
model
other geophysical and
to
learn
beneath
Grenville
about
two
and
the
adjacent
Appalachian
effort is also made to interpret the models
in light of, and to place constraints on a
origin for both orogenic belts.
plate
tectonics
150
TRAVEL TIME RESIDUALS
5.1
Teleseismic P-wave arrival times were collected
stations
50
which are part of the Northeastern Seismic Network
(Figure 5.1).
by
from
research
of
uniform,
Geological
Observatory,
Technology.
although
spacing.
operated
groups at Boston College (Weston Observatory),
Lamont-Doherty
Institute
The stations were installed and are
there
Station
are
and
Massachusetts
distribution is
areas
with
large
fairly
station
Not all of the stations were in operation for the
duration of this study.
Because the network was not in full
operation until February,
covered
a
1976,
events used
in
this
study
time range between February, 1976, and December,
1977.
Most stations are equipped with
short
period
1 or 2 hz geophones.
vertical
component,
Signals are telemetered
to central recording sites (located at
each
of
the
above
institutions) and recorded on develocorder film.
The relative arrival times
read
from
enlarged
copies
of
teleseismic
P-waves
of 16mm develocorder film.
were
In
general, strong scattering in the frequency bandwidth of the
incident P
coherency
waves
of
is
not
observed
as
by
the
the first few cycles across the network.
The
signals from each of the stations were
using
an
overlay
of
trough
early
visually
waveforms.
representative
arrival measurements were taken from
indicated
a
prominent
correlated
Relative
peak
or
in the signal, and readings were taken to the
nearest 0.1 second.
A
misidentification
of
the
peak
or
151
trough
would
cause
a residual error of 0.5 to 1.0 seconds
which is readily apparent once the residuals are calculated.
1822 arrival times from 68 events were read from stations
of the northeast network.
between
The epicentral
distances
25 and 95 degrees and azimuths were mainly from the
northeast (from Eurasia), south and southwest
South
ranged
America),
and
the
northwest
(Central
and
(Aleutians, Kuriles),
(Figure 5.2).
Elevation corrections were applied to the data and travel
times were reduced
Absolute
P-wave
to
a
datum
residuals
elevation
were
at
calculated
sea
level.
using
Herrin
travel-time tables and are defined to be
T;
where Ri
tables
time
is the absolute residual with
respect
to
Herrin
obs
station i , event j; Tli
for
using
event
bulletins; I;
Herrin
(S.0)
is
earth.
calculating
locations
the
The
relative
and
is the observed travel
origin
theoretical
residuals
residuals
were
with
times
travel
from
PDE
time through a
further
reduced
respect
to
a
by
mean
residual computed for each event;
where N is the number of stations reporting P
arrivals
for
event j.
Using
represent
the
late
above
relationships,
arrivals
positive
residuals
where the incident rays have been
152
slowed in the crust or upper mantle beneath the network.
should
be
observed
noted
in
that
the
no
values
significant
of
Jeffreys-Bullen travel time
Herrin
Tables.
An
the
differences
relative
tables
were
residuals when
used
instead
all
stations
the
structure
at
and
variations beneath the array are major causes of
the absolute residuals.
a
The
the source, heterogeneities
encountered along the major portion of the travel path,
structural
of
similarly
and will drop out when relative residuals are computed.
of
were
error in the reported origin time or a
source correction term will affect
effects
It
teleseismic
source
Intuitively, the cone of rays
from
to different stations in the network
will sample nearly identical travel paths until they diverge
into the upper mantle and crust beneath the array.
is reasonable to assume that the computed average
contain
the
Thus, it
residuals
information regarding this common travel path up to
point
where
subtracting
off
the
the
rays
diverge
average
significantly.
residual,
By
effects caused by
mislocation errors or heterogeneities encountered along
the
common path are greatly reduced.
The
above
approximations
network aperture is
the
which
are
reasonable
small become progressively less valid as
network aperture is increased.
If the apparent network
aperture is large enough, the curvature (second
of
when
the travel time curve becomes significant.
derivative)
The problems
involved in the analysis of relative P-wave
residuals
been
Using data from
discussed
by
Engdahl et al.
(1977).
have
153
Alaskan-Aleutian
primary
stations,
Engdahl
concluded
the
source of observed variations in relative residuals
was from local structure beneath the network.
separations
comparable
Northeastern U.S.
residuals
from
earth models,
more
that
residuals
Network
maximum
(600
km),
scatter
mislocations,
reading
accuracy.
station
diameter
of
in
the
relative
source structure,
were at most 0.2 seconds,
recorded
conclusions.
the
epicenter
etc.
our
than
to
For
which is
of
Analysis
little
relative
in the northeastern U.S. supports these
We found no systematic differences in relative
residuals from various depths in the same epicentral regions
where it is presumed rays would encounter
source
different
structures.
Two additional sources of error remain to
Because
of
down-time
for
some
stations,
be
discussed.
and
of
stations that became operational during the period
study,
other
of
this
slightly different station subsets are available for
each earthquake, and the mean residual subtracted off from a
given source region may vary for different events.
this problem is greatly
stations
(typically
reduced
25-35)
used
the
time
base.
compensated
fact
were
large
number
calculate
other
the
problem
of
mean
results
that each subnetwork records on a different
Each
subnetwork
operates
a
temperature
crystal oscillator clock and timing corrections
are generally less than
tests
the
to
The
residual for each earthquake.
from
by
However,
20
ms/day.
To
assure
accuracy,
made by comparing signals from a common station
154
recorded on more than on subnetwork.
time residuals was carried
The
distribution
out
The analysis of travel
relative
using
of average relative residuals,R, for each
station is shown in Figure 5.3.
The relative residuals as a
function of azimuth and
incidence
variations
network (Figure 5.4).
across
the
angle
show
suggest the presence of large scale lateral
in
the
crust
required
to
residuals.
significant
These trends
heterogeneities
and upper mantle, and considerable effort is
separate
the
factors
causing
the
observed
patterns.
Average
relative
azimuths.
each
Large positive residuals
throughout
central
and
northern
Maine and eastern Vermont.
al.
for
these
(1978)
residuals
in
southeastern
station
New
New
arrivals)
sharply
Vermont,
York,
with
Fletcher
large
northern
the
observed
York,
Connecticut.
result
varying trends between adjacent stations.
the slowly varying distribution of residuals
et
negative
New
southwestern
and
occur
Hampshire, southern
As was observed by
contrast
western
(late
Shallow, localized structural differences should
rapidly
were
ten or more readings from well-distributed
with
calculated
residuals
in
However,
suggests
that
variations are probably due to deep, regional
structures such as
differences
in
crustal
thickness
and
upper mantle velocity.
As a first step we compare
the
geologic and other geophysical data.
residuals
with
surface
Figure 5.5 illustrates
the relationship between average relative station residuals,
155
R , and the regional Bouguer gravity taken from each station
site (Kane et al.
(1972),
gravity
anomalies
regional
wavelength ( "100km)
long
the
Because
(1972)).
and Diment et al.
Simmons, (1964),
reflect
probably
variations
in
Moho
topography, (Simmons, 1964), the correlation between gravity
and
residuals suggests that for many stations, the
average
average
depend
residuals
variations.
It
on
partly
thickness
crustal
is also interesting to note the dependence
of average residuals on the age of the basement beneath each
station.
to
The two sets of symbols in the
the
York
and
New
England stations are atop younger (<
of
basement
the
stations
within
arrivals
relative
Bouguer
the
gravity
thickness
variations
regions,
1.0
b.y.)
Paleozoic
earlier).
Clearly,
see early
Province
Grenville
Appalachian
in
the
younger
because
of
the
relationship between
and
station
elevation
it
obvious
is
this separation totally to crustal
(Figure
In
5.6).
isostatically
crustal thickness should be correlated
elevations
illustrates
(Woolard,
that
there
1959;
is
Tseng,
1975).
a poor correlation
between gravity and elevation and more importantly there
no
the
those
attribute
to
surface
older
anomalies
difficult
compensated
described
to
However,
5.6
above
located
Province (the central mobile
Appalachian
belt, and eastern belt
Province.
are
Jersey
(> 1.0 b.y.) Grenville basement, while most New
Precambrian
Figure
correspond
inferred age of the basement for each station site.
Stations in New
with
figure
separation between the two regions.
is
To explain
156
to
the behavior of both Figures 5.5 and 5.6 it is necessary
profiles
by
This idea is supported
variations in crustal thickness.
refraction
possible
any
to
addition
in
changes
velocity
invoke
constructed
the northeastern U.S.
in
Although little detailed refraction work has
been
in
done
this region, existing studies and results cited in Chapter 3
higher average crustal velocities in the
slightly
indicate
Province.
Grenville Province, as opposed to the Appalachian
Table
3.5
shows
refraction models collected from regional
travel times in the
models
NEUS.
that
indicates
Appalachian Province is
slower, and it is
approximately
Comparison
of
the
refraction
crust beneath this part of the
the
and
on the average slightly thicker
possible to account for almost half of the
0.5
second
difference in relative residuals
between the two regions.
The dependence of average relative residuals
crustal
on
properties is also supported by the results of the time-term
analysis
indicates a positive correlation between Pn
which
residuals and teleseismic P-wave residuals (Chapter 3).
The
relative Pn and teleseismic P wave residuals are compared in
5.7a.
Figure
representing
sets
of
assuming
Also
the
residuals
a
simple
shown
in
theoretical
assuming
Figure
5.7a
is
a
line
relationship between the two
total
crustal
By
effects.
crustal model, we compare Pn time terms
with teleseismic "time terms" from a shallow focus event,
degrees away (Figure 5.7b).
50
From Figure 5.7b, we define the
crustal thickness h=35 km; crustal velocity Vc =
6.4
km/s;
157
upper
8.1
Vm
velocity
mantle
and the apparent
km/s,
velocity of the teleseismic P wave is calculated to be Va
The incidence angle for the refracted wave is
14.7 km/s.
=
If the variations in residuals across the
degrees.
are
wave ij
P
teleseismic
the
for
and
degrees
52
ic
= 26
network
differences in crustal thickness, Ah, then
by
caused
=
the resulting difference in travel time
for
the
refracted
the
slope
given by
wave through the crust is
C.
Similarly for the teleseismic P wave
The
ratio
(5.3)
of
(5.4)
to
gives
of
the
relationship to be expected
SI-(VcjvhA'
For the parameters given above, the slope
the
Because
will
equal
A T values represent the time it takes for the
wavefronts to move vertically upward through the crust,
two
set
of
residuals
P
in
mean
wave residuals are a result of variations in
crustal thickness, the trend of
shown
the
should show a positive correlation.
Because of the differences in incidence angles, if the
teleseismic
0.7.
Figure
5.7
should
the
have
Pn
vs.
Pt
residuals
a slope less than one.
Although there is a fairly good correlation between the
two
158
the
of
sets
about the line
in
variations
residuals, there is a large amount of scatter
should
cluster
teleseismic
P-wave
residuals
crustal thickness
appears
due
to
order,
it
are
first
the
the
that the distribution of average teleseismic P wave
by
affected
residuals is
effects.
To
differences.
if
about
they
which
thickness
crustal
velocity
or
these observations cannot fully explain
However,
three-dimensional
by
Figures 5.5 and 5.6 and, as indicated
models presented in the next section, structural differences
between the two regions extend into the upper mantle.
In addition to distinct patterns in the
average
residuals
Polar
shown in Figure 5.4.
arrivals
incidence
from
the
stations
northeastern
Moving from south to north we see
a number of interesting residual
for
and
azimuth
plots of relative residuals as a function of
azimuth and incidence angle for many
are
of
across the network, most stations show a
strong dependence in residuals with
angle.
distribution
In
trends.
northeast,
Connecticut,
become
residuals
the
increasingly less positive (arrive earlier) as the incidence
angle decreases until in southwest Connecticut and
New
Jersey residuals are largely negative.
northern
Rapidly varying
structure is observed to the south which will
be
reflected
presented
in
the
next
to
the
in
the
three-dimensional
section.
In
northwest
and
models
Massachusetts,
small
to
arrivals
are
late
the south and northeast while New
Hampshire and southern Maine observe late arrivals from
azimuths.
all
Negative residuals are observed in the Grenville
159
Province across
most
New
where
regions,
northern
of
York,
large
particularly
negative
in
the
residuals
are
observed from the northwest.
The residual patterns indicate that between the Grenville
differences exist
and Appalachian orogenic belts, structural
in the crust,
large
region
and into the upper mantle.
of
relatively
It
a
appears that
velocities occurs in the
low
upper mantle beneath central New England and that velocities
increasingly
become
Province
to
the
higher
distribution
similar
Grenville
older
the
From Figure 5.3 it is evident that
west.
most stations in close
beneath
proximity
in
to
residual
one
show
another
values
implying
a
that
Since the
lateral variations are not a near surface effect.
incidence angles are small for the teleseismic P-waves (15
-
30 degrees), lateral variations in crustal velocities cannot
account for the observed effects.
rays
enter
For example,
teleseismic
of equal slowness and incident from opposite azimuths,
the
crust
with
a
maximum
separation
of
50
km.
Azimuthal variations of one second and greater would require
unreasonably large lateral velocity differences.
The possibility of a dipping Moho as a cause of azimuthal
variations in residuals
order
in
was
investigated.
To
the
first
the dip,o( , the maximum differential travel time
for a teleseismic ray
approaching
from
opposite
azimuths
perpendicular to the strike of a dipping layer is given by
TsC
160
where
is the depth to
oc
station;
represents
(Taylor,
is
the
the
the
dip
beneath
of
angle
incident
1977).
interface
at
given
interface; G_
the
the
a
and (1Ci/i
interface;
Substitution into equation 5.6 implies that
unreasonably large regional
dips
of
the
Moho
-
(20
30
Thus, it
degrees) are required to satisfy the observations.
is reasonable to assume that laterally varying structures in
the upper mantle beneath the network are required to explain
the
pronounced
residual
versus azimuth and incident angle
variations.
THREE-DIMENSIONAL INVERSION
5.2
Qualitative description of residual patterns
previous
section
is
a
useful
estimating
the
encounters
beneath the network.
a
from
results
teleseismic
structual
but
inadequate
disturbances
time
illustrated by Aki et al.
in
means
incident
inversion
data
following
the
of
sub-divided
is
Using
blocks.
individual
relative
a
that
teleseismic
slowness perturbations
for
the
ith
the
each
series of right rectangular
block relative to a layer average.
shown
ray
The initial model used in
(1977).
into
of
techniques
the inversion consists of a plane-layered medium where
layer
the
In this section we present
three-dimensional
travel
an
as
station
P
wave
residuals,
are computed for each
Aki et
al.
(1977)
has
and jth event, relative
P
161
residuals (with respect to a mean) can be represented by
£CTJ#
57
*
V
where
1
;jk
T;Jk -~j~ -V
times
'
reduced
travel time through kth block
t
-
;j
- -(I,
percent perturbation in slowness
to the layer average (
Ok
travel
k:i
)
-
number
of observations for event j
-
number
of layers
In matrix form
relative
r = Am
where
r - n-length vector containing relative residuals
m - k-length vector
containing
unknown
velocity
perturbations
A - n x k symmetric
times
matrix
with
reduced
travel
162
Solution of the system (5.8) by classical
fails
because
there
exist
The first source can be
results
in
vertical
other
source
caused
by
"coupling"
of
insufficient
of
average
a
non-uniqueness
within
a
residual
given
determinant
from
layer,
only
to
the
the
common
is
and
sampled
ray
path.
inherent
data.
velocity
within
data
inadequately
formulation of the problem and results from the
the
squares
two sources of non-uniqueness.
blocks in separate layers which share
The
least
to the
removal
of
This implies that
perturbations
are
a constant and no information
regarding absolute velocities is attained.
technique
squares
least
(5.8) is solved by using a damped
Thus, the system
a positive constant is added to the diagonal elements
where
of ATA which reduces the effect of zero-eigenvalues
generalized
inverse
solution.
The
solution
on
the
to (5.8) is
given by
where
9
matrix.
is the damping parameter and
The
resolution
and
I
is
covariance
the
identity
matrices
are,
respectively
C rSLA*&t
where
Because
is
the
)IY ATA
estimate
of
the
data
variance, 6
.
addition of the damping parameter has the effect of
163
reducing the number of degrees
between
of
freedom,
resolution and standard-error
order to select a proper choice for 6
9
chose
the
trade-off
should be examined in
.
For this study
= 0.1 (sec/%).
Selection
of
the
experimentation
initial
with
model
different
geometry
requires
configurations in order to
derive a well-resolved solution with small standard
The
blocksize
of
errors.
depends on the station distribution, and the
number of observations.
minimum
Because it is desirable to
have
The inversion should be carried
to a depth of at least one array diameter which we
be 500 km.
height to
a
ten rays sample each block, we chose our blocks
to be one degree on a side.
to
we
selected
As suggested by Ellsworth (1977), a suitable
width
satisfactory.
ratio
is
1.5:1
which
we
found
to
be
Experimentation with displaced layers (in an
effort to decouple blocks) and
rotated
coordinate
systems
showed little, if any, improvement on the final model.
The initial model used for the ray tracing was a
spherical
model
with
constant
velocities
layered
in each layer.
Velocity differences of up to 10% do not substantially alter
the sampling of the blocks.
Herrin
earth
model
to
We averaged velocities
from
a
derive the layer velocities (Table
5.1).
The velocity perturbations and the number of observations
for blocks in each layer of the final
Figure
elements
5.8
of
and
the
listed
in
resolution
Table
model
5.2
matrix.
are
with
In
shown
in
the diagonal
these
figures,
164
negative
velocity
velocities.
perturbations represent relatively lower
We only included blocks which were sampled by a
minimum of ten rays which mainly
eliminated
the
outermost
elements.
Modeling of the crust is probably one of the most crucial
results we wish to obtain.
incidence
angles,
to
blocks.
the
directly
decouple
the
underneath.
effects
layer
were
increased.
blocks would then contain a
discontinuity
(the
large
This
makes
in
of the two superposed
Resolution could be improved if
surface
small
most rays pass through the crustal block
and the block lying
difficult
Unfortunately, because of
the
thickness
of
However, the surface
and
important
velocity
Moho) and information regarding crustal
structure would be lost.
Problems may also arise because
distribution.
crust,
a
If
number
potentially
of
the
uneven
station
rectangular prisms are used to model the
of
stations
located
in
areas
with
different structures may be included within the
same element.
To remedy this problem
perturbations
for each individual station rather than for a
given block configuartion.
It was
we
found
compute
that
velocity
using
this
approach had little effect on the upper mantle layers and it
facilitated
a
means to compute a three-dimensional crustal
thickness model which is
described below.
Although resolution is poor and standard errors are large,
the velocity perturbations show a good
average
station
residuals
(Figure
correlation with the
5.9).
This
further
165
supports
previous
conclusions
that
the
average
station
residuals are mainly dependent on crustal structure, and may
reflect crustal thicknesses and velocity
and Healy (1972)
model
crustal
successfully used a general
thickness
at
average station residuals.
homogeneous
crust
particular region
They made the
beneath
in the
they
section,
crustal
the
to
use
were
array
assumption
of
a
which
be
a
may
order crustal model in the
modeling.
U.S.
show
velocities
that we must account
order
relationship to
However,
in
the
we concluded that the two orogenic belts
northeastern
average
Iyer
LASA from the distribution of
reasonable assumption for a first
previous
variations.
for
regional
differences
and thicknesses.
lateral
velocity
in
This implies
variations
in
the average residuals for crustal thickness.
Combination of the velocity perturbations with
the
average
station residuals allows us to construct a crustal thickness
model.
Although
there
is
a
trade-off
between
crustal
thickness and lateral velocity differences we feel that
method
is
justified
because
suggests the dependence
of
independent geophysical data
average
station
residuals
crustal thickness and lateral velocity variations.
effects
of
certain
regions
the
upper
through
the
on
However,
mantle
may
leak into the model in
both
the
average
residual
and
velocity perturbation terms.
We
assumed
that
the
velocity
perturbations,liy
V
represent differences from an average crustal velocity, Vc
It
should
be
stressed
that
any
information
regarding
166
absolute velocities in the three
lost
and
the
technique
we
are
approximation and represents
model.
The
average
dimensional
using
only
crustal
a
is
first
velocity,
inversion
is
therefore
an
order
Vi,
crustal
beneath each
station i is then
100) +vc0
v; v)(()
and the crustal thickness is
V,;
+~
where hO is some average crustal thickness to be varied.
chose Vc = 6.5 km/s and
=
hO
38
km
and
calculated
We
the
crustal thickness and average crustal velocity maps shown in
Figure
5.10.
Overall,
Province appears to
Grenville.
be
Average
the
3
crust beneath the Appalachian
km
crustal
thicker
than
that
of
the
velocities differ very little
but may be slightly lower in many parts of the Appalachians.
There is a
eastern
region
Vermont,
of
New
greater
Hampshire,
western Vermont, and
western
thickness
where
gradients
crustal
and
thickness
southern Maine.
Connecticut
the
crust
there
thins
These features are located just to the east of
thrust
belt
and
beneath
are
In
high
to the west.
the
Taconic
in western Vermont, the gradients show an
impressive correlation with the serpentinite
belt.
Slight
crustal thinning is obseved in eastern Massachusetts, and it
is
not
clear if this represents a trend which may continue
eastward towards the outer edge of the
continental
margin.
167
Alternatively,
central
may
orogenic
earlier.
New
it
represent
belt
and
the
the
contact between the
eastern
belt
described
The average crustal thickness of 36 km in northern
York
agrees
very
well with refraction models of Katz
(1955) and those of Aggarwal
in Schnerk et al.
(1976).
The upper mantle (layer 2) between 35 and 200 km
5.8b)
depth is characterized by a northeast trending region
of low velocities beneath Massachusetts, New
southern
Maine.
parallel
with
structure.
the
The
suggests
orogenic
"grain"
resolution
the
the
Appalachian
Precambrian
into
upper
the
mantle
configuration in layer
2
incident
element,
waves,
each
elements, observe a good
because
azimuths
somewhat
the
are
surface
appear to increase to the west
Grenville
upper
Province.
is
number
of
limited
better
the
a
suited
of
outer
obsevations
to
The
Because the block
for
particularly
cross-fire
towards
mantle.
layer increases markedly
relative to that of the crustal elements.
degrades
and
structural differences between the two
extends
in
of
velocities
that
belts
Hampshire
The trend of this zone has an interesting
and northwest beneath the
This
(Figure
small
the
rays.
edges
sampling
Resolution
of the model
decreases,
sector.
resolution and standard errors are best for this
central
and
The
the
overall
particular
layer.
In layer 3 (200 - 350 km) the region of lower
is
shifted
velocities
west and northwest and is found beneath Vermont
and central Maine.
There is still some evidence
of
higher
168
velocities in the western-most blocks in the model.
The deepest layer (layer 4; 350 - 500
resemblance
to
the
overlying
layers.
appear to be of shorter wavelength
there is
little,
if
km)
shows
little
The overall trends
and,
not
surprisingly,
any distinction between the two geologic
provinces observed at the surface.
The
results
dependent
shown
in
the
block
and
Figure
not
200 km.
extend
are
configuration
inadequate to describe the case
did
5.8
where
highly
used
lateral
would
of
be
differences
below a depth significantly shallower than
Because of the relatively sparse network
addition
model
more
geometry,
layers or smaller blocks would seriously
degrade resolution.
However, qualitative
analysis
of
the
variation of residuals with incidence angle between stations
as
shown
in
Figure 5.4 suggests that major differences in
lateral structure extend to depths of at least 150 km.
In summary, we
suggests
have
presented
geophysical
data
which
that structural differences between two juxtaposed
orogenic belts exist to depths of 200 km and greater.
indicates -that
major
episodes have very long
collisional
lasting deep-seated effects as well as large areal
Crustal
thickness
and
thicker
Appalachian
crust
Precambrian
velocities
with
associated
and
Province
lower
Grenville
extents.
velocity variations are correlative
with many surficial geologic
Paleozoic
This
the
features.
The
appears to have a slightly
average
Province.
with
tectonic
velocities
The
Grenville
than
higher
the
average
Province
are
169
evident
to
Adirondack
extending
depths
dome.
to
of
A
depths
200
km
particularly
relatively
low
beneath
velocity
the
anomaly
of at least 200 km and dipping to the
northwest shows a spatial correlation with the Bronson
- Boundary Mountains Anticlinorium.
Hill
170
Table 5.1
Initial Layered Velocity Model For Three-Dimensional Inversion
Layer No.
Velocity (km/s)
Thickness (km)
Block Length
6.4
35.0
8.2
165.0
10
8.6
150.0
10
9.2
150.0
lo
(see text)
171
Table 5.2
Diagonal Elements of Resolution Matrix for 3-D Inversion
Laver 2
0
0.0
0.0
0
0
0.0
0.0
0
64
0.82
0.85
45
77
0.91
0.93
89
81
0.91
0.92
92
76
0.82
0.92
94
78
0.92
0.94
93
79
0.87
0.91
86
0
0.0
0.0
0
0
0.0
0.0
0
0.0
25
0.57
0
0.25
0
0.54
44
0.81
79
0.68
33
0.80
86
0.39
33
0.85
90
x
yer
0.0
0.42
0.60
0.32
0.60
x
32
0.91
91
64
0.85
88
0.0
0
0.82
88
0.0
28
0.83
81
0.0
0
0.48
0
0.0
0.62
0.0
0.0
172
Table 5.2
(continued)
Layer 4
0.0
0.0
0.0
0.28
0.27
0.52
0.60
0.69
0.44 0.0
0.0
0.0
0.42
0.55
0.44
0.51
0.0
0.0
0.35 0.0
0.50
0.74
0.79
0.74
0.75
0.70
0.67
0.66
0.52 0.36
0.66
0.69
0.79
0.87
0.86
0.76
0.77
0.43
0.43 0.0
0.62
0.72
0.81
0.86
0.86
0.85
0.85
0.0
0.37 0.0
0.33
0.79
0.89
0.88
0.88
0.89
0.86
0.52
0.25 0.0
0.76
0.85
0.89
0.91
0.89
0.87
0.74
0.64
0.33 0.31
0.72
0.85
0.88
0.89
0.87
0.80
0.79
0.67
0.0
0.55
0.77
0.87
0.87
0.87
0.85
0.57
0.52
0.29 0.0
0.58
0.70
0.86
0.89
0.91
0.85
0.73
0.33
0.0
0.0
0.47
0.73
0.86
0.88
0.87
0.65
0.38
0.0
0.0
0.0
0.45
0.72
0.83
0.85
0.79
0.52
0.23
0.0
0.0
0.0
0.0
173
FIGURE CAPTIONS
Figure 5.1
Seismograph
stations
used
for
three-dimensional inversion of teleseismic P
wave residuals. Labeled stations correspond
to those referred to in the text or shown in
Figure 5.4.
Figure 5.2
Epicenters of earthquakes
used as P wave sources.
Figure 5.3
Map of
average
relative
travel
time
residuals
in
seconds
for
seismograph
stations in northeastern United States.
Figure 5.4
plots.
projection
Station focal sphere
Relative residuals plotted as a function of
azimuth to the source and incidence angle.
Figure 5.5
Mean relative
teleseismic
travel
time
residual in seconds relative to Bouguer
gravity for northeastern
United
States
stations.
Open
circles
correspond to
stations located in the Grenville
Province
above
Precambrian
basement.
Solid circles
correspond
to stations
mainly
in
the
Appalachian Province located above Paleozoic
basement.
Figure 5.6
Bouguer
gravity
relative
elevation for northeastern
stations.
Figure 5.7a
Relative Pn residuals
from
time
term
analysis versus relative teleseismic P wave
residuals.
Solid line indicates theoretical
fit
assuming total crustal
effects
(not a
least squares fit;
see text).
Figure 5.7b
Terminology used
in deriving
line shown in Figure 5.7a.
Figure 5.8a
Percent velocity variations for crust and
upper mantle layer 1 beneath northeastern
in
parentheses
Numbers
United States.
correspond to the number of observations in
each element used in the inversion.
Figure 5.8b
Same as Figure 5.8a for layer 2; 35-200 km.
Figure 5.8c
Same as Figure 5.8a for layer 3; 200-350 km.
and
explosions
to
station
United
States
theoretical
174
Figure 5.8d
Same as Figure 5.8a for layer 4;
Figure 5.9
Percent velocity variations for the crustal
layer plotted against mean relative travel
time residual for the northeastern United
States seismic stations.
Figure 5.10a
Lateral average
second).
Figure 5.10b
Crustal thickness variations in
kilometers
across the northeastern United States.
velocity
350-500 km.
(kilometers
per
175
74
72
70
68
Figure
5.1
176
Figure 5.2
177
74
72
70
68
Figure
5.3
ptn
PnY
N
E
N
cbm
w
mdv
wnh
tbr
wfm
hdm
POSITIVE
NEGATIVE
o
E
IRI < 0.2
+
0 2 < IRI < 0 4
+
0.4 < IRI < 0.6
+
0.0
<
w
0.6 < IRI
0o
Figure 5.4
179
(mgal)
-g
50-
o
0
PALEOZOIC
o
PRECAMBRIA N BASEMENT
BASEMENT
0
0
I
I
1%
I
I
I
I
-0.5
0.5
p
0
0
-0
0
0
00
*
0
e
0
0
0
-- 50e
Figure 5.5
I1"l||
180
g
(mgol)
50
.
0
*
PALEOZOIC BASEMENT
o
PRECAMBRIA N BASEMENT
o
m
I
I
I
I
500
0
e
0.00
-
0
I
ELEV (m)
0
*
o0e
0
0
0
0
0
-50-
00
0
0
0
Figure 5.6
181
8.04
VPn=
0.5
I.
aa-I
*
I
w
-I--u
0
I
Rt
0.5
A-
S
0
I
-~
0
-. 5
0
~4,
0
S
S
*0e~
0
9
0
theoretical
assuming
relationship
total
crustal
effects
(not a least squares fit)
Figure 5.7a
182
Station
n- - i
1
vw'
Figure 5.7b
183
74
72
70
68
Figure 5.8a
184
74
72
70
68
Figure 5.8b
185
74
72
70
68
Figure 5.8c
186
74
72
70
68
Figure 5.8d
187
-3.0
3V
V
2.0
-1.0
I
0
I
I
I
I
17
I
0
i
1'
I
R
*.
-
I
I
I
a
0.5
-0.5
-1.0
-
-2.0
-
-3.0
-
Figure 5.9
188
74
72
70
68
Figure 5.10a
189
74
72
70
68
Figure 5.10b
190
CHAPTER 6
VARIATIONS OF
APPALACHIAN
CRUST
AND
OROGENIC
UPPER
BELT:
MANTLE
STRUCTURE
IMPLICATIONS
IN
FOR
THE
TECTONIC
EVOLUTION
In the previous chapters we have
data
from
measured
earthquakes
Although
with
the
blasts
surface
variations
and
wave
in
synthesized
regional
body
wave
and teleseismic
dispersion
measurements.
regional structure are subtle
(which is not unexpected in an ancient orogenic
belt),
structural
measurement
models
derived
using
different
techniques are relatively self-consistent and
important
constraints
northern Appalachians.
review
the
on
In
the
tectonic
this
provide
evolution
chapter,
we
will
the
some
of the
first
basic results of previous chapters and then, by
combining our results with other
geologic
information,
the
we
will
contrast
and
structure
geophysical
of the New
England Appalachians with the Grenville
Province
the
the results will be
southern
Appalachians.
Finally,
and
interpreted in a plate tectonic framework and simple,
order
with
first
plate tectonic models will be presented which satisfy
geological and geophysical constraints.
6.1
SUMMARY OF RESULTS PRESENTED IN PREVIOUS CHAPTERS
191
Figure
6.1
previous
summarizes
chapters.
the
features
observed
in
the
The Appalachians are characterized by a
two-layer, 40 km thick crust with a relatively high velocity
lower crustal layer.
To the west in the Grenville Province,
the crust thins by a few kilometers and appears to
homogeneous
belt.
except
This
Appalachians
in
also
contrast
in
and
Grenville Province occurs across the
the
crustal
structure
appears
to
eastern
block
(Avalonia)
the
structure
To
the
the
east,
Appalachians
described
Because of the proximity to the coastline,
in
between
be a contrast in crustal structure
between the central orogenic belt of
the
very
vicinity of the Taconic thrust
the
north-northeast trending serpentinite belt.
there
be
in
and
Chapter
this
2.
difference
(which may occur across the Clinton-Newbury -
Bloody Bluff fault zone in eastern Massachusetts) is
poorly
defined.
To depths of about 200 km, the
beneath
the
Province
Grenville
upper
are
mantle
velocities
about 2% higher than
those beneath the Appalachians.
Specific
observations
are
outlined
below
in
greater
detail.
Regional travel times recorded across the NEUS seismic
1.
network indicate that
a.
The
northern
well-defined
velocity
Appalachians
two
lower
are
characterized
by
a
layer crust, with a relatively high
layer.
The
upper
crustal
layer,
192
approximately
15
6.1
km/s,
and
3.6
km thick with P and S velocities of
respectively,
velocity
lower
crust
and
km/s.
The
4.1
overlies
a
high
with P and S velocities of 7.0
average
crustal
thickness
is
approximately 40 km.
b.
The crust of
the
Grenville
Province
is
vertically
homogeneous with nearly constant P and S velocities of
6.6 and 3.7 km/s, respectively, and an average crustal
thickness of 37 km.
c.
Pn velociities are 8.0 km/s for the Grenville and
8.1
km/s for the Appalachians.
d.
A time term analysis of the Pn branch defines a region
of thick
across
or
low-velocity
eastern
New
crust
York,
trending
western
northeast
Massachusetts,
southeast Vermont, central New Hampshire, and
Maine.
observed
Crustal
in
thinning,
northeastern
or
New
central
higher velocities are
York
and
northwest
Vermont and also along much of the coastline.
2.,
Analysis of Rayleigh wave phase and
group
in
models
the
region
yields
structural
velocities
that
are
relatively consistent with those described above.
a.
For a path along the strike of the Appalachians, a
km
40
thick crust with upper layer S velocities of about
3.6 km/s overlies a
relatively
high
velocity
lower
layer with S velocities around 3.9 - 4.1 km/s.
b.
A second path, mainly in the Appalachians (path A2) is
characterized by a 40 to 45 km thick crust.
The upper
193
crustal
layer
velocities
(approximately
20
km
thick)
has
S
of about 3.5-3.6 km/s and overlies a lower
crust of relatively high velocity (3.9-4.0 km/s).
contrast
In
to the other Appalachian path (path Al), the
lower crust is characterized by
more
of
a
positive
velocity gradient with depth.
c.
The Grenville path (path G) appears to have a
thinner
35 km crust with a slightly lower velocity lower-crust
relative to the Appalachian paths.
time
travel
In contrast to the
models which show a homogeneous crust,
a
two layer crust is necessary to fit the observed phase
and group velocities.
wave
However, part
of
the
surface
path crosses the Taconic thrust sheet in eastern
New York where a two layer crust in not unexpected.
d.
Phase
and
group
velocities
calculated
from
the
frequency-wavenumber power spectra in southeastern New
England
appear
to
be
relatively high which implies
that the high velocity lower crustal layer is
probably
well-developed.
Analysis of teleseismic
3.
structures
and is
which
useful
residuals
P-wave
delineates
correlate well with surface geology
for
studying
lateral
variations
in
structure.
a.
Structures down to at least 200 km can
be
correlated
with surficial geologic and tectonic features.
b.
The
Grenville
upper
mantle
is
characterized
by
velocities that are approximately 2% higher than those
194
beneath
the
Appalachians.
These
velocities
are
dips
the
maximum beneath the Adirondack dome.
c.
A
relatively
northwest
low
velocity
beneath
the
anomaly
central
mobile
to
belt
of the
Appalachians and shows a spatial correlation with
the
Bronson Hill - Boundary Mountains Anticlinorium in New
Hampshire and Maine.
d.
Crustal features are relatively consistent with
derived
from
the
time
term
analysis,
those
and
Appalachian crust appears to be slightly thicker
the
than
the Grenville.
e.
Rapid crustal thinning or high velocities in the crust
occur
in
northwestern
Vermont
and
southeastern
Connecticut.
f.
Thick crust is observed over the
Taconic
thrusts
in
east-central New York and western Massachusetts.
g.
There is some evidence that the crust becomes
thinner
along the coastline.
6.2
CONTRASTS BETWEEN GRENVILLE AND
APPALACHIAN
PROVINCES
IN THE NEUS
One of the most significant results of this study is
pronounced
difference
in
crustal
structure
between
the
the
Precambrian Grenville Province and the Paleozoic Appalachian
Province.
The observed
differences
in
crustal
structure
195
between
the
variations
two
orogenic belts are probably the result in
of
temperature,
petrology,
chemistry,
and tectonic evolution.
water
content,
These factors will be
examined in this section.
6.2.1
Recent
COMPOSITIONAL DIFFERENCES
summaries
of
geophysical,
geological,
and
geochemical information suggest that beneath the sedimentary
layer,
the
upper
crust
is composed mainly of schists and
gneisses of the amphibolite facies which grade downward into
migmatites and finally basic and intermediate granulites
the
lower
crust
(Smithson,
1977).
velocities increase rapidly from
Because
amphibolite
to
in
seismic
granulite
facies rocks, the depth of the Conrad discontinuity may mark
the
location of this change in metamorphic grade (Fountain,
1976).
Numerous
crustal
layers
characterized
by
low
velocities, high and low velocity gradients, etc., have been
observed
and/or
techniques (cf.
reviewed
postulated
Mueller,
here.
using
1977; Giese,
crust
in
a
1976)
sounding
and will not
be
a
highly
conductive
the Adirondack Mountains in New York State
(Connerney et al., 1979),
underlies
seismic
Electrical measurements in the northeastern
United States suggest the presence of
lower
deep
while
a
resistive
lower
crust
slightly conductive 15 km thick upper crust in
New England (Kasameyer, 1974).
The slightly
conductive
15
196
km thick upper layer in New England correlates well with the
15 km thick, upper layer observed in this study and probably
corresponds
to metamorphosed eugeoclinal rocks of the major
synclinoria.
This implies that the observed differences
in
velocity and conductivity of the lower crust between the two
belts
may
be
the result of a hydrated lower crust beneath
the Grenville Province.
crust
may
be
Although the
chemically
rocks
similar,
of
the
lower
a hornblende-granulite
petrology beneath the Grenville would yield lower velocities
than
a
pyroxene-granulite
(Christensen and Fountain,
beneath
the
Appalachians
1975).
The existence of a low velocity lower crust
Grenville
beneath
the
Province is also supported by the study of the Sp
phase across eastern Canada by Jordan and Frazer (1975), who
found evidence for a lower crustal layer with
Poisson's
ratio
of
0.33.
identify
a
very
high
Because we only acquired travel
times of first arrivals, it
positively
a
was
low
not
possible
velocity zone.
for
us
We found shear
velocity models with low velocity crustal layers that
fit
the
observed surface wave dispersion curves.
these models were
inadequate
and
eliminated
the
model
because
errors
the
Using
velocity
regional
derived
from
could
However,
resolution
the
P
and
S
which
wave
travel times, the
Poisson's ratio of the lower crust beneath the Grenville
0.27
was
too large to positively
identify a low velocity layer.
models
to
is
is slightly higher than the value of 0.24 found
beneath the Appalachians.
197
The values of Poisson's ratio and shear velocity for
and Appalachian Provinces are shown on Figure 6.2
Grenville
(modified from Jordan and Frazer, 1975) which is a
Poisson's
ratio
versus
shear
velocity
number of rocks that may exist in the
that
the
at
plot
of
10 kbar for a
lower
crust.
Rocks
may be classified as amphibole granulites (Christensen
and Fountain, 1975) and
granulites;
Manghani
graph (note that these
temperature).
From
pyroxene
et
al.,
granulites
are
6.2,
it
granulite
beneath
the
not
corrected
for
can be seen that the
observed lower crustal velocities may
amphibole
gabbroic
1974) are also shown on the
velocities
Figure
(or
be
explained
by
an
Grenville Province and a
pyroxene granulite beneath the Appalachians.
Interestingly,
the Grenville point on Figure 6.2 plots in the
vicinity
of
gneiss
Province
is
and
anorthosite.
characterized by a number
bodies.
Dewey
and
The
of
Burke
large
(1973)
Province is a deeply eroded zone
similar to a Tibetan plateau.
lower
crust
Grenville
anorthosite
suggest
of
intrusive
the
basement
Grenville
reactivation
Partial melting of a dioritic
during the Grenville Orogeny may have resulted
in potassic granitic melts
which
rose
to
higher
crustal
levels leaving an anorthositic refractory residue.
The above
mineral
interpretation
phases
beneath
of
the
hydrous
versus
Grenville
and
Appalachian
observed
resistivity
Provinces is also consistent with the
models.
anhydrous
However, the cause for the observed differences in
water content is unknown.
198
Temperature
observed
in
pressures
may
the lower crust.
representative
geologic
on
differences
of
affect
the
velocities
However, at temperatures and
the
lower
crust
in
belts (Blackwell, 1976), the effect of temperature
seismic
velocities
(Christensen,
1979).
is
small
relative
Christensen
(1979)
to
pressure
concluded
critical thermal gradients resulting in low velocity
can
older
that
layers
be reached at temperatures and pressures representative
of the upper and middle crust
in
shield
areas.
This
is
particularly apparent for coarse grained rocks with euhedral
crystals
such as granites, amphib olites, anorthosites, and
granulites which have grain boundaries that open
temperatures.
However,
at
greater
at
pressures,
boundary cracks remain closed even at elevated
higher
the grain
temperatures
and it is more difficult to reach critical thermal gradients
in the
lower
crust.
As
will
be
discussed in the next
section, temperature differences may also
the
upper
mantle
and
be
important
in
may account for the observed P-wave
delays.
6.2.2
CONTRASTS IN TECTONIC EVOLUTION
The rocks of the Grenville and Appalachian Provinces
show
contrasts
in their
chemistry and petrology that are
caused by differences in their tectonic evolution.
section,
causes' for
the
may
observed
In
this
crust and upper mantle
199
differences between the two provinces will be discussed
and
related to their orogenic history.
The northern Appalachians
crustal
layer
relative
have
to
the
a
high
Grenville
appears to have a vertically homogeneous
this
observation
velocity
lower
Province which
crust.
Combining
with resistivity models suggests that the
differences may be due to variations
in
caused
However, compositional
by
hydrous
mineral phases.
changes may also be important.
6.2,
As
was
rock
conductivity
noted
from
Figure
rocks of the lower crust in the Grenville Province may
be very similar to those found on the surface.
models
suggest
that
some
Plutonic series in central
reaction
of
members
New
of
Geochemical
the White Mountain
Hampshire
were
formed
by
fractionated mantle derived alkali basalt with
metamorphosed tholeiitic (oceanic) basalt at the base of the
crust
(Loiselle,
representative
1978).
At
temperatures
and
pressures
of the lower crust, a tholeiitic basalt will
alter to a garnet or pyroxene granulite (Green and Ringwood,
1972).
From Figure 6.1, the upper 15 km layer
Appalachians
probably
subjected to
a
shortening
high
during
the
in
the
northern
corresponds to rocks which have been
degree
of
compression
and
crustal
Taconic and Acadian orogenies.
rocks of the Appalachian belt probably were associated
a
cycle
of
oceanic
opening and closure.
The
with
It is therefore
possible that the chemistry of the lower crust was
strongly
affected by tectonic interaction of these sediments with the
200
underlying
basement
during
orogeny.
Thus, involvement of
ocean floor within the Appalachians would
higher
velocities
account
for
the
found in the lower crust relative to the
predominantly ensialic crust of the Grenville Province.
The homogeneous character of the crust in
the
Grenville
that
the
Province
crust
thickened,
is
became
substantial
vertically
Grenville orogeny (Dewey and Burke,
the
thickening,
the
of
consistent with the hypothesis
underwent
and
this portion
crust
was
reactivation,
uniform
1973).
during
the
Subsequent
to
eroded to relatively deep
levels, as evidenced by the surface
exposure
of
granulite
terrains (Putman and Sullivan, 1979).
Based
data
on
residuals,
it
P-wave
teleseismic
and
residuals
Pn
appears that the transition zone between the
Grenville and Appalachian Province in the NEUS occurs in the
vicinity of the Precambrian
belt
(Figure
6.1).
uplifts
and
the
This north-northeast trending belt may
mark the suture zone between the
two
orogenic
many locations along this postulated suture,
northwest
Vermont,
there
are
geological
features such as high crustal velocities, a
a
high,
serpentinite
belt,
Precambrian
Taconic thrusts which show many similarities
in
zone
serpentinite
northern Italy (Giese and Prodehl,
belts.
At
particularly in
and geophysical
linear
gravity
uplifts, and the
to
the
Ivera
1976; Fountain,
1976).
There is also the possibility of a second suture
in
the
eastern section of the study area.
located
This feature is
201
marked by the Clinton-Newbury - Bloody Bluff fault zone
(CN
-
and
BB
F.Z.)
in
eastern Massachusetts (see Figure 6.1,
Chapter 2) and other structures such as the Norumbega
zone
in
eastern
Maine
(Loiselle
eastern Massachusetts, the CN that
are
BB
Ayuso,
F.Z.
1979).
separates
In
rocks
probably correlative with Avalon rocks from those
of the central mobile
zone
and
fault
is
belt.
The
northwest-dipping
fault
also well-marked by such features as the offset of
metamorphic isograds, a strong
mylonite
zone
that
gravity anomaly is
is
also
up
magnetic
signature,
to 1.5 km thick.
associated
with
and
a
A pronounced
the
fault
zone
(Taylor et al., 1980), and the Bouguer gravity is relatively
high
over the eastern basement (Figure 2.2a).
Loiselle and
Ayuso (1980), present evidence suggesting that
post-Acadian
strike
slip
juxtaposed
faulting
plutonic
along
rocks
of
the
Norumbega
differing
fault
has
geochemistry,
texture, and mode of emplacement.
The deep crustal structure of the eastern
to differ from that of the central belt.
Pn
block
appears
Refraction models,
and teleseismic P-wave residuals indicate that the crust
of the eastern block is, probably thinner than
central
belt
and
may
be
missing
a
that
of
the
high velocity lower
crustal layer.
Although there are a few localities along
F.Z.
highly
the
CN
-
BB
where mafics and ultramafics are exposed that resemble
altered
communication,
ophiolites
1980),
(P.
Osberg,
personal
the paucity of ophiolites along this
202
zone is problematical.
of
intense
erosion
As discussed by Dewey (1977),
suturing undergo the most uplift and subsequent
and
may
ophiolite.
In
exhibit
general,
the
most
the
a
deeply
eroded
cryptic
suture
high
structural
zone
ophiolites.
For
example,
few
levels.
little
evidence
ophioite
bodies
observed along the eastern portion of the
the
of
may be observed as a
narrow high-strain or thrust zone with
any
suture
ophiolites are thrust in the
late stages of orogeny and occupy
Thus,
zones
Indus
of
are
suture
of
Himalayas where the collision appears to have been more
intense (LeFort, 1975).
have
become
a
Additionally, the CN - BB F.Z.
transform
fault
(Skehan, 1968; Ballard and
in
Uchupi,
late
1975)
Paleozoic
which
may
may
time
have
obliterated any evidence of ophiolites.
Alternatively, the suture may be located further west and
the CN - BB F.Z. may have had a history similar to the
Main
Central Thrust or the Boundary Fault of the Himalayas.
This
hypothesis
which
is
supported
suggest
north-central
that
recent
by
Lower
Devonian
volcanics
from
Maine have paleopoles closer to Avalonia than
to North America (Brown, 1980).
the suture
paleomagnetic results
remains
cryptic
and
Even in this case, however,
numerous
other
tectonic
problems are encountered.
Irrelevant of its mode of emplacement, the eastern
has
undergone
than that of the
crustal
a
significantly
central
structure
belt,
across
the
block
different orogenic history
and
CN
differences
in
-
are
BB
F.Z.
deep
not
203
unexpected.
Three
dimensional
illustrates
that
inversion
structures
of
down
travel
to
greater can be correlated with surface
the
important
implication
effects that reach
stable
for
will
extended
billion years.
of the crust
that
into
time
perhaps
data
200 km and
geology.
This
has
major orogenic belts have
the
lithosphere
which
are
periods of time, perhaps as long as 1
The lateral variations in seismic properties
and
upper
mantle
beneath
the
northeastern
United States are very small relative to those observed over
similar distances in active tectonic regions such as central
Asia
or
the western United States.
that absolute P-residuals
square
root
indicates
are
a
Poupinet (1979) showed
linear
function
of
the
of age inside stable continental plates.
that
the
crust
and
upper
mantle
This
become
increasingly more uniform with age during evolution toward a
state of equilibrium.
In addition to the regional differences existing
the
two
structural
between
provinces in the northeastern U.S., we
see smaller scale features
that
are
related
to
specific
segments of each orogenic belt and to the intervening suture
zone.
As
discussed
previously,
the
Taconite
belt, the
eastward-lying Precambrian uplifts (The Berkshire
Highlands
and
Green
Mountains),
and
serpentinite
belt
are
Lower
Ordovician structures that may be related to the closure
an
of
inner-arc basin and to a continent-island arc collision.
This region is not only
a
site
of
large
scale
geologic
204
deformation
but
it
is
also
characterized by geophysical
anomalies such as apparent crustal
velocities,
and
(Figure 2.2a).
related
large
It
is
thinning,
high
crustal
positive
Bouguer gravity anomalies
possible
that
these
effects
are
to deep-seated thrusts emplaced near the end of the
Taconic orogeny which carried oceanic crust and upper mantle
material to higher levels within the crust.
would
have
high
velocities
'This
material
and densities relative to the
surrounding eugeoclinal
lithologies
model
the observed geophysical anomalies.
consistent
with
and
would
provide
There are at least two objections to this model.
is
that
higher
The
a
first
crustal velocities are obseved just to the
west of the Taconic thrust belt at
stations
PNY
and
WNY.
Secondly, we see that geophysical anomalies are not observed
along
the
entire
Taconide
belt.
A
similar
pattern is
observed on the map showing station time terms (Figure 3.9).
This gap in the zone of high crustal thickness and
gradients,
east
of
and
parallel
to
the
thrust belt in
southwestern Vermont and western Massachusetts,
in
the
vicinity
of
the
Taconic
klippen
velocity
is
located
and a regional
northeast trending gravity low extends from southeastern New
York into this zone
velocities
and/or
(Figure
thick
2.2a).
This
region
of
low
crust may be related to the thick
pile of thrusts of the Taconic klippen.
As pointed out by Fletcher et al.
residuals
beneath
ultramafic bodies
PNY
whose
may
be
presence
(1978),
the
anomalous
related to buried mafic or
is
indicated
by
local
205
gravity highs (anomaly 22 of Simmons, 1964).
readily
apparent
that
all of the stations in northern New
York record very early arrivals from
implies
the
However, it is
existence
of
the
regional,
northwest.
deep-seated
extending to the northwest beneath the Adirondack
is
supported
5.8).
by
the
three
This
effects
dome
and
dimensional inversion (Figure
Interestingly, the large negative residuals from
northwest
the
are not observed at stations farther south, which
suggests that the
velocities
is
Adirondacks.
zone
of
controlled
relatively
by
a
high
structure
It has been postulated
that
upper
mantle
unique
to the
the
Adirondacks
and associated Grenville basement represent deeper levels of
an
ancient
"Tibetan
Plateau"
thickening and shortening
zone
characterized
behind
a
continental
crustal
collision
(Dewey and Burke, 1973; Toksoz and Bird, 1977).
not clear when the Adirondack dome
cause
of
relatively
high
mantle beneath the region
Grenville
belt
does
was
elevated,
velocities
remains
represent
found
an
analog
then
possibly
another
Adirondacks
depth
(Putman
Isachsen, 1980).
surface
geologic
in the upper
of
If
a
average
the
Tibetan
36
Rocks presently exposed in
appear
to
have
been
temperature and pressure conditions found
km
the
km,
15 km of crust has been eroded away
since the Late Precambrian.
southern
It is
and
problematical.
Plateau, and crustal thicknesses presently
20
by
and
Sullivan,
This implies that
features
of
the
the
subjected
the
to
at
approximately
1979;
McLelland and
presently
Adirondacks
exposed
represent
206
lithologies deformed, metamorphosed, and intruded
at
great
crustal depths.
Another prominent feature in the
apparent
crustal
thickening
and southern Maine.
of
highest
Devonian
in
is
England
highland
orogeny
the
beneath central New Hampshire
New
compensated
Acadian
model
Topographically, these are the
elevations
isostatically
crustal
had
and are therefore
areas.
a
regions
severe
The
Lower
impact
on
the
structure as evidenced by high grade metamorphism, intrusion
of granitic plutons,
and
large
scale
westward
folding of many of these plutons (Naylor, 1968).
of
evidence
belt.
York
suggest
the
recumbent
Many lines
uplift of a significant mountain
Early Devonian miogeoclinal sediments in eastern
are
overlain
by
a
sequence of the Catskill
derived
from
the
(Rodgers,
1970).
northern
Maine is
thick
clastic
-
Delta
thick
Devonian
clastic
wedge
uplifted landmass in central New England
The crustal thinning towards
central
and
correlated with the drop-off in the grade
of metamorphism (Thompson, 1968).
continental
a
Middle
New
collision
of
the
This
implies
Acadian
that
orogeny
the
was
particularly severe in southeastern and central New England,
and we would expect to see greater
crustal
thicknesses
in
these regions.
In eastern Massachusetts we again see an apparent crustal
thinning over much of
earlier
section.
the
eastern
belt
described
in
an
These contours conform very well with the
position of the middle Paleozoic thrust belt and the
abrupt
207
falloff
to
the
southeast
in
metamorphic
isograds
from
sillimanite to chlorite (Thompson, 1968).
The low velocity anomalies in the upper mantle (35 km)
beneath
Massachusetts, New Hampshire, and southcentral
Maine strike northeast parallel to the structural
the
Appalachian orogenic belt.
km.
grain
of
There is some evidence that
this feature dips to the northwest to
200
200
depths
greater
than
Because of the geometry of the initial model, the
vertical extent of this structure is only constrained to lie
somewhere between 200 and 350 km.
It is interesting to note
the spatial correlation of this low velocity trend with
Bronson
-
Hill
Boundary
Mountains
Anticlinorium.
discussed previously, these structures probably
sites
of
a
complex
active in the Early
orogeny.
If
it
east-southeast of
direction,
we
series
of
Devonian
is
the
true
As
the
island arc sequences last
time
that
Bronson
occupy
the
prior
to
subduction
Hill
in
a
the
Acadian
last occurred
west-northwest
may expect to observe some anomalous feature
at these depths.
Assuming that a subducted oceanic slab can produce such a
long-term anomaly, the
lower
than
the
existence
of
velocities
are
surrounding mantle material is surprising,
yet not necessarily inconsistent with its
evolution.
that
possible
thermal
Thermal models of downgoing oceanic lithosphere
(Toksoz et al., 1973) illustrate that in the early stages of
subduction, the slab is
surroundings
to
a
cold
and
depth
of
dense
at
relative
least
600
to
its
km.
At
208
approximately 100 m.y. from the cessation of subduction, the
slab reaches thermal equilibrium.
Thermal
models
suggest
that beyond about 100 m.y. the subducted oceanic lithosphere
starts
al.,
to
heat
1971).
induced
up relative to the surroundings (Toksoz et
The
anomaly
is
not
necessarily
and other explanations related to the compositional
changes of the descending lithosphere
If
we
thermally
assume
the
velocity
may
be
anomalies
constructed.
are
produced
by
temperature changes, and take the temperature coefficient of
velocity for dunite, a 1% velocity decrease corresponds to a
temperature increase of about 100 - 200
observations
are
consistent
with
degrees
C.
These
preliminary unpublished
heat flow measurements in central New England corrected
radioactivity
which
show
regions
for
of highest heat flow in
central and southeastern New Hampshire relative to
northern
New Hampshire and southeastern Massachusetts (Jaupart, pers.
comm.).
Geomagnetic
data
from
the
northeastern
anomaly
States suggests a 200 degree C temperature
United
in
the
lower crust beneath central New Hampshire and southern Maine
(Bailey et al., 1978).
Alternatively, the
oceanic
lithosphere
in
lower
filling the vacated Benioff zone.
This
totally
subducted
consistent
dipping
with
westward
California
resulting
observations
beneath
(Cockerham
the
may
have
velocity
been
material
interpretation
is
of relatively low velocities
Great
Valley
and Ellsworth, 1979).
in
central
In this case,
the oceanic slab would not have had sufficient time to
heat
209
up
(5
m.y.
at
most) and if still present, would probably
result in higher rather than lower velocities.
It is also interesting to note
teleseismic
PP
that
similar
trends
in
residuals are observed beneath Newfoundland
(Stewart, 1978).
Newfoundland is a northward
the
orogenic
Appalachian
that the crust and upper
belt
mantle
extension
of
and it is not inconsistent
structures
appear
to
be
similar to our observations in New England.
6.3
CONTRASTS BETWEEN NORTHERN AND SOUTHERN APPALACHIANS
Recent
southern
COCORP
seismic
Appalachians
reflection
indicates
profiling
that
the
in
the
platform rocks
overlying the Grenville basement can be traced
beneath
the
Blue Ridge and continue at least 150 km to the east (Cook et
al.,
1979).
show
many
history,
Because the northern and southern Appalachians
contrasts
it
may
in
structural
style
and
tectonic
not be possible to extrapolate the COCORP
results to the northern
Appalachians
(north
of
about
41
Appalachians
is
degrees latitude).
The tectonic history
reviewed
of
the
southern
by Hatcher (1978) and Cook et al. (1979) and shown
in Figure 6.3 (from Cook et al., 1979).
As will be seen
in
the next section, the tectonic evolution of the northern and
southern Appalachians is very similar up through the Acadian
orogeny.
However,
the
southern
Appalachians
have
an
210
additional orogenic episode (the Alleghenian orogeny; Figure
6.3f) which resulted in the westward thrusting of
Ridge,
Inner
Piedmont,
and
Carolina
the
Slate Belt.
Blue
In the
northern Appalachians, the Alleghenian orogeny was only felt
in southeastern New England
further
north.
and
by
strike
slip
faulting
It has been suggested that the Alleghenian
deformational belt truncates the Appalachian-Caledonian belt
in southern Connecticut and Rhode Island and is
with
the
1974).
correlative
Hercynian belt in central Europe (Dewey and Kidd,
The
Paleozoic
extensive
crustal
shortening
of
Alleghenian
marginal
fold
confined mainly to the
southern
Appalachians.
relatively
and
the
thrust
late
belt is
Slices
of
unmetamorphosed carbonates are found to the east
of the Blue Ridge in the Brevard zone
and
Mountain
The ultramafics found
window (Cook et al.,
1979).
the
Grandfather
in the southern Appalachians are diffuse and are irregularly
distributed throughout the Piedmont
involvment
in
the
numerous
zone
thrusts
north-northeast
the
northern
trending
their
of the allochthonous
crystalline belt (Misra and Keller, 1978).
ultramafics of
indicating
Appalachians
In contrast, the
form
a
narrow
belt and lower Paleozoic platform
rocks are not found east of the Precambrian outliers in
the
northern Appalachians (Figure 6.1).
The COCORP
results
indicate
that
the
suture
between
proto-Africa and North America is located at least 150 km to
the
east
of the Blue Ridge.
However, by combining gravity
and geologic information, Diment
et
al.
(1972)
suggested
211
that the suture (which would actually separate North America
from
Avalonia)
cuts across southern New England and trends
north-northeast up the coast of New England (boundary EF
Figure
6.4).
Figure 6.4) is
In the southern Appalachians, boundary EF (in
actually
on
a
thin-skinned
'allochthonous
of the westward-directed thrusts may
Reconstruction
belt.
in
allign the two segments of boundary EF.
Seismic refraction
crustal
structure
Appalachians.
in
west
data
also
between
suggests
the
differences
northern
and
The structure to the west of the
in
southern
Ridge
Blue
the southern Appalachians (Table 3.5) is similar to that
of
the
Appalachians.
Precambrian
Both
regions
lower crustal layer and
Grenville basement.
outliers,
the
relatively
Appalachians.
missing
composed
of
northern
a high velocity
the
homogeneous
However, to the east of the Precambrian
southern
homogeneous,
to
contrast
are
are
the
in
outliers
Appalachians
low
velocity
crust
two-layer
the
These
continue
similarities
in
crust
to
show a
in
of
the
crustal
marked
northern
structure
across the Blue Ridge are consistent with the interpretation
that
crystalline
the
rocks
of
the
Ridge,.
Blue
Inner
Piedmont, and the Carolina slate belt are allochthonous
overlie
structure
.Grenville
across
Appalachians
basement.
the
suggest
The
serpentinites
contrasts
in
the
crustal
northern
that they are located in the vicinity
of the suture separating the Grenville from the
Province.
in
and
Appalachian
212
Observation
residuals
zone
and
in
of
3-D
the
southeastern
relatively
parallel
to
inversion
the
low
trend
of
the
vertically or to the southeast
P-wave
United States delineates a
velocities
of
teleseismic
(approximately
Appalachians
under
the
1-2%)
and dipping
Piedmont
(Volz,
1979).
6.4
TECTONIC EVOLUTION OF THE NORTHERN APPALACHIANS
A possible scenario for the
Appalachians
will
evolution
of
the
be outlined in this section.
northern
Figure 6.4
shows cross-sections (taken approximately across line AA' in
Figure 6.1) illustrating the
Table
possible
tectonic
evolution.
6.1 lists major orogenic episodes in the Appalachians
and the maximum manifestation in the area of influence (from
Rodgers, 1970).
It must
over-simplified
first
be
order
defined, conflicting geology.
scale
features
are
emphasized
model,
that
is
an
based on often poorly
However, many
correlative
this
with
of
the
observed
large
velocity
anomalies described in previous section.
The oldest rocks in the study area
Adirondacks
and
the
Precambrian
are
outliers
exposed
of
in
the
the
Green
Mountains, Berkshires, and Hudson Highlands. On the basis of
petrological and structural arguments Dewey and Burke (1973)
suggested that
levels
of
part
the
of
Adirondacks
represent
deep
erosional
an ancient Tibetan-type plateau formed
213
behind a continental collision
("
orogeny
1,100 m.y.).
may be due
to
affecting
zone
during
the
Grenville
Doming in the southern Adirondacks
intersection
of
regional
fold
structures
Precambrian rocks (McLelland and Isachsen, 1980).
Since the late Precambrian, the Adirondacks have
remained
a
regional
high,
as
suggested
apparently
by the onlap of
Paleozoic sediments (Rodgers, 1970).
It is currently thought that a continental rifting
initiated
approximately
formation of the
The
1976).
820
Iapetus
m.y.
Ocean
leading
(proto-Atlantic)
to
the
(Rankin,
and Cambrian geology of the
Precambrian
late
ago
stage
western belt is characterized by
the
establishment
of
an
Atlantic-type, stable continental margin (Figure 6.5a).
Late Precambrian lithologies on
indicate
a
the
eastern
belt
also
rifting stage with the development of an active
continental
margin
paleomagnetic,
and
(Kennedy,
1976).
paleontological
Geochemical,
evidence suggests that
the western and eastern belts were located on opposite sides
of the Iapetus Ocean (Strong et
Cocks,
1976; Kent and Opdyke,
Early
or
characterized
(Figure 6.5b).
Mid-Ordovician
by
al.,
1974;
McKerrow
and
1978).
through
Permian
times
are
the episodic closing of the Iapetus Ocean
The
BHA
was
a
site
of
major
volcanic
activity in this time period as evidenced by the presence of
thick
to the
volcanic sequences.
northwest)
volcanics
and
the
The curvature of the BHA (convex
asymmetrical
distribution
of
(Osberg, 1978) in the central mobile belt suggest
214
an eastward dipping
However,
in
Benioff
zone
existed
at
this
time.
a later section we will present evidence for a
reversal of the polarity of subduction following the Taconic
orogeny.
Major deformation occurring
Ordovician
time
marked
the
phase
Middle
deep
seated
west
of
the
BHA
(Figure
thrusts involved the Grenville basement
emplacement
1975).
(Ratcliffe,
the
Precambrian
were
emplaced
at
altered,
Cambrian
probably
represent
highly
Ordovician
(Chidester,
1968)
Iapetus
of
massifs
The linear belt of ultramafics found to
the east of the massifs
the
time,
to
obducted oceanic crust
and
Lower
of
the
Ocean or of a marginal sea behind the volcanic arcs
of the central mobile belt.
metamorphic
long-term
events
heating,
reactivation
subducted
is
The sequence
indicative
increased
resulting
lithosphere.
of
of
effects
ductility
from
induced
This
tectonic
and
is
1977) as well as on
active
continental
margins
oceanic
lithosphere
and
subductive
collisions (Burchfiel and Davis,
zones
(Toksoz
that
Bird,
involving
arc-continent
metamorphism
the Taconic orogeny in New England probably
was an episode of arc-continent collision.
segments
and
in
1975).
Evidence based on styles of deformation and
indicates
above
observed
convergence
by
basement
convection
effect
and
caused
continent-continent
arc
Late
The Taconic klippe were thrust at this time and late
resulting in the
only
and
climax of the Taconic orogeny
which affected rocks within and
6.5c).
in
and
inner-arc
Numerous
island
basins now located within the
215
central
mobile
deformation.
belt
were
Although
a
probably
involved
in
the
major unconformity was formed in
the CVS at this time, the lack of any major unconformity and
Ordovician deformation in the MS (Moench and Zartman,
indicates
that
oceanic
terrain
continued
continental crust of the eastern belt
However,
the
from
1976)
to
separate
North
America.
amount
and
type of volcanism in the central
mobile belt following
the
Taconic
closure
of
the
Iapetus
orogeny
indicate
was nearly complete.
that
It may have
been the close approach of the eastern belt and possibly the
attempted subduction of an oceanic ridge
island
arcs
which
to converge onto North America.
(1978) suggest that the middle Ordovician was
caused
the
Delong et al.
a
period
of
a
period
of
ridge subduction in central Newfoundland.
The Silurian to Early
relative
quiescence
(Boucot, 1968).
of
increased
and
Devonian
erosion
time
was
of the Taconic highlands
In the Early Devonian era there is evidence
tectonic
activity
as
indicated
by
the
deposition of vast thicknesses of turbidite sequences across
the major synclinoria (Littleton Formation of New Hampshire)
and
renewed volcanism along arcs in the central mobile belt
(Figure 6.5d).
the
This episode of major deformation is
called
Acadian orogeny and appears to have spanned a period of
approximately 30 m.y. (Naylor, 1971) which is similar to the
duration of the main collisional
(Toksoz and Bird,
stages
of
the
Himalayas
1977).
The Acadian orogeny (Figure
6.5e)
is
typified
by
the
216
following
overlapping
sequence
of
events:
metamorphism in southeastern New England,
granitic
plutons,
of many of the
development
3)
of
2)
large scale westward
plutons,
and
large
4)
belts.
intrusion
of
recumbent folding
brittle
thrust
1) high grade
deformation
These
and
styles
of
documented
in
deformation show many parallels
with
other
zones
(Dewey,
1977).
period of metamorphism, intrusion, and
ductile
deformation
continental
convergence
those
The
are deep crustal processes characteristic of a major thermal
event
associated
below resulting
collision
and
with
from
initial
asthenospheric
1975)
Plutonic
are
of the crust from
convection
prior
to
post-collisional radioactive heat generation
(Toksoz and Bird, 1977).
Hampshire
heating
The binary
Series
indicative
of
granites
of
the
New
(dated around 360 m.y.; Naylor,
extensive
crustal
heating
and
partial fusion of crustal sediments and are similar to those
found throughout much of the Himalayas (Bird, 1976).
Three major events
recorded
in
New
following
England.
the
Acadian
Alleghenian
Pennsylvanian to Permian times strongly
southeastern
New
England.
deformation
affected
Iapetus
collision
of
America.
suggested
(Dewey
and
with
Kidd,
rocks
are
in
in
The Allegheny orogeny probably
represents the final closure of the
Africa
orogeny
North
1974)
that
Ocean
the
It
by
the
has been
Alleghenian
deformational belt truncates the Appalachian-Caledonian belt
in
southern Connecticut and Rhode Island and is correlative
with the Hercynian belt
in
central
Europe.
Strike
slip
217
faulting
in
the
northern
Appalachians
may
have
been
important in the late Paleozoic (Rodgers, 1970; Arthand
and
Matte, 1977; Ballard and Uchupi, 1975) although the sense of
motion is not well defined.
In Late Triassic time large
were
developed
rift-valley
graben
along the trend of the Appalachians.
grabens were filled with thick accumulations
red
beds.
The
rifting
was
eruption of basaltic lavas and
diabase
systems
dikes,
sills
and
accompanied
the
of
stocks.
non-marine
by
intrusion
This
These
the fissure
of
numerous
period
of time
represents the initial opening of the modern Atlantic Ocean.
The most recent major tectonic activity in New
England
was
the emplacement of the White Mountain Magma Series, intruded
over
a
100
(Chapman,
m.y. interval from Jurassic to Cretaceous time
1976).
The northeastern U.S. is presently an
adjacent
to
a
intraplate
stable continental margin, characterized by
relatively low-level, diffuse seismicity.
at
The
this
time
region
Province
compressive
controlled
It is
not
clear
what structures control seismicity patterns.
within
is
region
and
possibly
characterized
stress
and
east
of
the
Grenville
by a northeast trending maximum
some
earthquakes
appear
to
be
by reactivated Paleozoic faults (Sbar and Sykes,
1977).
In New England, the stress pattern
complex,
with
distribution
local
and
appears
to
be
more
stress concentrations controlling the
mcechanism
of
earthquakes
(Pulli
and
218
Graham, 1979).
Table 6.1
219
Orogenic Movements in the Appalachian Region
Orogenic episode and
approximate date
Appalachian movements
Palisades
Late Triassic
(Carnian-Norian)
190-200 m.y.
Known area of influence
Maximum manifestation
Belt along central axis of
already completed mountain
chain
Fault troughs, broad warping,
basaltic lava, dike swarm
West side of central and
southern Appalachians,
southeast side of northern
Appalachians, perhaps also
in Carolina Piedmont
Strong folding, also middle-grade
metamorphism and granite
intrusion at least in southern
New England
Early Ouachita
Mid-Mississippian
through early
Pennsylvanian (Visean
to early Westphalian)
Only in southernmost
Appalachians'in
central Alabama
Clastic wedge, also possibly broad
east-west structures that influenced
later deformation
Acadian
Devonian, mainly
Middle but episodic
into Mississippian
(Emsian-Eifelian)
360-400 m.y.
Whole of northern
Appalachians, except along
northwest edge; as far
southwest as Pennsylvania
Medium- to high-grade metamorphism.
granite intrusion
Salinic
Late Silurian
(Ludlow)
Local on northwest side of
northern Appalachians
Mild angular unconformity, minor
clastic wedge
General on northwest side of
northern Appalachians,
local elsewhere; an early
phase in Carolinas and
Virginia, perhaps general
in Piedmont province
Strong angular unconformity, gravity
slides (?), at least low-grade
metamorphism, granodioritic
and ultramafic intrusion
Local on northwest side of
northern Appalachians
Strong angular unconformity,
slaty cleavage, possibly some
intrusion
Southeastern Newfoundland,
Cape Breton Island,
southern New Brunswick;
probably also central and
southern Appalachians
(Florida?)
Probably some deformation, uplift
of sources of coarse arkosic
debris, gravity slides(?)
Southeastern Newfoundland,
Cape Breton Island, southern
New Brunswick; perhaps
eastern Massachusetts
Mostly low-grade metamorphism,
granitic intrusion
Alleghany
Pennsylvanian and/or
Permian (Westphalian
and later) 230 -260 m.y.
Taconic
Middle (and Late)
Ordovician (Caradoc,
locally probably older)
450-500 m.y.
Penobscot
Early Ordovician
or older (Arenig
or older)
Avalonian
Latest Precambrian
Late Precambrian
about 580 m.y.
Grenville (pre-Appalachian)
movements
- Late Precambrian
800-1100 m.y.
Eastern North America
including western part
of Appalachian region
High-grade metamorphism,
granitic and other intrusion
220
FIGURE CAPTIONS
Figure 6.1
Generalized geologic map of the northeastern
United States (King, 1969) and schematic
structural cross-section along profile AA'.
Key to abbreviations:
T - Taconic thrust
belt;
GM
-
Green
Mountains;
CVS
-
Connecticut Valley Synclinorium;
BHA
Bronson Hill Anticlinorium; MS - Merrimac
Synclinorium;
CN-BB
-
Clinton-Newbury
-
Bloody Bluff fault zone.
Figure 6.2
A plot of Poisson's ratio versus shear
velocity at 10 kbar for a number of rocks
that are possible constituents of the lower
crust.
Ranges of Poisson's ratio versus
shear velocity for amphibole granulites from
Christensen and Fountain (1975) and gabbroic
granulites from Manghnani et al.
(1974).
Symbol A corresponds to Poisson's ratio and
shear velocity for Appalachians and G for
Grenville using regional travel times in
this study. Figure modified from Jordan and
Frazer (1975).
Figure 6.3
Schematic illustration of plate tectonic
model for evolution of southern Appalachians
from Cook et al. (1979).
Figure 6.4
Some tectonic features of eastern North
America.
Line EF represents line across
which there are marked
differences
in
Bouguer gravity (Diment et al., 1972).
Figure 6.5
Schematic illustration
model
for
evolution
Appalachians.
of plate
of
New
tectonic
England
221
EXPLANATION
Thrust fault, barbs on upperblock
wuam"Normalfault,
STRATIFIED
hachureson downthrown
side
ROCKS
Cenozoic
glacialdeposits
Triassicred beds
Carboniferous
Silurion- Devonianeugeoclinal
rocks
Cambrian
- Ordovicianforeland rocks
- Ordovicion
Cambrian
deformedmiogeoclinal
rocks
Cambrian - Ordovician
eugeoclinal
rocks
Precambrian
rocksof the easternblock
uplifts, Grenvillebasement
Precambrian
Precambrian
Grenvillebasement
IGNEOUSROCKS
74
72
- *Mesozoic
70
68
WhiteMountainPlutonicSeries
Series
Plutonic
Devonian
NewHampshire
- Ordovicianserpentinites, ultramofics
Cambrian
.
GRENVILLE
A
Precambrian
anorthosites
APPALACHIANS
T
GM
CVS
BHA
MS
CN-BB, A
-'61
MOHO
-100
1% HIGHER VELOCITY
1% LOWER VELOCITY
100 km
-200
Figure 6.1
222
Vs (km/s)
Figure 6. 2
223
800-700 Ma.
700-600 Ma.
BO
600-500 Ma.
C.
500-400 Ma.
400- 350 Ma
C>.0.
E.
7'~2
PRESENT
VR
F.ANI
KMB
1 100 km.
100 km.
Figure 6.3
224
70*
800
600
40
4tt
X~
4.
00
Kiometersj
C 0 E3
1
2
El
3
13
4
5
MI'
6
Za1
1
1
is
1
Some tectonic features of eastern North America. Geologic features generalized
from King (1969). (1) Precambrian rocks. (2) Paleozoic metasediments, metavolcanics,
and plutonic rocks of core of the Appalachians. (3) Niogcosynclinal rocks. (4) Paleozoic
platform deposits. (5) Cretaceous and later deposits of the coastal plane and Mississippi
embayment. (6) On the land, post Paleozoic alkaline intrusive rocks; in the oceans,
sCamounts. (7) Areas of unusual concentrations of small alkaline Cretaceous and early
Tertiary intrusions. (8) Fault systems in the platform deposits. (9) Depth contours: in
ocean areas depth of water, in continental areas depth to Precambrian basement. (10)
Province boundaries as discussed in text and line M which is the trace of the magnetic high
that closely follows the continental margin except in the south where it changes form and
turns inland (from Taylor et al., 1968). This magnetic high is continuous except at the
intersection with the Kelvin seamount chain. (11) Cross-trending structural trends
discussed in text.
Figure 6. 4
225
EOCAMBRIAN - EARLY
EARLY - MIDDLE
ORDOVICIAN
MIDDLE ORDOVICIAN
-
114P
ORDOVICIAN
TACONIC OROGENY
AA
SILURIAN - EARLY DEVONIAN
MIDDLE DEVONIAN ACADIAN OROGENY
I~
~5
I-
,
-
-'41h
Figure 6.5
'
226
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Willmore, P.L. and A.M. Bancroft, The time term approach to
refraction seismology, Geophys. J., 3, 419-432, 1960.
Woollard, G.P., Crustal structure from gravity and seismic
measurements, J. Geophys. Res., 64, 1521-1544, 1959.
Wu, F.T. and R.P. Allen, dT/dD
measurements
Geophys. J.R. astr.
USA,
observatory,
537-543, 1972.
at Weston
26,
Soc.,
Zandt, G., Study of three-dimensional heterogeneity beneath
seismic arrays in central California and Yellowstone,
Wyoming,
unpublished
Massachusetts
Institute
of
239
Technology Ph.D. thesis, 1978.
Zandt, G., Three-dimensional seismic velocity anomalies in
the crust and upper mantle under southwest Japan,
(abstract), Trans. Am. Geop. Un., 56, 39 4, 1975.
Zarrow, L., Naylor, R.S., and F.A. Frey, Precambrian age of
the Lynn Volcanics at Pine Hill in the Middlesex Fells
Reservation, North Boston Quandrangle, Massachusetts,
(abstract), N.E. Geol. Soc. of America, 10, 91, 1978.
Zen, E-An, The Taconide Zone and the Taconic Orogeny in the
western
part of the northern Appalachian Orogen, Geol.
Soc. Am. S.P. 135, 1972.
Zietz, I. and E. Zen, Northern Appalachians,
24-28, 1973.
Geotimes,
18,
240
APPENDIX A
GENERALIZED AND STOCHASTIC INVERSION
In this appendix, the generalized and stochastic
for
a
1961;
inverse
linearized system are briefly reviewed (see Lancsoz,
Aki
and
details).
Richards,
In
1980;
and
Wiggins,
1972
for
Appendix F, the problem for the simultaneous
inversion of fundamental mode Rayleigh wave phase and
group
velocities using a maximum-likelihood method is formulated.
Given a set of experimentally observed
velocity
data,
theoretical
E.
and
and
group
phase and group velocities are
calculated using the propagator
(1953)
phase
matrix
method
of
Haskell
the variational principle described in Appendix
Assuming the surface wave velocities, v, are not rapidly
varying and the
small,
the
perturbations
problem
can
be
to
the
linearized
initial
model
by expanding in a
Taylor series about the initial model to the first order
i y...
v;
os
-
Aj-
V
-
eroder
dex
d;Herenvce beAteen obstrved and\I
iueoretical velocill at per;od i
f~~fl~nv~~rfor
JCA~j~
f
pcrameter correc'onr
for lager ,j
Equations 1 can be re-written in matrix form
v1
mo j of\
1Y±
Afj
are
(z)"
241
or
b =Ax
(3)
Following the generalized inverse
technique
of
Lancsoz
(1961), the matrix A in equation 3 is decomposed into
AzukAv T
where
(4)
U- contains n eigenvectors u; of
data space
A
V
length
m
from
-
diagonal matrix with n eigenvalues
-
contains n eigenvectors vjof length n from
the
model
space
The matrices U and V satisfy the relationships
AAN\A'
(5)
ATAvv
-(V)
The matrices U and V are
coupled
through
the
p
non-zero
only
non-zero
eigenvalues by
A u-p=- GAf
where,& ? is
a
eigenvalues.
diagonal
The
matrix
eigenvectors
containing
associated with (n-p) zero
eigenvalues in U and V become independent
A vO\
In
the
presence
of
zero
semi-orthogonal and
T
I
eigenvalues,
U
and
V
are
242
But because the non-zero eigenvalues may not span either
both
the
data
or
to
equal
guaranteed
identity
matrices,
model
the
spaces, LAPA
m-dimensional
respectively.
AV= A[vV 01 [UuuO]f
or
are
not
n-dimensional
Equations 6 and 7 can be
written as
and since
and VVf
or
1)
0
VVTZJ
A
OD
yk
-
The generalized inverse operator is given by
A-'V
(to)
As discussed by Lancsoz (1961),
and
VO
space,
A-
minimizes
in
the
the
presence
of
UO
length of the error
vector
in the data space and the length of the solution vector
in the model space simultaneously.
This second property
is
useful in that the perturbations to the model are kept small
which tends to stabilize the inversion.
A measure of uniqueness of the solution
the
calculating
resolution
matrix, R.
solution and x the "true" solution.
and
Then
is
obtained
by
A
Let x be the model
from
equation
3
the properties discussed above, the inverse solution is
given by
A
=vT
243
If there is no VO space V\4 1:.
and -g
and
is unique even in the presense of UO space.
of VO space,\V~jl
the
of VV
terms
In the presence
Thus, VO space is the
.
source of non-uniqueness in the solution
parameters
are dependent.
filters the true solution x to
supplies
information
results
R
equals p.
when
The resolution matrix R
give
regarding
and
the
the
2.
estimate
it
numbers of degrees of
freedom (uniqueness) in the system (m-p) because
of
solution
and the solution will be dependent on
off-diagonal
various
the
the
trace
The rows of R are called resolving kernals
(Jackson, 1972).
Similarly, the information density matrix,
the
resolution
in
data
space.
properties of the eigenvectors
predicted
From
predicted
of
system) u u I*
b,
are
above,
the
data
by
data
UC-space
and
equals
(for
the
the
expressed
system UO=O, VA\Ae
observed
example
model
flexibility to predict the data.
data
equation 3 and the
discussed
For a symmetric or underdetermined
presence
describes
by the generalized inverse, bg, is related to the
observed data,
the
S,
does
in
data.
In
and
the
an overdetermined
not
have
enough
In this case the predicted
as a weighted average of the observed.
The information density matrix provides information
on
the
inter-dependency of elements of the data vector.
The covariance matrix gives an estimate of the
the solution &,
due to errors in the data
ao
error
in
and is given
244
by
=(-A)
The covariance matrix is defined by
If the data are uncorrelated
and
c-ov= 61 VfP uTeAfIl
r
p 1
It is clear that the errors
large
when
suggests
the
eigenvalues
eliminating
eigenvalues.
in
This
have
the
the
eigenvectors
variance
(1is)
= 6AA~Ve
solution
become small.
decreases
same
become
Wiggins (1972)
associated
with
small
the magnitude of the errors,
but the number of degrees of freedom is increased and
the resolution is
Another
inverse
on
(damped
hence
degraded.
method
eigenvalues
very
of
off-setting
the
effects
of
small
the solution is obtained using a stochastic
least
illustrated as follows.
squares)
Franklin
(1970)
and
is
Given a system of equations 3
A()
the least squares solution is
X
given by
0
(ArA)_'A1
However, in the presence of VO space, a pure
solution
fails.
constant term E
A
The
by adding a
A"A
which gives
+(TA
1)(A)
+b
squares
solution can be "damped"
to the diagonal elements of
X=
least
245
where G
and
are the variances in data and
respectively.
spaces,
model
Rather than minimizing jAX-'o\
are now minimizing 1A4X
e
we
.
The damped least squares operator is given by
(Aki
and
Richards, 1980)
where
eAV
and
p
is
non-zero eigenvalues.
(r8)
V-~T
L =(A TA 4I)AT
the
order
of
space
spanned
by
From 18 the resolution matrix is seen
to be
For uncorrelated errors the covariance matrix is
Cov 6f (A'A+ SI ' (-V
Vf
V6j
(o)
Note as &' goes to zero, the stochastic inverse operator and
its resolution and covariance matrice reduce to those of the
From equations 19
generalized inverse discussed previously.
and 20 it can
parameter
to
be
the
reducing- the model
Thus,
in
actual
seen
that
generalized
error
at
the
addition
inverse
the
of- a
the effect of
has
expense
of
resolution.
use, the trade-off between resolution and
errors must be examined in order to select a proper
parameter.
damping
damping
246
APPENDIX B
NON-LINEAR INVERSION
OF
TRAVEL-TIME
DATA
FOR
CROSS-OVER
DISTANCES AND APPARENT VELOCITIES
Given a complete set of travel time data,
a fairly simple
and suprizingly stable least squares technique can
to
solve
for
apparent
be
used
velocities, critical distances and
corresponding intercept times
for
a
plane
layered
earth
model following the technique of Mitchell and Hashim (1977).
For a layer over a half-space model, the two branches
of
the travel-time curve can be described by
where
th
- calculated travel time at distance xi
- critical distance and corresponding time
V, V
Vt)
- velocity of upper and lower layer, respectively
- slope of travel time curve for branch i
-
Heaviside step function
To the first order, the difference between the calculated
and observed travel time at distance xi is
whre
where
lit
4
ar perturationstoAt
are perturbations to the model and
&)k~
from()
C).=1
C)t C
=Xk
)(<
(2)
X x
.1
247
For m observations we solve for
given
)<
an
initial guess using
(3)
In matrix terms, (3) becomes
(Q)
6,-MA 5
And the least squares solution is found by solving
AT b AAx
()
using LU decomposition
(A"A)-
(Steinberg, 1974)
(6)
A
Although the problem has been
higher
o's
,
order
terms
in
the
linearized
neglecting
Taylor series expansion about
non-linear
the equations (1) still contain the
involving
by
distance divided by refractor velocity.
terms
However,
test cases show that the system (5) converges accurately and
rapidly to a
final
solution
given
a
reasonable
initial
guess.
For three
travel
time
branches
(see
Figure
3.3
definitions) the travel time is given by
U(c)[X;-XC)I,+
1.AC)/Vct1
A X-X,)(+t].
A.(Y-
for
248
Linearizing the problem by expanding in a first order Taylor
series about
i
&ICA;';~~L
*~
~),
+
+
AX 4 ~
)~o
+
A
(8)
where
tcO.~
4
C
q
Vt
and the partial derivatives are given by
al
A. -
t
X
S-4,
0
X4 XCI.
Xgt
ax
C
0
(to)
X
O
<
As before the system (8) is transformed into the form
of
(5) and solved using the LU method.
Although equation (7) represents the
for
three
travel
curve
branches, the first branch generally has a small
non-zero intercept time which is either due to
of
time
effects
the
a thin, relatively low velocity upper layer or the focal
depth of the events.
function
To calculate the velocity
with
a three layer over a half-space model must be used
where the velocity of the upper layer, vO, is fixed.
the
depth
terminology
Using
shown in Figure 3.3, the thickness of each
layer is computed by calculating the zero-distance intercept
time of each travel time branch and
following equations.
1I.YL
X
~~4(r~
i
substituting
T-*
VV 0
.
__1
___
'~~4)4 /
V~ .i)
V
into
the
(Ti
249
The convergence of the solution is checked by calculating
the RMS fit of the predicted to the
observed
travel
times
(Bevington, 1969)
66)
where
-
number of observations
-
number of parameters
= m - n = number of degrees of freedom
(dimension of UO - space; see Appendix A)
The model
calculated
errors
from
caused
by
errors
the covariance matrix.
in
the
data
are
Given the solution
to a system of equations (6), the covariance matrix is
(see
Appendix A)
Cov
<ex
= (A A A T~
4 ,b>
A (ATA)o
(13)
For uncorrelated errors (13) becomes
(14)
7-ov'
(9
Cov= 6 (A*A
where
G
is the data variance (12).
Because of the large number of degrees of freedom in
determination
of
the apparent velocities, the variances of
the calculated velocities are very small.
assumed
the
the
velocities
are
It
well-determined
is
therefore
and that the
250
errors in the thickness of each layer, A z, are proportional
to
the
distances,
errors
xs,
in
calculated
the
.
Thus,
layer thickness are estimated by
11Cs
critical
the relative errors in
251
APPENDIX C
TIME TERM ANALYSIS
Given a set of travel times for waves
given
layer,
it
velocity, V1,
is
possible
to
refracted
solve
from
a
for the apparent
and the zero-distance intercept time, a, using
the equation
where Tij is the travel time from source i
and
Dij
is
the
VO,
receiver
j,
distance between the source and receiver.
For a single layer overlying
velocities
to
V1,
a
horizontal
respectively,
refractor
equation
(1)
with
becomes
(Dorman, 1976)
Equation (2) indicates that the intercept time is a function
of upper layer thickness, velocity, and refractor velocity.
In a time term analysis, the intercept time is broken
into a source term, Si, plus a receiver term, Rj,
34+~
A7-V.2=G
VIVO
Then (2) becomes
-D ''
(3)
up
252
In the case of a
layer
over
a
horizontal
refractor
and
constant lateral velocities
For the case of lateral variations in layer thickness and
velocities,
the
variations.
station
For
time
terms
if
example,
will
will
stations.
source
have
If
a
larger
these
a station consistently shows
delayed arrivals relative to all others,
term
reflect
positive
the station terms
are
this
value
station
time
than the other
well-constrained,
the
time terms will absorb errors in source location and
origin time.
location
To see this, consider two events at
where
times
same
one event has an error in origin time.
calculated velocity and
arrival
the
about
the
the
distribution
mean
(assuming no other errors).
velocity
of
the
should
station
be equal
Then the only parameter left to
absorb the error in the origin time is the source term.
will
The
As
be discussed below, the source and receiver time terms
are non-unique because their sum can only be
determined
to
within a constant and there are infinitely many solutions to
equation (4).
The time term method is
based on the fact that the travel
time between a source and receiver can be represented
by sum
of three terms, a source and receiver time term, and a
term
consisting of the distance divided by the refractor velocity
(Scheiddegger
and
Willmore,
1960)
weJ
1957;
Willmore and Bancroft,
253
where
travel time from source i to receiver j
i-
R. V
source time term (delay time)
time term
receiver
-
distance between source and receiver
-
mean refractor velocity
As illustrated in Figure 3.8, the travel time from
S
to
R
can be written by the sum of three terms
1S
o4e
Rv
+ -Dco
)
The symbols are defined in Figure 3.8,
dip
of the refractor.
is
the
apparent
If the dip of the refractor is small
(5) reduces to
vo
v
or
The source and receiver time terms represent the time
takes
for
vertically
the
critically
the
through
refracted
upper
wavefront
layer.
For
a
it
to travel
horizontal
refractor, the vertical apparent velocity is
to
0
tet G
For n separate events recorded at
every
station
m
stations
(assuming
records the head waves), there will be n x m
equations in n + m + 1 unknowns; the source and station time
254
terms and the average refractor velocity.
However,
because
the signals from an event are recorded at every station only
rarely,
the number of equations is
reduced somewhat.
The resulting system of equations (4)
is
written
in
the
matrix form
where
;.=1
.0.
if event i is recorded
j,
otherwise
In matrix shorthand
V
-A
0()
Ax
In order
decompose
at station
to
A
solve
into
the
system
of
equations
(7),
we
its eigenvalues and eigenvectors using a
singular value decomposition (see Appendix A).
A = AAVl
Using
the
solution to
generalized
(7)
(N)
inverse
is given by
of
Lancsoz
(1961),
the
255
However, because of the non-uniqueness
receiver
terms,
the
rank
of
the
this
and
of A is one less than the total
number of parameters resulting in one zero
remove
source
indeterminacy,
the
one
eigenvalue.
zero
To
eigenvalue
is
truncated (Wiggins, 1972).
As discussed in Appendix
A,
the
covariance
matrix
is
)
given by (for uncorrelated errors in the data, Gg
{
CovGtVjft
.
and the model resolution matrix by
R
Initial
perfectly
\V-
runs
(1I')
demonstrated
that
the
Pn
velocity
was
resolved (i.e. R11 = 1) and that all the diagonal
elements of R corresponding to the source and station
terms
were equal to
where NT is the number of source
This
and
station
time
is a problem similar to that encountered by Aki et al.
(1977) and results from the fact that the rank of A
less
terms.
than
the
time terms + 1).
number
is
one
of parameters (number of source and
As discussed in Appendix A, the
trace
of
the resolution matrix equals the rank of A and therefore the
diagonal elements of the best possible resolution matrix are
given
by
equation
(12).
If more than one eigenvalue was
truncated, the resolution would be degraded and
the
values
256
of the Rii terms would be correspondingly less than those of
equation (12).
257
APPENDIX D
COMPUTATION OF FREQUENCY-WAVENUMBER POWER SPECTRA
The data used in
this
study
consist
of
a
number
of
temporal signals distributed across a seismic network and is
thus
suitable
for
analysis
processing techniques.
using
space-time
Beamforming is the spatial analog of
temporal filtering because it is possible
separate
out
signals
within
to
identify
with a prescribed frequency response.
narrowband
Similarly, if
the signal propagating across a region is sampled
locations,
the
array
can
and
a given band of wavenumbers.
Each seismometer in the array acts as a temporal
filter
signal
at
given
be used as a spatial narrowband
filter with a spatial frequency response referred to as
beampattern
or
array
response.
between spatial and temporal
allows
for
the
direct
Because
frequency,
computation
the
of the relation
f=ck,
beamforming
of phase velocity, c,
group velocity, u=df/dk, and the direction of propagation.
Because the array elements lie along a
narrow
range
of
azimuths, we make a plane-wave approximation and assume that
the
stations
form
a
linear,
non-uniformly
oriented radially from the source.
In
this
spaced array
way
the
only
distance parameter for each station is a normalized distance
relative to the array origin and the event.
Computation of the
first
involves
the
frequency-wavenumber
calculation
of
the
power
spectrum
two-dimensional
258
Fourier transform
JtAo
where s(t,4) is
the
output
of
a
single
()
seismometer
at
position A , time t.
Opposite signs are used for the two Fourier transforms so
that the waves travel in the positive A
spectrum is calculated in two steps.
Fourier
transform
is
computed
direction.
First,
the
The f-k
temporal
for the signal recorded at
each station
where
f = (m-1) / Tat
,
mth frequency component
t
-
sampling inverval
T
-
number of time samples
-
postition of station
j
the
phase
or
where A and < are
amplitude
and
spectrum
for
frequency component f.
A phase shift is then applied
corresponding
in
the
frequency
domain
to the distance between two stations, ax, and
a frequency-dependent phase
velocity,
c(f).
Incrementing
the wavenumber k through a given range of values,
k~x=
c(LI;)
4
259
and given that
yields the phase shift
Therefore, all frequency components of all
phase shifted by A4
phase
velocity)
stations
corresponding to a given wavenumber (or
and summed.
This is equivalent to a delay
and sum stacking technique commonly used in the time
(Lacoss
et
al.,
are
domain
1969) and is referred to as phase stacking
by Nolet and Panza,
(1976).
As will be discussed below,
phase
stacking
shifts
the
main lobe of the array response over any desired position in
the
wavenumber
plane
which
signals with a range of phase
approach.
allows
for
velocities
the detection of
and
azimuths
of
Thus, the f-k spectrum is given by
and the f-k power spectrum in decibels is
P(f~k)=- 20
los
I F1
(8)
Once the power spectrum was
scheme
was
used
the maximum power.
group
maximum
computed,
an
interpolation
to select the wavenumber corresponding to
In order to
facilitate
calculation
of
velocities, a polynomial was fit to the f-k points of
power
using
the
wavenumber
as
the
dependent
260
variable.
The phase velocity was calculated from
k
and the group velocity from
As
will
be
calculations
discussed
indicated
in
a
a
later
frequency
section,
initial
range with abnormally
high phase velocities indicating the presense
of
laterally
refracted or multipathed arrivals coming in off-azimuth.
confirm
To
this, it was necessary to steer the array to select
beams in order to identify the azimuth of approach of
frequencies.
To
do
this,
given
the relative distances between
stations were recalculated along a given beam direction
and
the f-k power spectrum was computed for a set frequency as a
function
of
azimuth
azimuth to the source
computed
for
a
range
using equations 7 and 8.
was
of
known,
the
azimuths
Because the
spectrum
of
was
approximately
only
30
degrees.
If the number of stations is small,
will
be
characterized
(Figure 4.10).
the
the
array
response
by a main lobe flanked by sidelobes
These allow for the leakage of
energy
into
phase stack with undesired wavenumbers, and can make it
difficult to
separate
out
overlapping
modes
of
similar
wavenumber.
Also, if the recorded signal is contaminated by
multipathed
arrivals,
the
f-k
spectrum along a specified
beam may yield unreasonable phase velocities.
One
way
to
261
eliminate
these
effects is to move a group velocity window
function, D (tu), across the array where
velocity
(Nolet and Panza, 1976).
u
is
the
group
The signals are windowed
along a specified beam direction in the time domain and
are
given by
Dj
The amplitude and phase
spectrum
for
each
station
is
calculated and the phase shift applied before stacking is
L4:(kf )
Thus,
the
frequency
wavenumber
spectrum
for
the
group
velocity windowed signals is
)
N.Ait;
U- (
;)A
where the amplitude and phase spectrum are now functions
of
u.
Sources of errors include those caused
processing
response.
problem,
Because
and
influence
of
uncorrelated
proportionally by 1/ifW,
inadequacies
measurement
spectra is essentially a delay and sum
any
general
of
the
f-k
stacking
errors
in
spectrum
assumes
the
power
technique,
will
decrease
where N is the number of sensors.
The plane wave approximation used in calculating the
power
data
errors such as digitizing errors, approximations
made in setting up the
array
by
a
f-k
laterally homogeneous earth and
neglects local structure beneath each station.
Beamsteering
262
allows some
control
on
these
arrival of energy off azimuth.
effects
by
computing
the
The plane wave approximation
also assumes that the stations lie on a narrow azimuth range
and the variation of the source phase is nearly constant for
all
stations.
This
is a valid approximation assuming the
stations do not lie near a
nodal
pattern
waves where the source phase can
of
the
vary rapidly.
been
Rayleigh
plane
in
the
Although a fault plane solution has
compiled
the either earthquake,
for
radiation
not
yet
the high surface
wave amplitudes suggest that New England lies along an
lobe
of the radiation pattern.
A significant cause of errors is
probably
introduced
by
inadequacies in the array response for the six stations used
to
measure
the f-k power spectra.
Most other short period
stations in New England have an analog high-pass
filter
at
each
caused
by
station
microseisms,
site
and
were
to
cut
down
therefore
of
noise
unable
to
detect
the
long-period surface waves.
To define the
array
response
we
refer
to
the
above
discussion where it was seen that beamforming is a shift and
sum
stacking technique.
If we add the outputs, s(t,Ag), of
the seismometers together, the stack, y(t), is given by
0
where N is the number of stations.
of
constant
temporal
and
Assume that a plane wave
spatial
frequency
respectively, propagates across the array
S(t ) 4) = e
6
%1
fo,
kO
263
In electronics, a common
technique
function
is
of
a
network
to
find
the
transfer
to input a complex exponential
source and divide the output by the input (see Senturia
Wedlock,
1975).
Therefore,
complex exponential,
e P
we
drive the system with the
and divide
,
and
the
output
by
the input giving,
The normalized array or spatial frequency response
defined
to
be
|w(k)j
.
determining
the
that
unwanted
Rica
important
in
wavenumber resolution of the array and the
sidelobes
will
have
energy into the system.
on
the
"leakage"
of
The wavenumber resolution
lobe.
is determined by the width of the main
array
Costa
illustrated in Figure D.1.
Detailed analysis of the array response is
effects
then
The array response for the six
M.I.T. stations along the beam direction of the
the event is
is
Because
the
response shown in Figure D.1 is for a broadside array
using unshifted summation, the mainlobe is located at k =
which
implies
the array will selectively pass waves having
infinite apparent
discussed
0
wavelengths
and
velocities.
phase
As
in the previous section, we are using a delay and
sum stacking method which has the effect of placing the main
lobe over selected wavenumbers, k5.
In
this
becomes
W(k) = Z
Se
21(&()
~
(3
case
(2)
264
The array will
velocities
be
of
selective
c5
and
to
plane
horizontal
waves
with
apparent
phase
wavelengths o
S
given by
f
The width of the
resolution
and
main
is
lobe
mainly
diameter of the array.
determines
controlled
by
This is directly
the
wavenumber
the
length
analogous
to
or
the
Uncertainty
Principle and analysis in the time domain which
states that
the
length
of
a
time
series
is
inversely
proportional to the range of resolvable frequency components
(Claerbout,
1976).
Similarly,
the
diameter of the array
,a d, is inversely proportional to the
range
of
resolvabe
wavenumbers, Ak,
As can be seen from Figure D.1,
characterized
waves
with
amplitude
largely
by
sidelobes
unwanted
and
by
the
respectively.
number
An
of
and
is
an
differing
response
is
permit the "leakage" of
into
these
the
stack.
sidelobes
position
of
evenly
illustrated
The
are governed
the
stations
spatial
in
Figure
D.2.
spaced, linear array recording the
arrival of two plane waves with equal
and
array
extreme case of leakage of other spatial
frequencies into the stack is
Pictured
which
wavenumbers
position
the
frequencies.
undelayed summation of each wave will
temporal
In
result
frequencies
both
in
cases
the
an
same
265
stack.
However, the delay and sum technique or steering the
array will allow discrimmination of the two wavetrains.
sidelobes
are
caused
by
the
The
finiteness of the array and
again are analogous to convolving the Fourier transform of a
time series with a sinc function (the Fourier transform of a
rectangular truncation function).
effect
is
to
taper
wavenumber domain
sidelobes
Arnold
of
which
the
(1978),
in
space
this
before transforming to the
decreases
truncation
various
One way to minimize
the
amplitude
function.
spatial
shading
As
of
the
discussed by
(or
tapering)
functions such as a Chebyshev or cosine taper may be used to
decrease
the
amplitude of the sidelobes.
stations were used in this study,
it
was difficult to select
a useful shading function because the
two
outermost
sensors
would
be
Because only six
contribution
of
the
minimized and resolution
would be degraded.
Another undesirable effect that can occur
and
space
is
both
time
that of inadequate sampling or aliasing.
For
an evenly spaced array
with
station
in
separation
a x,
the
array response is a periodic function of the wavenumber with
a
period of 1/Ax.
Aliasing (or folding) occurs for spatial
frequencies above the Nyquist frequency
.
-L
The problem of aliasing is reduced somewhat by
irregularly
spaced
points.
sampling
at
The network used in this study
have an approximate station spacing of 25 km so the
highest
266
resolvable spatial frequency is .02 km.
arrivals
with
wavelengths
of
frequencies of obout .067 hz (T
These correspond to
approximately
15
50
seconds)
km
and
assuming
a
phase velocity of 3.4 km/sec.
As discussed by Clay and Hinich (1970),
in
the
phase
velocity
measurements
standard
for
a
errors
plane
wave
propagation along the line of the array are given by
Ig
SO) I
C
where
N
-
number of stations
. -wavelength for frequency f
D - array diameter
f)I/S(1ho
- signal to noise ratio.
Thus, the errors in the dispersion measurements depend on
the signal to noise ratio, the square root of the number
seismometers,
array.
and
of
the number of wavelengths traversing the
A large array aperature increases the
precision
of
the measurements (by reducing the width of the main lobe) at
the expense of spatial resolution.
267
FIGURE CAPTIONS
Figure D.1
Normalized array response for
six
MIT
stations shown in Figure 4.10 as a function
of wavenumber along beam direction of 204
degrees from north.
Figure D.2
Schematic illustration of energy leakage
into a broadside array stack. Two plane
waves of
differing
wavenumber
produce
identical array response resulting in a main
lobe and a sidelobe of equal amplitudes in a
figure such as that in Figure D.1.
268
Figure D.1
269
C)
-4
270
APPENDIX E
CALCULATION OF PHASE AND GROUP VELOCITY PARTIAL DERIVATIVES
Because there are fewer boundary conditions to be met, it
is generally more convenient to demonstrate the
of
calculation
phase and group velocities and their partial derivatives
using
Love
frequency
(W
waves.
,
Consider
propagating
a
in
displacement parallel to the y-axis
plane
wave
of
angular
the x-direction, with the
as
a
function
of
z,
v(z);
f(k, z,W)=v(z)exp(i(wt-kx ))
The kinetic and potential energies averaged over a cycle are
(Aki and Richards,
I
where
1980; Takeuchi et al.,
1964)
0=
is the density and y
is
the
rigidity.
The
1/4
comes from averaging of cosine and sine squared terms over a
cycle.
Because the kinetic and potential energies averaged
over a cycle are equal
where
IT
271
Using the variational principle under the condition of no
body forces or surface tractions, it can be shown
energy
equation
1
that
the
is unchanged for a perturbation of v(z)
about the actual motion.
As an extension of this
fact,
it
can be shown that there exists a linear relationship between
fractional
changes
in
changes in
elastic
parameters
phase velocity with respect to small
and
equation 1 becomes to the first
dSI,
Thus,
2p
that
for
a
fixed
k
order
e=S~2
(3)
I
once a root of the period equation
for
a
particular
has been found as a function of wavenumber k
F(c)k) =o
the phase
various
velocity
layer
equation 3.
(4)
partial
parameters
derivatives
can
be
found
The group velocity \A:
in terms of the energy integrals
with
respect
to
immediately from
can also be expressed
(2).
By
differentiating
equation 1 with respect to k it can be shown that
(S)
__
The variational
chase
D.G.
velocit
principle is
partial
used
in
computation
of
erivatives in a program written by
Harkrider.
A program was written to
partial
derivatives
calculate
(1975).
the group velocity U with respect to the
in the relationship
U:
the
group
velocity
using numerical differention following
an approach used by Rodi et al.,
and
the
(C
By differentiating
phase
velocity
C
e
272
where m represents the layer parameters,
it
can
be
shown
that
C-U.) 51;C
+ f U
Z*2-
if))
f
(7)
Defining
)
C0 z-
+ C-
)
C~1=
'hA
~ ~&
0
C04
k~.
4
41
jtC.
1)
*C41
where fO is the frequency at which the period equation 3
is
being evaluated, then
UO
CO
U0
~C)41
4M..Iwft
C.j
dM
em
(R)
273
APPENDIX F
MAXIMUM-LIKELIHOOD INVERSION OF PHASE AND GROUP VELOCITY
In Appendix A, it was assumed that the errors in the data
are uncorrelated and have the same variance.
in
Chapter
4,
the
As
errors in the phase and group velocity
vary as a function of period and, in general, the
for
the
group
velocity
phase velocity.
phase
discussed
curve
variances
are greater than those for
In addition, the
partial
derivatives
for
and group velocity are a function of layer thickness.
Thus, it is necessary to weigh the solution
in
both
model
and data spaces.
As
described
equation
in
Annendix
A
a
lineari7Ped
systqiem
of
is set up for the simultaneous inversion of phase
s
and grou
velocities.
only
shear velocity is adjusted while the compressional
th
For reasons discussed in
Chapter
velocity and density are held fixed.
,
eeia
C:4
I0/
A; F.
L-.
-&O)
where
and
j
-
shear velocity
-
adjustment to shear velocity in layer
in
layer
j
4,
274
In matrix form,
DC,
C2.
r1k
&CA
DL,.
9'L
Civ
~Cff t~
C) A*
&ctm~
J,\AA
b = Ax
Let RA
(a)
and W be the data covariance and model
weighting
matrices, respectively,
'/4"
G .
"4'
R
(3)
0
1/4
where G
thickness
the variance of the ith data point, and 4 -is
of
the
ith
layer.
Because
R,\
and
non-singular symmetric matrices they can be decomposed
a
product
of
1961).
orthogonal
simultaneously.
are
into
matrices (Lancsoz,
Rnv%= NAjN
V n
The generalized
eigen-vector
W
the
inverse
With
(4)
A o1a
operator
the
minimizes
weighting
in
bothjI Axi' and
data space it is
iji
275
desired to minimize
(b~~
P,,
such that
the
according
to
(b-A2!)
-|b-A
perturbations
the
in
the
length
of
the
model
errors in the data.
weighting is inversely proportional
weighted
(s)
*f
weighted
In model space, the
to
solution
are
the
thickness
vector
is
and
minimized
according to
xTW'x=
X x-1
(6)
The coordinate transformation that satisfies 5 and
6
(Wiggins, 1972; Aki and Richards, 1980)
-'K
h:A~
NL~
a
rvie 6'/k
,
~:A~A
r~'~
(S)
N~A ri'~A"~
-~K'~
MT
1/lt
A: t
Then we solve
b*=At
(q)
using the stochastic inverse (see Appendix A)
X*=A
= (A A* 4 Gl)A
3*
(10)
Transforming back to original coordinates using 7
A
A
and
A
A-
I
x
(11)
is
276
where R is the resolution matrix.
The covariance matrix
given by
cov = A3' Rnn (A3~'
(T
is
277
APPENDIX G
INTERSTATION TRANSFER FUNCTION USING WIENER DECONVOLUTION
Given two seismograms positioned
circle
path
from
a
source,
along
we
want
interstation transfer function (also
impulse
response
or
Green's
the
to
known
same
estimate
as
function).
great
the
medium
The phase of the
transfer function gives the phase delay of the system
will
be
which
used to calculate the interstation phase velocity.
The shape of
provides
the
the
transfer
information
on
function
the
in
the
time
domain
dispersiveness of the system
which will be used to estimate interstation group velocity.
Figures G.1a,b illustrate the problem
frequency
in
time
and
domain where the input signal at station 1 drives
the system and produces the output recorded
The
the
convolution
is
given
by
the
at
station
frequency
2.
domain
representation
where the subscripts 1,2 and m refer to station
2,
and
the
interstation medium, respectively.
deconvolve the output by
dividing
computing the transfer function
(1)
by
the
1,
station
We wish to
input
and
278
This
simple
particularly
deconvolution
in
the
presense
can
be
very
of spectral holes for which
frequencies the filter parameters (transfer
be indeterminant.
to
find
unstable,
function)
will
Various deconvolution schemes can be used
the filter
coefficients and we have chosen a least
squares or Wiener deconvolution (Wiener, 1949;
Treitel
and
Robinson, 1966; Peacock and Treitel, 1969).
Let the vector b represent the input (signal
1)
to
at
station
the system f, and d be the output (signal at station
2) where
b
=(bb
We wish to construct a filter, f, that
the
desired
f
best
estimate
output, d, when driven by an input b.
the n+m length vector c
design
will
such
that
represent
the
actual
Letting
output,
we
the difference between the actual and
desired output
t
-
is minimized in a least squares sense (Figure G.1.c).
requires
that
the
length
E,
of
the error series, e, is
minimized
"1
E e
2
Ze
Ix t
Ct)
This
2
(3)
279
and we design f such that
b*
s
(4%)
or
tro
where * denotes convolution.
Using
notation,
matrix
the
convolution is given by
* 0
0
C0
i'
o
CI
b
0
iV
0
(fm 4 k) 4 )A (A.,
1)
Introduce the desired output d, which is
station
(S)
*y
2,
the
signal
at
and solve for f such that the length squared of
the difference vector
1r.
oC~
b0
b,
b' o%
b60b
0
is
minimized
C,0
280
In matrix shorthand
Solve for f using least squares
It turns out that the terms B B give the autocorrelation
of
the input b
tro0
and BTd is the cross-correlation vector of b and d
t :0
Thus,
the
m-length
Wiener
filter
results
the
from
solution of the normal equations of the form
C0
.
k16z
.
4
~cc
Q 44 1
C
1I CAoaI
C;
C.
(6)
L
.
or from equation (1) we are solving
F, It
-;C
z
The autocorrelation
Toeplitz
diagonals
F I F2. e
matrix
in
S%
. $ 1)
equation
( -7)
(6)
is
in
a
form with an interesting symmetry where all of the
are
the
same
and
the
main
diagonal
is
the
281
autocorrelation
of
the
input at zero lag.
Because of its
symmetry, the system (6) can be solved efficiently and
a
minimum
of
computer
storage
using
Levinson recursion
(Wiener, 1949; Treitel and Robinson, .1966).
Although
system (6) is always nonsingular (assuming a. /
Herne, 1966),
For
this
the
problem
framework
contaminated
the
0) (Ford and
numerical instabilities may occur for large m.
case
stochastic
with
by
where
can
the
be
formulated
input
signal,
using
a
b,
is
noise, n, and the actual input x, is given
by
Assuming the noise
is
stationary,
the
system
can
be
solved using the damped least squares technique discussed in
Appendix
A.
To
do
this
we
add a small constant to the
autocorrelation function at zero lag
which
stabilizes
the
solution.
As discussed in
suggest
that
the
Chapter
4,
Landisman
interstation
when
earthquake.
the
(1969)
of
the
interstation
a source is applied at the station nearest the
Comparison of equations (2)
cross-correlogram
gives
but not the group delay.
impulse
al.,
cross-correlogram gives an
approximation of the impulse response
medium
et
response
function where the
of
the
output
and (7)
shows
that
the phase delay of the system
To test this, we assume
interstation
equals
the
medium
input.
that
the
is a delta
Using
the
12/9/72 seismic records recorded at WES shown in Figure 4.2b
282
we
compute
the
cross-correlation
output (Figure G.2a,
of
the
which is
above
(Figure
least
the
actually
input at station WES)
function using the
of
the
input with the
autocorrelation
and the interstation transfer
squares
deconvolution
described
Both signals shown in Figure G.2a,b
G.2b).
are then windowed between lags of 0-400 seconds.
of Figures G.2a and
approximates
a
b
shows
delta
"cross-correlogram".
that
function
The phase and
Comparison
the
transfer
much
better
amplitude
function
than
the
spectrum
of
windowed transfer function gives a better approximation
the
to that of a
Also
shown
delta
than
function
the
in Figures G.2 a and b is
fit to the narrow bandpassed signals
As
can
be
seen
from
Figure
G.2a,
cross-correlogram.
the envelope function
for
the
amplitude is at a lag of 10 seconds which
velocity
errors
of
about
8%
over
two
frequencies.
time of maximum
can
group
cause
of 500 km.
distances
Between periods of 17 to 50 seconds, the lags of the maximum
amplitude for the
function
transfer
are
all
within
two
seconds or one digital point in this case where the sampling
interval
was
2
seconds.
For periods below 17 seconds the
error increased to 4 seconds (two digital points)
which
is
the portion of the spectrum that was not flat.
Although Landisman et al., (1969) were correct in stating
that the cross-correlogram gives
an
approximation
of
the
impulse response of the interstation medium, test cases show
that
substantial
errors
of
interstation
group
velocity
determinations can occur for short station separations.
283
FIGURE CAPTIONS
Figure G.1
Schematic illustration showing the meaning
of the interstation transfer function.
Figure G.2
Comparison
of
performance
for
cross-correlogram (a) versus interstation
transfer function (b) for modeling
the
interstation medium response. Input equals
output and medium response should be a delta
function. (a) Cross-correlogram, spectrum,
and narrow band-passed signal and envelope
function; (b) Transfer function calculated
using
Wiener deconvolution, spectrum,and
narrow band-passed signal
and
envelope
function
ei
FL((-))
(ca)
Z.
111
Figure G. 1
285
12/9/72
wos
3
autocorrelation
X10-
0.2
0.1-
e.0
129/72
MMPLITUDE
0.004
was autocorrelation
cm*sec
0.00210
20
30
40
50
60
70
0
60
70
30
PERIOD (sec)
PHASE (cycles)
030
£0
'10-4
0
30
BAND- 0.250
I
.
40
50
PERIOD (60c)
.pha*
fiequencg=
0.04950
0.5-
0.0
-
Ples'"
0
840
200
300
-W"
41
x1,0
Figure G.2a
286
TRANSFEP FUNCTION
12/9/72
was-wes
damping-1.
0.4
0.3
0.2
0.1
-e.6
12/9/72 TPANSFER FUNCTION
kMPLITUDE cm*sec
damping-1.
Wes-we3
4
10
60
50
40
30
20
as
70
PERIOD (see)
PHASE (cclea)
I
46
-36
76
GO
so
PERIOD (sac)
BAND-
0
250
al
ha*
0.0
0.04980
frequencg-
000-
-0.1
,
*
9
BAee10ee
2O
a
he-'0
300
ar
frequen
-
f
"'"ne-
0.48
44
0.03283
-0.05-I
-11
,,
- 10
,i
a3ea0
,,
44
Figure G.2b
287
BIOGRAPHICAL NOTE
The
author
was
November
10,
1952.
born
in
He
Rottenchester,
fell
New
York
on
in love with pizza at Ray's
Pizza Place where he worked in 1968 and with Heather Goff at
a party in 1969.
High school earth science and
with
Co.
Mobil
Oil
as
experiences
a Petroleum Distribution Engineer
convinced him that geology for fun and profit was a suitable
life endeavor.
Heather and he then set off for
University
where
they
(from
45701
and
Ohio
both tooled for four years emerging
with a B.S. in Geology,
horsemanship
Athens
an
AA
Meredith
in
Science,
a
degree
in
Manor) and a marriage license
betwixt them.
Without knowing the difference between
phase
and
velocity (a concept that continues to elude him),
naively
decided
to
study
learned the fine arts
organizing
of
geophysics
hand
waving,
the author
at M.I.T.
There he
computer
hacking,
boondoggles, eating 16 inch pizzas with 1/2 of a
steak and mushroom sub w/ mayo and a quart of coke,
the
puck
group
on
Arthur's
putting
stick, and telling people that they
stink.
Fortunately, the author
before
COCORP
ran
a
managed
to
finish
his
thesis
line across New England and he prays
nightly that drilling technology never
enables
mankind
to
penetrate the crust.
The author is presently living with Heather and at
least
288
two
crazy
parrots
in
sunny
California and is working at
Lawrence Livermore Labs in Livermore, California.
Publications along the way include:
Taylor, S.R. and M.N. Toksoz, Three-Dimensional crust and
upper mantle structure of the northeastern United States,
J. Geophys. Res.,84, 7627-7644, 1979.
Taylor, S.R., M.N. Toksoz, and M.P. Chaplin,
Crustal
structure of the northeastern United States: Contrasts
between the
Grenville
and
Appalachian
Provinces,
Science,208,595-597,1980.
Chaplin, M.P., S.R. Taylor, and M.N. Toksoz, A coda-length
magnitude scale for New England, Earthquake Notes (in
press), 1980.