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MAAY198
A LONG-PERIOD MAGNETOTELLURIC STUDY IN CALIFORNIA
by
BRIAN ROBERT BENNETT
Submitted to the Department of Earth, Atmospheric, and
Planetary Sciences on May 24, 1985 in partial
fulfillment of the requirements for the Degree of
Master of Science in Geophysics
ABSTRACT
We conducted a long-period (20 minute to 72 hour) magnetotelluric survey in California. We used electriic field data
from dipoles
in the Palmdale and Hollister areas.
A
technique was developed to predict the magnetic field based
upon the fields recorded at observatories in Tucson and
Boulder.
Three estimates of the magnetotellur ic
impedance
tensor were computed, the conventional Zh and Ze estimates
and
an
estimate
(ZPC)
based
upon
the
sin gular
value
decomposition method of Park and Chave (1984).
We found that
only the Zh method gave reasonable results. The tensors were
analyzed using the eigenstate analysis of LaTor raca (1985).
The principal direction of current flow was found to be
perpendicular
to
the
ocean-continent
bounda ry
both
at
Palmdale and Hollister.
The apparent resis tivities
and
phases in the principal directions were computed and compared
to the results from a 2-D forward modelling progr am.
Our analysis yielded similar
apparent
resistivities and
phases for Hollister and Palmdale, suggest ing that the 1ocal
geology is not important at long periods.
We found models
which fit our data reasonably well.
The interpretation was
limited by lack of a 3-D modelling program and 2- or 3-D
inversion programs and the fact that we had only one site at
both Palmdale and Hollister.
We were able to estimate the
resistivity thickness product for the ocean crust.
We found
that large values were required (on the order of 280,000
ohm-m and 100 km).
These values are in reasonable agreement
with the 30,000 ohm-m and 40 km predicted for New England by
Kasameyer (1974) but are a departure from the 200 ohm-m and
50 km estimated for the Pacific Ocean crust by Oldenburg
(1981).
Thesis Supervisor:
Title:
Dr. Theodore R. Madden
Professor of Geophysics
ACKNOWLEDGEMENTS
My education at MIT involved much more than problem
sets,
papers, and exams, although there were occasions, especially
at 2am, when I lost sight of that fact.
I have learned much
about myself and others from my friends here at school.
Enrique Sabater and Jeff Collett put up with me as a
roommate freshman year and are still good friends.
I have
enjoyed numerous discussions with my office mates on topics
ranging from politics to fourier transforms.
They were
always willing to help when I needed it. They were:
Steve
Park, JiaDong Qian, Earle Williams, John Williams, Richard
Wagner, Karl Ellefsen, Ted Charette, and Randy Mackie.
I
also thank Gerry LaTorraca and Dale Morgan for their help.
I would like to express my deelp gratitude to Professor Ted
Madden.
He has been a friend, advisor, and mentor for the
last four years.
He was ne ver too busy to answer my
questions.
He's also given me a few good games of tennis
over the years.
I hope that I am as young as he when I am
his age.
While at MIT I have received financial support from the
U.S. Air Force as an ROTC cadet, the Department of Earth,
Atmospheric and Planetary Sciences as a teaching assistant,
and
Professor
Madden's
oil
consortium
as
a
research
assistant.
I gratefully acknowledge this support.
Finally,
I would like
to
thank my parents,
Richard an d
Ionell Bennett, for their
support and encouragement.
I
dedicate this thesis to them for all they have done for me.
-
i i i
-
TABLE OF CONTENTS
PAGE
Abstract ...............................................
ii
Acknowledgements .......
iii
Table of Contents ......
.iv
Chapter 1:
Introduction and Background ..................1
Chapter 2:
Electric Field Data ........................ 26
Chapter 3:
Magnetic Field Data ........................ 32
Chapter 4:
Tensor Calculations ........................ 40
Chapter 5:
Modelling and Interpretation ................ 58
Chapter 6:
Conclusions
................................ 89
Appendix
Magnetic Field Prediction
Appendix
Tensor Rotation
Appendix
Complex Singular Value Decomposition
Appendix
Data (impedance eigenstate parameters)
123
Appendix
Data Processing Steps ................
150
......
................
...... 92
..... 117
.....
.
References ............................................
121
151
Biographical Note ..................................... 155
CHAPTER 1:
INTRODUCTION AND BACKGROUND
In this thesis, we
to
investigate
the
conductivity
crust and upper mantle
use
the
electrical
from
near
data
predicted the magnetic
data
use the magnetotelluric (MT) method
In
two arrays
fields for
at
edge
of
the
four
earth's
Tucson,
describes
the
suggestions
six
for
prediction of
trick
we
of
data,
and
of
and
the
Boulder,
and
our
work.
respectively.
the
MT
basic
We
the
data
in
the
form
Chapter
tensors.
our
value
We
the earth's
in
chapter
some
technique
in appendix one.
singular
ocean-
conclusions and
give
in
processing
interpretation
the magnetic fields
for
the
discuss the
discuss the modelling of
includes our
further
found
our
We
based upon
Arizona
structure,
for
Appendix
We describe
decomposition
of
In appendix four we list
complex matrices in appendix three.
all
We
California.
two is our method for rotation of the MT tensor.
a
earth's
conduction mechanisms
three
calculation
structure
Chapter
two and
and magnetic
the data and
conductivity
five.
conductivity
Chapters
electric
summarize
the
this chapter, we derive the basic equations of
effect.
the
in
the region
MT and review studies of electrical
rocks,
of
an ocean-continent boundary.
from
observatories
Colorado.
structure
of
apparent
resistivity,
coherency, and eigenstate parameters of the impedance tensor.
Appendix five
in
is a list of the data processing steps we used
this study.
- 1
-
The
magnetotel Sur i c
Cagniard
in 1953.
magnetic
fields
method
was
It uses measurements
at
the
earth's
introduced
to
Hertz)
usually used
Ifor
the primary source
layers around the
magnetotel-lurics
These
currents are
the solar wind and the rel ative motions of
and
sun.
into
Electromagnetic
the earth.
Their
earth because of the
waves
di rection
and are
is
created
nearly
to magnetic
periods,
we
can
probe
to
the
the
and
propagate
in
the
- 2 -
at
into
the
the
boundaries
We will
show that
the field depends upon
Hence,
magnetic
conductivity
function of depth.
of
The frequency or period is
related to the depth of penetration.
electric
I
ionized
the result
These waves propagate
both frequency and conductivity.
the
than
vertical
reflected and transmitted
the ratio of the electric
of
(less
the earth, moon,
between layers of different conductivity.
ratio
In the
large conductivity contrast between
atmosphere and solid earth.
solid earth
are
the
These fields arise from
is currents flowing in the
earth.
and
infer
a wide variety of sources, both natural and man-made.
frequencies
Louis
of the electric
surface
conductivity structure of the earth.
by
by measuring the
field
of
the
at
various
earth
as
a
the
derive
To
we
begin
wi th
time-
1aw,
fi elds.
el ectric
produce
fields
magnetic
varying
MT,
Farada y's
to
According
equations.
Maxwell's
of
equations
basic
In
differential form
(1.1)
Simi 1arly ,
time-var ying
magnetic
fields.
produces
a
form,
Als o,
magnetic
will
fields
electric
a current or constant
field.
Amperes
law,
produce
E field
in
differential
is
v-H4cE + gE
where
7
tivity.
factor
of
is
the conductivity and
In
the earth,
106
can neglect
to
the
last
Hence,
term
is the electric
typically greater
r is
1011.
f
(1.2)
than
permitE
by a
to a good approximation,
in
1.2,
t
EE-
the displacement
we
current.
We now have:
(1.3)
Both H and B are used to represent magnetic fields, but
they do have different
induction, measured
in
physical meanings.
tesla (mks).
-
3 -
B is the magnetic
H is the magnetic field
intensity, measured
They are
in amps/meter.
related
by the
constitutive relation:
B
=
(1.4)
mH
where u is the magnetic permeability.
Mo = 41r X 10~7
With
the
exception
permeability
space.
is
of
In free space,
henries/meter
strongly
approximately
magne tic
equal
to
the
materials,
value
for
the
free
Thus, for our purposes,
)U =
(1.5)
Al
Now, using Ampere's and Faraday' s laws, we determine the
behavior of
electromagnetic waves
to be
the earth
into
and
in the earth.
assume an
direction and a magnetic field in the
electic
y
field
We
take +
in
the
direction:
E = E (z)e-iwt
(1.6)
H = Hy(z)e-iwt
(1.7)
where w is the angular frequency:
w = 27f
P =f
where P is the period in seconds.
- 4 -
(f
in
hertz)
(1.8)
(1.9)
x
Our goal
to calculate
is
Ex(z)
and
Fir s t ,
Hy(z) .
we
combine equation 1.7 and Faraday's 1aw:
(1.10)
PY
Similarly,
we substitute
the expression for E, equation 1.6,
into 1.3:
z0{x
-~
(1.11)
We differentiate 1.10 with respect to z and use 1.11
Differentiating
1.11
(1.12)
.
9'EX
using
and
to get:
we
1.10,
obtain
a
similar
expression for Hy:
fly
Q2-Lj
Equations
equations.
-
jA VO-H7
(1.13)
1.12 and 1.13 are second order
Their
solutions
can
be
linear differential
expressed
in terms
of
complex exponentials:
Ex(z) = alExe+ikz + a 2 Exe-ikz
Hy(z)
where a,,
a 2 , bl,
= bHye+ikz + b 2 Hye-ikz
and b 2 are arbitrary constants.
-
5 -
(1.14)
(1.15)
The constant k
is
given by:
k2 =
k =
and can be
value,
the
(1.16)
juwd
i
+
(1
(1.17)
2
the wave s
faster
depends
dissipation
dissipate.
frequency
the
upon
cannot
Physically, we
conductivity.
Hence,
or
its
larger
The
thought of as a damping constant.
of
the rate
the
and
period
grow
allow waves which
exponentially so a2 = b2 = 0 and
Ex(z) = aExe+ikz
(1.18)
= b 1 H>ye+i kz
(1.19)
Hy(z)
A measure of
the depth of penetration of
given by the skin depth,
which E and
H drop
to
S.
is
It
defined as
their
1/e of
is
the EM waves
distance in
Using
surface Val ues.
1.17 and 1.18, we have:
(1.20)
V =2/
for
a
propor t i onal
penetrate
to
deeper
conductivity
The
earth.
homogeneous
the
frequency.
increases,
Thus,
intuitively
we
(as
skin
the
skin
depth
inversely
depth
is
longer
period waves
expect).
decreases.
As
the
Physi-
cally, this results because a higher conductivity means
that
charges are freer to move about and set up a field opposed to
any
applied
fields,
a
manifestation
-I
of
Lenz's
law.
Using
we
1.20,
generated
of
table
a
conductivies and periods (table
TABLE 1.1
depths
skin
for
various
1.1).
ELECTROMAGNETIC SKIN DEPTHS
(in kilometers)
1000
Resistivity (ohm-meters)
1
100
10
.1
Per i od
10 min.
390
120
39
12
3.9
30 min.
680
210
68
21
6.8
60 min.
950
300
95
30
9.5
2 hours
1400
430
140
43
14
5 hours
2100
680
210
68
21
950
300
95
30
2100
660
210
66
5 days
1000
330
100
10 days
1500
470
150
20 days
2100
660
210
10 hours
2 days
.001
We now know that
upon
the
cal cul ate
.01
Conductivi ty
1
.1
(mhos/meter)
the propagation
conductivity and
the
period.
of
The
10
EM waves depends
next step
is
(: from the measurements of E and H.
Different iating 1.18:
kF~
- 7 -
(1.21)
to
Combining this with 1.10:
(1.22)
iAwH, = ikEX
or
H-
Sk
i
-
(1.23)
'
Solving 1.23 for 0
where we have used 1.17 for k.
y
:
11)(1.24)
The resistivity, p, is defined as
and is given by,:
(1.25)
Thus,
if we
know
the
values of
(found by taking a fourier
E
and
H at
transform of
a given
period
the time series), we
can calculate the resistivity the earth would have if it were
homogeneous.
The earth
is never homogeneous so we
call
the
expression in 1.25 the apparent resistivity, pAA more useful expression for PA can be derived by taking
E
to
be
in
millivolts
(1 gamma = 10~
per
kilometer,
B
(=uH)
The
units
in
gammas
tesla):
'2 P(1.26)
where
P
is
the
period
in seconds.
ohm-meters.
- 8 -
of
PA
are
When
the
earth
approximately
is
one-dimensional
(horizontally layered) the measured ratios of Ex:Hy and Ey:Hx
be
will
and
equal
1.26
equation
In
suffice.
will
many
important cases, however, two- and three-dimensional features
(lateral
the
distort
inhomogeneities)
directions.
current
This can be understood by considering a time-varying magnetic
field incident upon an anisotropic earth.
can be resolved
see
fC-
induce
and
resistivities
different
the principal
into components oriented along
the anisotropy ellipse.
directions of
The magnetic field
components will
currents.
unequal
Hence,
I|
iH11
and
induced
describe such
and relate
angles
to
the
(or EY) depends upon both Hx and
Hy.
To
currents
magnetic field.
Ex
(1.27)
will
not
be
at
:Z12
H
relationships, we measure
them by a tensor:
--
r ight
Z
EX,
Ey,
Hx,
and
Hy
(1.28)
Ey
Z22
221
Hy
(1.29)
E = ZH
or
The tensor Z is a complex functi on of frequency.
In
the case
of a 1-D structure,
Zi
=
-9-
22 = 0
(1.30)
For
impedance; Z is
an
The ratio of E to H is
strike.
structural
(x
the
to
perpendicular
and
parallel
oriented
are
y)
and
axes
the
if
true
also by
1.30 will
a 2-D structure,
called the MT impedance tensor.
the
near
made
were
measurements
study,
this
In
ocean-continent boundary so clearly a 1-D interpretation will
to
perpendicular
Z
of
terms
The
adequate.
not be
be
to
tensors
the
of
analysis
Our
small.
diagonal
the
expect
so we do not
the coast
and
parallel
electric dipoles are not
is
discussed in chapter four.
magnetotellurics
of
application
entire crust
made
Some
and the upper mantle.
arrays
dipole and Schlumberger
dipole
spacings
of
is
applied
is
measured (Cantwell
huge current
kilometers,
limited such surveys to shallower structures.
avoids
such
which
MT
surveys
can
penetrate
structure itself and the length of
time series.
sources and
however,
have
The MT method
naturally
occurring
The only factors limiting the depth
electromagnetic signals.
to
using
by
problems
have been
in which a current
of
hundreds
attempts
the
dipole-
The requirements of
1965).
of
as
to the ground and the resulting voltage
et al.,
of
surveys such
resistivity
using conventional
study
the
conductivity
electrical
the
in determining
in
There has also been
exploration.
sedimentary basins for oil
interest
been
has
common
the most
1950's,
the
in
its development
Since
are
the
conductivity
the electric and magnetic
Only long-period signals can penetrate into the
-
10
-
mantle
and
table
1.1).
conductivity
the
of
Interpretation
(see
high
too
not
is
conductivity
the
if
only
profiles
requires a basic understanding of the conductivity of rocks.
function
electrical
conductivities of
a function
of
the fluid
experimental
the
shows
1.1
Figure
pores.
the
filling
composition
the
pressure,
and the conductivity of
the rocks,
and porosity of
the
temperature,
the
of
The conductivity is a
10+4 mhos/m.
10~7 mhos/m to more than
than
less
from
range
conductivity
rock
of
Values
as
proposed mantle compositions
In
temperature.
all
the
cases,
conductivity
increases with increasing temperature.
conductivity
of
and others have explained the
(1955)
Runcorn and Tozer
activated
thermally
of
terms
in
rocks
processes of the form
o{T~c7
where
T
is
conductivity
conduction
temperature,
absolute
the process,
energy for
the
the
at
processes
E&
infinite
activation
the
is
and
three
into
0,
is
dominant
The
temperature.
separated
be
can
EA
Boltzmann's constant,
is
k
(1 .31)
types:
impurity, intrinsic, and ionic semiconduction.
to conduction because
Impurities contribute
can
be
excited
conduction
impurity
band
levels
from
and
the
from
(creating
-
impurity
valence
the
conducting
11
energy
-
band
holes
electrons
into
level
into
in
the
unoccupied
the
valence
Log 10 PA ohm-ml
3
2
-5
1000 K
T
-4
-3
-2
-1
0
+1
BASALT 2.5kbar
BASALT 2.8 kbar
+3
+4
+5
100% Fayalite
18 kbarl
+6
+7
18 kbarl
Figure 1. 1 Electrical Conductivity Versus Temperature for Various Rocks at
Specified Pressures (after Cox, 1971).
-
12
band).
Conduction by
impurities dominates at relatively low
temperatures, less than about 600 0 C.
Electrons
may
be
excited
into
without the presence of impurities.
is
known
larger
as
intrinsic.
than
required
for
for
conduction
this
The
the
so
mechanism
to
band
The resulting conduction
activation
impurities
conduction
energy
higher
be
is believed to dominate
required
temperatures
important.
at
is
are
Intrinsic
temperatures of
about
600 0 C to 1100 0 C.
At
defects
even
in
the
higher
temperatures,
structure
of
crystalline
mobile and dominate the electrical
band model
of a semiconductor
above
11000
conduction.
in figure 1.2.
El
IMPURITY LEVELS
E3
VALENCE BAND
tE
I
E= 0
FIGURE 1.2 ENERGY LEVELS IN A SEMICONDUCTOR
-
13
-
become
We show the
E2
--------------------
1200 0 C,
materials
CONDUCTION BAND
El
or
is the
activation energy for
E2
the energy gap.
called
intrinsic semiconduction and is
E3 are
and
energies for
the activation
impurity (extrinsic) semiconduction.
- A
mechanism
conduction
fourth
important
is
some
in
iron-bearing minerals such as magnetite and possibly olivine.
It
electron
as
known
is
neighboring
Fe+ 2
and
Fe+ 3
of
transfer
states)
the
Unlike
ions.
a
is
valence
equivalently,
(or
electrons
and
hopping
between
other
mech-
anisms, electron hopping cannot be described by a band model.
In table
the
1.2 we give a summary of
for olivine and the
conduction mechanisms
temperatures at which they dominate.
Conduction Mechanisms for Olivine
TABLE 1.2
Mechanism
o in mhos
Temperature Range
Impurity
10-1
< 600 0 C
Intrinsic
10+2
600-1100 0 C
Ionic
10+6
> 11000C
the conductivity of most rocks
Near the earth's surface,
is dominated by the electrolytic contribution from the
free
Porosity, which is defined as the
water filling their pores.
volume fraction of accessible cracks and pores, can vary from
.001
to
Keller
.3
(1971),
electrical
near
for
the
naturally
even
conduction
surface.
occurring
a porosity
the
at
14
only
According
.001
will
low
temperatures
of
the
Studies
-
of
rocks.
-
state
of
and
to
dominate
pressures
water
as
a
indicate
function of temperature and pressure (Kennedy, 1957)
but
ionic
in a liquid form in the upper mantle,
be present
it will
that
expected
is
conduction
overwhelm
to
electrolytic
conduction at mantle temperatures.
of
mobility
ions
compared
negligible
a
factor
to
effects of
The
sition.
by
from
a
relatively
in
changes
but
effect
change of
is the
to a
is
compo-
and
important when
pressure become
they
olivine
spinel
denser
such a change would
showed that
(1969)
this
temperature
solid structure
open
Ringwood
structure.
two,
of
An example
induce a phase change.
the
the upper mantle may reduce
found in
The pressures
occur at a pressure of about 130 kilobars, corresponding to a
of
depth
denser
about
400
structure
The
kilometers.
increases the
to
transformation
a
by a
conductivity of olivine
factor of about 100 (Akimoto and Fujisawa, 1965).
Based on rock conductivity data, we could theoretically
the
estimate
the
given
The
composition
kilometers,
plicating
melt
is
and
however,
the
are
not
information
temperature
continuously
to
the
put
profiles.
constraints
We
earth
a
expect
15
effect
the more
-
of
few
com-
partial
common procedure
and
use
this
composition
and
to
vary
on
the
the
conductivity
as a function of depth when
-
below
Further
known.
conductivity
earth's
earth
profiles.
possible
Hence,
the
temperature
the
well
the
is
situation
measure
of
temperature
in the upper mantle.
to
and
pressure,
composition,
of
profile
conductivity
electrical
the
variat ions are
due
temperature gradient but to exhibit discontinuous
to the
changes when there is a change in composition or state of the
earth.
profiles
tivity
and
of
1971;
called
method
relationships between
the
uses
variations which
geomagnetic
Keller,
a
used
have
Others
1983).
Roberts,
on
Keller et al.,
1971;
Cox,
1969;
Swift,
and
Madden
1966;
results
the
and
1966;
Rikitake,
surveys (see
magnetotelluric
based
mantle
upper
pressure
and
composition
of
estimates
and
crust
the
of
conduc-
electrical
proposed
have
researchers
- Several
the three components of the magnetic field, H, the horizontal
intensity; D,
data,
the
Before discussing the results,
vary greatly.
results
the
and
techniques,
processing
data
Schmucker,
quality of
The
1981).
Greenhouse,
and
Law
and
1963;
1963;
Eckhardt et al_.,
1930;
and Price,
(Chapman
intensity
and Z, the vertical
the declination;
we will
the
all
give a
brief review of the structure and nomenclature of the earth's
interior.
We often consider
(see
iron,
kilometers
Based
on
velocity,
way.
thick,
but
changes
the
rocks, and
crust
Continental
rocks.
earth
The upper
in
crust
oeanic
physical
can be
100 km (the
-
three
to consist of
a
is
only
about
such
crust
of
to
40
30
typically
is
properties
divided
outer
thin
as
in a somewhat
layers
metallic
of
primarily
composed
core
dense
of
a mantle
lighter
a
1.3):
figure
the earth
10
seismic
different
crust and part of the mantle)
16
-
km.
is
/e
/
L.it
I
/WIquCA
UII
U5LE4,
ItI%
Liquid
outer
core
5140 km
Core
Solid
inner
core
6371 km
Figure 1.a Cross Section of The Earth. Right Side Shows Compositional
Layers; Left Side Shows Divisions Based on Physical Properties.
The lithosphere
cal led the I i thosphere.
plates
ride
which
into rigid
which
asthenosphere
the plastic properties begin to
350 km where
extends to about
plastic
more
a
on
is broken
disappear.
in
conductivity profiles calculated in different
the electrical
Although differences in
studies.
diff erences
are substantial
We mentioned that there
data quality and methods of
impedance estimation could account for some of the
variation,
is
important.
is
In
figure
it does not represent
generalized;
usually
a
crust
less
conductive
a
(in
the
sense,
from
Below thi s there
less
are
rocks
the
where
There
resul ting
zone
rocks containing large amounts of water.
resistive
highly
is
profi le.
a global
near-surface
conductive
"typical"
a
this
that
emphasize
We
for
model
general
a
show
area.
continental
is
we
1.4
surveys
the
of
location
the
that
clear
it
bee
has
water
hence
and
porous
is
squeezed
I
more
conductive
Finally,
is
third zone
The
out).
some
higher
a jump
surveys have shown
i
but
defined
the
of
result
a
as
well
not
probably
tem pe ratures.
condu ct ivity at
in
about 400 km, possi bl y due to the phase chainge of oli v ine.
In
resistivity
prof i 1es
C)
are
profil es
show
we
1. 5
based
demonstrate
continental
areas.
figure
upor
large
the
crustal
areas, mobil
(1971)
Keller's
several
studies
The
for
stable
differe nces
plates,
i dealized
and
volcanic
Many zones of high mantle conductivity (as
associated
areas
wich
-
18
-
of
high
heat
flow
in
r
prof
and
Variation period
(Penetration)
Conducting sediments
and/or oceans
.2-50-m
0.1-100 sec
(5 km)
Resistive crust
10,0000 -m
Less resistive mantle
20 - 1000 'm
100-1000 sec
(30-40 km)
100-10,000 sec
(400 km)
Conducting mantle
.1-10 'm
100 sec - 27 days
(1200 km)
mw
Figure 1.4 Generalized Electrical Resistivity Model of a Continental Area
(after Hermance, 1973).
RESISTIVITY, ohm-m
10
10 2
10 3
104
10 5
106
0
DEPTH,
km
100
200
300[-
40oL
Figure 1.5 Highly Idealized Resistivity Profiles through the Crust and Upper
Mantle. Profile A Pertains to a Stable Continental Nucleus, Profile B to a Mobile
Crustal Plate, and Profile C to a Volcanic Rift Area. (from Keller, 1971)
that
the
fits
cools
it
thickens as
which
lithosphere
a
the hypothesis of
than
lithosphere which
for older
deeper
is
layer
conducting
the oceans
found
also
He
areas.
continental
stable
below
beneath
shallower
is
mantle- conducting zone
the
that
and concluded
plate
Pacific
the
on
(1980)
Filloux
melt.
collected by
data
analyzed magnetotelluric
Oldenburg (1981)
partial
of
regions
be
may
and
velocity
seismic
time.
with
The
the
beneath
zone
or
effect
shore
has
come
Anomalous
Parkinson
by
possible
one
is
ocean-edge
the
called
be
magnetic
fluctu-
for
several
(1962)
Schmucker
the world.
throughout
lines
to
effect.
noticed
first
ations were
and
coastal
the
conducting mantle
the
continents
oceans
what
for
explanation
depth of
the
in
difference
(1963)
showed
The
that the anomaly was present along the California coast.
anomaly
of
consists
inland.
which gradually diminish
are
by
reduced
15
Z-variations
enhanced
to
30Y
along
inland station such as Tucson.
by a band of
The magnitudes of H and D
the
shore
This effect could be
an
to
relative
caused
the
enhanced electric currents flowing beneath
ocean and parallel
mentioned
coast
the
along
to the shore resulting from the previously
continents.
The
conductivity
of
other
ocean
beneath
differences
conductivity
explanation
likely
(about
water
3
21
-
and
the
high
is that
mhos/m)
enhanced currents within the ocean and parallel
-
oceans
results
in
to the coast.
effects
Both
probably
disputed point
contribute
is which,
to
anomaly,
the
but
is dominant.
if either,
We now demonstrate how ocean currents could produce
the
observed effects;
argument
is
essentially the
currents within
the mantle.
Figure
magnetic
produced
a
Figure
been
field
shows the
1.6b
that
shown
for
by
total
1.6a shows
circular,
field
a uniform
a
around
same
the
for
induced
conducting
disk.
the disk.
It
ocean
hemispherical
the
the
has
edge
effect would enhance the vertical magnetic component by 20 to
30% of the
inducing field (Rikatake, 1966).
and 1.7b we
basement
show models of
is
entirely
homogeneous
to the
the coastal
and
ocean.
The
the
repulsion
concentration
continental
is
the
ocean
current
ocean.
primarily
The
the
ocean
enhances
magnetic
due
near-
ionospheric currents.
currents
current
is
from the
electric
deep
the
effect
anomaly results
in
horizontal
that
the
In figure
and
the
1.7a
fields
causes
just
the
near
a
off
the
vertical
and
the
coast.
assumes that the conducting region below the ocean
so deep
ocean.
of
shelf.
diminishes
This model
of
In
effect.
coastal
surface oceanic currents induced by the
Mutual
In figures 1.7a
by
this
currents flow primarily
in
the
1.7b there are conductive regions below the
continent,
In
telluric
but
at
the
case,
a
shallower
enhancements
telluric currents flowing
ocean.
-
22
-
in
depth
of
Z
beneath
are
the
caused
rocks beneath
the
5
60
-
20
--- -30
---
60
90
Figure 1. 6 a
Rikitake, 1966).
Magnetic Field Induced Around a Circular Disk (from
Figure 1. 6 b
Rikitake, 1966).
Total Magnetic Field Around a Circular Disk (from
)
Jy
IONOSPHERE 0
0
e
;
cm
Figure 1. 7 a
Coastal Effect Solely Due to the Ocean
(after Cox, et al., 1970).
Jy
0
IONOSPHERE
)
A
0
0
0 0
0
CRUST
CRUST
Coastal Effect Due to the Ocean and the Laterally
Figure 1 7 b
Inhomogenous Crust and Mantle (after Cox, et al., 1970).
- 24
effect
in
within the
(1970)
ocean
complicating the
argument
Peru.
in
a
the
entirely
Based upo n
roughly
est imated
the
observed
that
coastal
due
to
magnetic
currents
Schmucker's data
the electric fields in the ocean, Cox et
currents within
is
1.7a.
figure
,
and measurements of
al.
almost
is
California
ocean
concludes
(1963)
Schmucker
few
Richards (1970)
equal
the
and w ithin
is the
cases
from
c ontributions
mantle.
fact that no coastal
incl uding Vic toria,
Further
effect
Canada
and
analyzed c ata from Peru and concluded
that there is hic )hly conducting m aterial wi thin 160 km of the
ocean
bottom but
conducting matter
effect,
that electric
beneath
the
in
the
shallow
el iminates
the
coastal
current
Andes
flow
1 ike figure 1 .7b.
supporting a model
-
25
-
CHAPTER 2:
The
electric
collected
from
two
Palmdale,
about
50
the other
in
of
San
Fault;
electical
Palmdale
at
arrays
about
Both
have
resistivity
array
in
recorded
been
in
used
to
up
in
This
study
one
were
centered
of Los Angeles,
straddle
with
San
and
Andreas
changes
in the
earthquakes.
since
1977.
1977,
but
study
uses
in
south-southeast
the
study
operation
1979.
this
140 kilometers
associated
has been
until
in
California,
arrays
Hollister was also set
not
used
kilometers northeast
Hollister,
arrays
data
field
Fransisco.
the
ELECTRIC FIELD DATA
The
The
digital
data
array
data was
from
both
arrays for 1979 and 1980.
Each array consists of eight dipoles ranging
from
10
to
antennas.
with
50
The
silver
kilometers.
electrodes
chloride
potassium chloride
about four
consist
immersed
of
in a
and enclosed
in
feet long and are buried
starting about
1 ines all
Telephone
one
terminate
foot
in
under
the
a central
are
lines
a silver
saturated
The
location where
as
coated
solution
upright
surface.
used
mesh
a porous pot.
in an
in length
They
of
are
position,
telephone
the measured
voltage differences between the electrode sites are amplified
and passed
through
a
low
pass
seconds) to prevent aliasing.
figure
2.1.
The
Modules (TIM's) .
filter
constant
=
500
This is shown schematically in
recorded
data are
(time
by Telemetry
Interface
Once a day, the TIM's are queried and the
-
26
-
100K
-OUT
HI
10
IN
HI
IN
LO
10K
30K
1.
.002
100K
10K
.01
IA - INSTRUMENTATION AMPLIFER ANALOG AD522A
OA - OPERATIONAL AMPLIFER PRECISION MONOLITHIC
RESISTORS-1%
CAPACITORS <lmf 10%
>lmf 1%
GAIN=10
OUT
LO
TO 1000
FIGURE 2.1 ELECTRIC FIELD PREAMPLIFIER
OP-15
data (8 channels for each array, sampled every five minutes)
to
transferred
and
periodically
M.I.T.
these data are sent to
Tapes of
are recorded on a computer.
floppy
disks
on
an
HP9825 system.
Hollister A and
Two dipoles from each array were used:
B,
C and D.
and Palmdale
they are
the
the
and perpendicular
to being parallel
closest
locations
The
structure.
assumed
these dipoles because
We selected
of
the
segments of
Several
this study.
selected
data were
The criteria were
electric or magnetic data and
that
numerical
Bessel
longer
ranging in
time
length
five-minute
from
separate
hours,
filter
with
cutoffs at
scale
data
was
from 10
hourly
to
a
intervals,
and a 36 hour
to 40
based
days.
values
the segments of filtered data were
and last
of
in length from
and
minutes.
90
three
order
segments,
filtered
cutoffs
at
using
2
and
two
36
low pass.
To avoid undesired sidelobes
first
on
the
These were converted
and
with
bandpass
10
in
The shorter time
passed through a fifth
These were
hours.
used
amount
least an average
at
scale data was based on four sections ranging
to 20
to be
there be no gaps in
power. Two different time scales were used.
The
are
in figures 2.2 and 2.3.
shown
nine
dipoles
to
1OX of
in
the frequency spectrum,
tapered by multiplying the
the points by sin(10nt/2L)
the length of the data.
This window is shown
where L
is
in figure 2.4.
The resulting signals were converted to the frequency domain
-
28
-
370
122'
lIV
Unit Number
1
2
3
4
Description
Franciscan formation
Cretaceous marine (Great Valley)
liocene volcanics
Granitic
Tertiary non-marine
-
6
Mlesozoic ultrabasic
7
Tertiary marine
limestone
.
Pre-Cretaceous
or dolomite
Franciscan volcanics
9
UnnuMbered unitz are either Quaternary alluvium (e.g.
fNote:
the Santa Cla-ra Valley) or sirply unspecified (e.g. much of
the south.:estern corner of the map).
FIGURE 2.2: MAP OF COYOTE LAKE AREA, CALIFORNIA
SHOWING HOLLISTER ARRAY (AFTER THURBER, 1981)
- 27
-
15'
0
10
20MILES
MOUNTAINS AND HILLS ARE INDICATED
BY DARK PATTERN
FIGURE 2.3 MAP OF WESTERN MOJAVE DESERT REGION,
CALIFORNIA SHOWING PALMDALE ARRAY
-
30
with
a
fast
fourier
transform
from
(adapted
program
Claerbout, 1976).
Then,
the
effects of
the RC
filter on
the
electrical
data we.re removed using:
a + bj
where
a0
and
estimates, RC
frequency
in
bo
is
= (a0
are
the
Hertz,
+ boj)(-JRC2?f
the
time
(500
j=(-1)-1 / 2 , and
spectral
electrical
original
constant
(2.1)
+ 1)
a
seconds),
and
b
are
f
is
the
the
new
spectal estimates.
1-4
-
s in (107r T/ 2L)
-
I-I
L/10
9L/ 10A
L
-r
FIGURE 2.4 TAPERING WINDOW APPLIED TO
TIME SERIES BEFORE FFT
MAGNETIC FIELD DATA
CHAPTER 3:
the
only the
this study,
In
two
sites,
magnetic
field
at
Castlerock,
Castlerock
Unfortunately,
Francisco).
San
California (near
obser-
magnetic
was
observatory
nearest
The
vatories.
The
California.
from
obtained
were
data
Palmdale,
and
Hollister
was measured at
electric field
was shut down in 1974 and our electric dipole arrays were not
operational
1977.
until
Magnetic data was obtained from the World Data Center
Golden,
Tucson,
Colorado for
Colorado;
the observatories at Boulder,
Vi ctori a,
Arizona;
British
Honolulu,
Columbia;
It was
Hawaii; and Castleroc k, California for the year 1974.
in the form of
Z, vertical
grams,
H, ho rizontal
intensit y'.
The
copie s,
and
paper
two-and-one-half-minu te,
were
digitized
copies were
on
typed
t he
in ,
intensity, D, declination,
data was a
mixture
containing
tapes
the
values
magneto-
one-minute,
the
from
tapes were
the magnetic
and
of
and
The magnetograms
and hourly values.
HP9825,
in
paper
read
on
MIT's Multics system and transferred to the HP computer.
Time
domain
three components of
other stations.
o perators were
developed
to
predict
the Castlerock data from the data at
The details are given
in
appendix
one.
all
the
We
found that we obtained the best prediction operators by using
only Tucson and Boulder to predict Castlerock.
-
32
-
The
for
and
Tucson
'Tucson,
for
as
same way
to
converted
only
and
5-minute
up.
and
hours
D
renamed
Hme
(magnetic
tion).
The
horizontal
field
in
the
intensity,
The
is
magnetic
and
gammas
to
magnetic
H,
transform
fourier
converted
was
into
to 36 hours, and
data.
filtered
the
degrees),
(in
declination,
fast
and
window
to
applied
were
2
10 to 90 minutes,
The
filtered
and
data
hourly
segments were
The
data.
electric
the
three frequency bands:
(FFT)
to use
necessary
it was
values
three components of the magnetic data were processed
All
36
hourly
the
time.
predict Castlerock for the long-period data.
Tucson to
in the
so
1979-1980
for
Boulder
in
segments
many missing data
There were
fields at
over
remains constant
and Castlerock
Boulder,
This method
the magnetic
the relationship between
assumes that
an
generate
to
Castlerock.
at
field
the magnetic
estimate of
1980
and
1979
for
Boulder
data
appi ld to magnetic
operators were
prediction
east
referred
to
direcas
Hmn
throughout the rest of this thesis.
Typical plots of the filtered electric and magnetic data
are given
in figures 3.1
to 3.5.
of electrical
data from Palmdale
periods of 10
to 90 minutes.
the
signals
electrical
in
figures
between the
all
from
data
3.2
is
3.3.
filtered for
obvious.
is
The
same
the predicted magnetic
data
is
There
a
definite
electic and magnetic fields.
-
shows 16 hours
The strong correlation between
dipoles
four
3.1
and Hollister,
plotted with
and
Figure
33
-
correlation
The correlation
is
al so apparent
i n f i gures 3.4 and 3.5 wh i ch show magnet i c and
electric data for the other periods.
-
34
-
Hollister
Ho 1ister
Dipole
A
Pa mdal I e
Dioole B
Dipole C
Palmdale
Dipole
D
1 hour-
FiSur-e 3. 1
Electri
27 Oct
Fields at Hollister and Palmdale
Filter-ed for- 10 to 90 Minutes
1979
c
Hollister- Dipole A
Hollister Dipole 3
Horizontal
v-Magnetic
ManlQretio
Field
Decl ination
K~\
I
V
1 hour-
Fig ure
3.2
27 Oct
El ectr-ic and Magnetic Fields
10 to 90 Minutes
Fi lter-ed
1979
Palmdale
Dipole C
Palmdale
Dipole
Horizontal
Magnetic
C
Malgnetic
Field
Declination
V,
1 hour~
Figur-e 3.3
El ectr- i c
Fi lter-ed
and
Magneti
10
to
Fields
90 Minutes
27
Oct
1979
Hollister- Dipole A
L I
I i
i )&
:sS 4 er :iOo'
Ce
Hor i zontia
Magne t
ic
F i eld
Magnetic Declination
2 dce
Figurbe
3.4
E
ectr i c
Magneti
For-
Filter-ed
02-25
and
Nov
1979
to
36
Fields
Hour-s
Palmdale
Pa
mc"4 e
HorizontcI
.
-..
.-...
Dipole
i
1
o.,
C
e
Magnetic
Field.
Magnetic Declination
1K.-'
Fi gure
3.5
El ectr'ic
and
Fi1ter-ed
for- 36+
01-19
Feb
Magnetic
1980
Hours
Fie
2 days
TENSOR CALCULATIONS
CHAPTER 4:
We
have been
as
tensors.
impedance
magnetotelluric
used for several
the Ze and Zh
developed by J.
For the Ze method,
The
two
first
methods
They give what are known
The
third method was recently
( 1984).
Chave
we start wi th the definition of Z:
(1.28)
E = Z H
rows
the
Similarly,
from
estimates
of
two
the
represent
H
segments
frequencies
at
data
of
a
from
a
single
results by using both methods
the
magnetic
frequency
single
data
dipoles.
from
estimates
spectral
the
represent
electric
two
The columns of E and H
directions, magnetic north and east.
may
rows of E represent
The
and H are 2 by N complex matrices.
spectral
E
tensor and a function of frequency.
Z is a 2 by 2 complex
the
the
estimate
years.
estimates.
Park and A.
to
methods
different
three
used
or
time
neighboring
obtained
We
set.
different
the
best
For example, we had
together.
four sections of hourly data for Hollister, each at least ten
days long.
11.9,
The
FFT
10.9,
11.4,
yielded periods of
10.4,
10.0,
... 13.8,
...
9.7
estimate, we averaged over 6 frequencies.
of
11.6 hours,
11.9, 11.4,
of
24
we used the spectral
10.9, and 10.4 hours.
(= 4 X
6)
rows.
We
-
For
12.5,
each
Thus, for a period
estimates at
13.1,
12.5,
The matrix A was composed
decided
40
hours.
13.1,
upon
the
number
6
by
trial-and-error;
it was
the
smallest
number
which
impedances and phases which were relatively smooth
of
frequency.
is
similar
This method of
(or
possibly
gave
functions
using neighboring frequencies
equivalent)
to
smoothing
the
data
immediately after the fourier transform, a common practice
spectral
We
in
analysis.
postmultiply
both
sides of
1.28
by
the
conjugate
transpose of E:
EE = ZHE
(4.1)
Ze = (EE)(HE)~l
(4.2)
and solve for Z:
where (EE) and (HE) are 2 by 2 complex matrices given by:
EAE
EAEg
Ef =J(4.3)
EBEA
EBEB
an d-
HMN
A HMNEBJ
HE
=(4.4)
EB
HMNis
HMNEA
-
41
-
The estimate of Zh is calculated in a similar way except
that both sides of 1.28 are postmultiplied by H:
(4.5)
EH = ZHH
Solving for Z:
1
(4.6)
Zh = (EH)(HH)~
The
Park-Chave
decomposition of
the
uses
estimate
singular
the spectral
a matrix composed of
of the E and B fields to compute the MT tensor,
Tipper,
T.
value
estimates
ZpC, and the
We write 1.28 as two scalar equations:
Ex = Z11Bx + Z12BY
(4.7)
Ey = Z21XB
(4.8)
+ Z 2 2 BY
The Tipper is a complex vector, T =
[Tx, Ty]
defined by:
(4.9)
Bz = TxBx + TYBy
Tx
and
Ty
into
the
vertical
for the elements of
ZPC
and T at
B-field
horizont al
"tip" the
direction.
Our goal
is to solve
Park and Chave suggest forming the matrix A:
each frequency.
Ex
Ey
B
Bx
Bz
(4.10)
A1
v
-
42
-
where each row of A consists of a single spectr al
E,
Ey,
may
Bx, By,
and Bz.
correspond
either
estimates
data.
at
a single
As
with
estimate of
They say that the var ious rows of
to
frequency
and
Ze
frequ enc i es
neighboring
from
Zh,
we
differen t
used
A
or
to
segments
both
of
metho ds
simul taneousl y.
The solution of 4.7 - 4.9 is equivalent to finding three
linearly independent vectors x such that:
A-x = 0
(4.11)
A simple example of an eigenvector solution
Ey,
(Ex,
B>, By,
Bz) = (0, 0, a, b, -1)
In this case the tipper (T) equals (a, b)
In
complex.
general,
is:
the
solution
is
not
(4.12)
where a and b are
this
simple,
but
given the three eigenvectors we can solve for the six complex
scalars of Z and T.
The
least squares solution for the vectors x
in
(4.11)
is given by:
x = (ZA)
1 %b
(4.13)
where A denotes the conjugate transpose of A.
of
noise,
equation
4.13 would be
vector b would be all
non-trivial
(A)
is zero.
This
zero
equality and
if
the determinant
is equivalent to saying that (A)
In
to zero.
eigenvalues,
this problem,
corresponding
each
-
the
In this case, the only way
zeroes.
solution for x can exist is
eigenvalue equal
three
an exact
In the absence
43
-
we
of
has an
would
to
a
have
linearly
(A
independent eigenvectors x.
is
N X 5 so (AA)
is
5 X 5 and
has 5 eigenvalues.)
data always has noise so we never have eigenvalues
Real
exactly
I nstead,
zero.
to
equal
the
eigenvec tors corresponding to
positive square roots of
actual ly
to
have
and are hence complex.
(1970)
equal
empha s ize
p hase
T contain
tric ck
outlined
in
to the
did
that
not
the
informat ion
u se d the algorit hm of
We
the
and
We
and
as ZPC
eige nval ues
eigenval ues of (AA)t we
(Ar
form
eigenvec tors as well
Re insch
the
thr ee smallest
values of A are
singular
the
Since
of ,(AA).
three
the
select
we
Golub
appendix
and
3
to
cal cul at e the eigenvalues and e i genvectors of A.
We found the scaling of Ithe
We bel ieve
a lso scal ing the noise in
the electric
We est ima ted the noise in
the magnetic
this to be a result of
and magnet ic
fields to
be
fields.
ten
in the matrix A
for ZpC and T.
the resulti ng
influenced
E and B data
time s
values
greater
than
in
the el ectri c
fields
and scal ed the columns of A accordingly.
At this point
at
each
orthogon al
frequency.
in the data analysis, we
Our
tensors,
however,
components of E and H because our
have a t ensor Z
do
not
rel ate
electric
dipoles
were not perpendicular to each other or coincident with the
t
This can be seen byletting A = UAV (singular value decomposition). A is then
V.!U and AA is VA*UUAV or VA@V" . Thus, the singular values of XA are the
squares of the singular values of A. The singular values of a square Hermitian
matrix such as AA are also its eigenvalues.
-
44
-
as described
many
s tr ik e.
In
1967
Davis,
that
data,
sh own
and
parallel
oriented
dipoles
max im ized
to determine the principal direction of
structure or a two dimensional
one dimensional
angl e
is
We showed in chapter one that Z11=Z22=0 for a
current flow.
and
the
tensor
minimized
Zi
and
and/or
221
et
methods
are
He
modified
analysis
e i gen value
of
Lanczos
the reader
The
an
LaTorraca
us ing
the
shifted
(1961).
We
will
briefly
descr ibe the results of the work by Eggers
refer
has
by
methods
Eggers'
developed
tensor.
e igen state analysis of the magnetotelluric
(1985 )
real
For
Eggers (1982)
incomplete.
an
researchers
1977).
these procedures are not equivalent.
these
(Swift,
through
Other
al.,
the
to
surveys,
2 was r otated
222.
(Reddy
structure with
perpendicular
previous magne totelluric
1979)
212
that
tensors
in Appendix 2.
The next step
the
corrected this by rotating our
We
magnetic fields.
and LaTorraca;
we
to their papers for the de tails.
analysis of
standard eigenvalue
a matrix
A solves
the equation
(4.14)
Ax = Ax
where x are
matrix A must
its
A are
the eigenvectors and
eigenvectors orthogonal.
The
(equal
to
the eigenvalues will be real and
the
however,
the
If
be square.
conjugate transpose)
the eigenvalues.
it
is
not Hermitian,
A is
If
-
45
also Hermitian
-
eigenvectors
so-called
will
not
be
orthogonal.
matr i x,
defective
eigenvectors are parallel
In
or
two
the
more
case
or
of
of
a
the
and hence the eigenvector set does
not span the solution space.
Lanczos solved this problem by
defining the matrix S as:
A
(4.15)
0
S is
guaranteed to be Hermit ian and hence has a complete set
of orthogonal eigenvectors.
The matrix A need not be square.
In our case A becomes Z, the 2 by 2 MT impedance tensor.
eigenvalue equation for 4.15
is:
Sw =
We break
(4.16)
_w
the eigenvector w into two parts:
h[
so
that
The
e is
in
the
column
space
of
Z and h is
(4.17)
in
the
row
space:
Zh
=
(4.18)
Ae
(4.19)
Ze = -Ah
Since
Z
is
fields, we
defined
can think
as
the
ratios
of
electric
and
magnetic
of e as being the electric eigenvector
and h as the magnetic eigenvector.
-
46
-
Any m by n matrix
A can
expressed as a product
be
of
three matrices:
A = UJLV
where
U
consists
of
left
eigenvectors
of
and V contains the right eigenvectors of A. (In
where A
Reinsch (1970)
is
a
the case
the
are
's
the
This technique is known as singular value
eigenvalues of A.)
used
before, we
As
decomposition.
U = V and
and Hermitian,
square
is
A, AL
the singular values along the diagonal,
matrix with
diagonal
the
(4.20)
the method
of Golub
and
extended to the complex case (Appendix 3).
The decomposition of the MT tensor can be expressed as:
e2x
eIx
in
the
4.21
0
eIy
e2y
L
Z = EAH =
where
1
2Kh
* represents complex
are
complex.
h 'V
hI
(4.21)
2
J
conjugation.
Instead,
we
The
can separate
eigenvalues
them
into
a
magnitude and a phase:
e 1x
e2x
[A:
0
]eie9
hf
h
2=Etei OH=
e l,
e2y
A non-uniqueness resu
are,
in general,
out
L
e
A2 JL0
LaTorraca
phase.
47
thx hy
the components
because
-
I
-
j
(4.22)
of e (or
resolves
this
h)
by
requiring that the phases of e and h be defined so that e and
h have their maximum ampli tudes simul taneously.
If we take 'A > )2
the eigenvalues,
then
maximum and minimum possible
92
and
this
Physically,
says
just
(current) will
The
there
that
equal,
meaning
tensor
we should be
Hence,
eigenvalues
and
their
and
Zh'
the
defines
le
equal.
preferred
the
that
Z consists of four complex numbers or
field
phases
principal
eight
able to uniquely describe
with another set of eight real parameters.
the
no
is
the
In
parameters.
vary with direction.
real scalars.
it
smaller
and
induced by a unit magnetic
(voltages)
electric fields
angles 91
eigenvalues are
the
not
are
eigenvalues
the
the
In most two and three dimensional
direction of current flow.
cases
The
larger
these
of
layered earth,
1-D or
a
case of
four
all
influence
will
ratios.
the
of
give
and )2,
N1
The conductivity structure of the
eigenstates, respectively.
earth
IEI/IHI
phases
the
repesent
interpretations.
physical
simple
eigenstates have
The
In addition to
parameters),
(4
axis directions
LaTorraca
for
the
larger eigenstates of the electric and magnetic eigenvectors.
ge
gives the preferred direction of current flow.
parameters are
and
magnetic
Ee and
Ch,
the ellipticities of
for
eigenvectors
the
larger
The final
the electric
eigenstates.
Ellipticity is defined as the ratio of the minor to the major
axis of
the polarization ellipse.
The signs of Ee and Ch can
be used to indicate the handedness of the waves.
-
48
-
three methods and
We calculated the MT tensors using all
computed their eigenstate parameters
the
from
calculated
were
resistivities
apparent
The
as outlined above.
principal
e igenval ues:
wi th
P
in
seconds
and
(4.23)
.2PNI 2
=
PA
Logar i thmi cally
ohm-me ters.
in
pA
spaced averages (weighted by the coherencies) of the apparent
resistivity
and
phase
of
the
larger
plotted against period in figures 4.1
AI
eigenstate,
are
to 4.4 for Palmdale and
!Hol1ister.
The
significantly
phase for
phases
figures
different
Palmdale
for
show
impedance
The estimates of
tensors.
Holl ist er
are
4.4)
(figure
v ariable,
more
The esti mates of
the magnitude of the apparent resistivity at Palmdale
differ
frequencies.
for
by more
periods of
10
to
15
Zh
hours.
tha n one day).
similar
The
anomalies.
estimates strongly violate
will
order
of
magnitude
is
nearly
Also , Ze and Zpc are extremely
periods (greater
exhibit
an
than
(figure
at
some
Specifi cally, Ze and Zpc show a large increase
these periods.
4.3)
The
(figure 4.2) are fairly consistent.
especially at periods longer than 15 hours.
4.1)
yield
methods
three
the
that
large at
data
Hollister
Both
con stant
the
Ze
at
long
(figure
and
Zpc
the minimum phase cri ter ii on which
be discussed i n the next chapter.
-
49
-
We
bel ieve
that
estimates of apparent
only
the
Zh method
resistivity for our data.
these estimates in the remainder of
will
briefly
qives
use
We will
this thesis, but first we
possible
some
explore
reasonable
reasons
for
the
fields
each
differences in Ze, Zh, and 2pc"
We
assume
that
the
electric
and magnetic
contain a noise contribution:
E = EO
+ NE
(4.24)
H = H0
+ NH
If the electric and magnetic noise are uncorrelated, then:
NE-NH*
= 0
(4.25)
Electric and magnetic noise dotted with
itself, however, will
not give zero:
NE-NE* =
INEi
2
(4.26)
NH-NH* =
INHi
2
Thus, the Ze estimate, equation 4.2, becomes:
Ze = (EE +
INEi 2 ) (HE)~ 1
-
50
-
(4.27)
and
biased up
is
by
i n E.
noi!
in H:
4.6, is biased down by noise
As we
expect,
every
frequency for
INHi 2 y-l
(Hf4 +
Zh = (EII)
estimate, equation
The Zh
the values of PA are
(4.28)
larger
for Ze than Zh
at
(fi gures 4.1
and
and Palmdale
Hollister
4.3).
not
the
give
values
coherency
Even
comparable to the Zh values.
E totally accounts for
one and similarly for NH and Zh,
biased by
account
about
for
20%
the
f or
observed
but
Ze,
in
.9.
We
they
are
if we assume that noise in
Ze be ing less
than
each estimate would only be
Clearl y,
(1-.92) .
given
t ypi call y about
c oherency for
the
are
e stimates
Zh
The values vary but are
appendix 4.
do
the
of
coherencies
The
differences
this
in
cannot
alone
the
Ze
and
Zh
est imates.
We speculate that the differences may be related to the
distribution of
matrices,
(EH)
the noise
for
Ze
(HH)
and
the
the eigenvalues of
in
for
Zh.
If
the
inverted
noise
uncorrelated with the electric and magnetic signals,
the
be evenly distributed between
If
matrices.
which are
of
the
eigenvectors
two
it will
eigenvectors of
correspond
different orders of magnitude,
to
is
these
eigenvalues
the eigenvector
of the smaller eigenvalue may be dominated by noise and give
poor results (see Madden (1983) for a similar example).
-
51
We
and (HP)
ratio
calculated
condition numbers
matrices.
The
a
condition number
few
the
of
(EH)
is defined as
.of t he largest to the smallest eigenvalue (in this
there were
matr i c es
a
only
two
typically
eigenvalues).
had
a
We
condition
tha n the corresponding (HH)
l arger
is
for
prob ably
a
result
of
dipole s an d may account for
estimates.
A similar
found
number
matrices.
the
c ase
that
the
(EH)
about
5
t imes
This differ ence
coherency
of
the
elec tric
in the 2,
the differences
problem may explain
the
an d Zh
the anomalous
ZPC
estimates, but this problem should be studied further.
f igures 4.1
In
to 4.4 we
show the
overlap
sets of PA and 8 for periods of 25 to 40 hours.
represent
the same
fi lters
through
to
are
allow
not
(figure
4.1),
however,
there
scaling
mentioned
The
two
two sets
Hence,
The cutoffs of
enough
power
the
Zpc
are
estimates
large
2
the
1eaks
cutoff.
estimates to be comparable
For
the estimates.
in the
sharp.
overlap.
they
36 hours.
impedance estimates beyond the
expect the two sets of
in which
the
data sets filtered with a band pass of
to 36 hour s and a low pass of
digital
of
We
for periods
for
Palmdale
differences
between
We believe this to be a result of differences
of
earl ier.
the
The
A matrix
scaling
power in the frequency band.
(equation
was
based
4.10)
upon
which
the
hour data of the 36+ hour data set.
-
total
Hence, the 36 hour data of
2 to 36 hour filtered set was scaled differently than
52 -
we
the
the 36
All
three
discontinuity
are
fairly
in
between
PA
smooth
estimates
for
for
one
these
Palmdale
and
data
two hours.
periods,
around
-200
show
The
to
a
phases
-300.
Based on minimum phase, the small phases should correspond to
increasing
the
apparent resistivities.
apparent
Different
drop
data
sets
in
PA
from
one
were
used
to
Thus, we
to
two
calculate
do not believe
hours
the
is
10
real.
to
90
minute and the 2 to 36 hour tensors so a small discrepancy is
not unreasonable.
-
53
-
10 4
V
0
SA
0
AA&
00
A0
0 0
Li
-a
A
0
A
A0
0
A6000
0
0o 0
H-
10
0
0
oe0
Hl-
C/
0000
00
00ca
0
il
103
I
I
I
i
I ii
10 4
I!i I
10 5
PERIOD (SECONDS)
SYMBOLS
*
A
A
o
*
estimate, f il tered
ZPC estimate, f i I tered
ZE estimate, f il tered
ZE estimate, f il tered
ZH estimate, f i I tered
ZH -est imate, f i I tered
FIGURE 4.1:
for
for
for
for
for
for
10-90 minutes or 2-36 hours
36+
hours
10-90 minutes or 2-36 hours
36+ hours
10-90 minutes or 2-36 hours
36+ hours
APPARENT RESISTIVITY VERSUS PERIOD FOR PALMDALE
- 54 -
I
I
I
I
-101
0
0
-20
o
o0
A
o
0
-30
AA
-IN
Aa0A 0O
-40
A
00
-50
0
0
'o
y
0
-A
-60
-
a
0&a
AA
Ali
(n
0
0
-70
0
0
AA
00i i
11i
-80
io l
- f*
-90
105
10 4
103
PERIOD (SECONDS)
SYMBOLS
o ZPC
estimate,
ZPc estimate,
A
og
ZEE
ZE
ZH
ZH
estimate,
estimate,
estimate,
estimate,
FIGURE 4.2:
tered for 10-90 minutes
fi
f i1
I
fil tered
fi 1tered
fil tered
fil1tered
tered
for
for
for
for
for
or 2-36 hours
36+ hours
10-90 minutes or 2-36 hours
36+ hours
10-90 minutes or 2-36 hours
36+ hours
PHASE VERSUS PERIOD FOR PALMDALE
-
55 -
A
E
0
0
104
U
0
5)
Ld
Fw0
0
o
F-
z(n
w'
A
A
00
103 -0
00
0 000
o *
oo
A
8000
f1MC
00oo
0o
0
CL
K
-
I
0
IJ
0
I
1 11
I Afi
L
10 5
10 4
PERIOD (SECONDS)
SYMBOLS
O
*
A
A
o
0
ZpC estimate, fi tered
ZpC estimate, fi tered
ZE estimate, f iI tered
ZE estimate, f il tered
ZH estimate, f il tered
ZH -estimate, f il tered
FIGURE 4.3:
for
for
for
for
for
for
10-90 minutes or 2-36 hours
36+ hours
10-90 minutes or 2-36 hours
36+ hours
10-90 minutes or 2-36 hours
36+ hours
APPARENT RESISTIVITY VERSUS PERIOD FOR HOLLISTER
- 56 -
0
o
-20
0
a
g
0
000
cn
oo2
-40
w
('
0
z&
00
oo
-60
EQg
0
0
-80
00
-
-v
e
-100
-120
104
10 5
PERIOD (SECONDS)
SYMBOLS
o
ZPC estimate,
A
ZE
ZE
A
o
*
ZP
ZH
ZH
estimate,
estimate,
est imate,
estimate,
estimate,
FIGURE 4.4:
+1
tered
-Fi 1Itered
fi 1tered
tered
fil tered
fil1 tered
+or
for
for
for
for
for
10-90 minutes or 2-36 hours
36+ hours
10-90 minutes or 2-36 hours
36+ hours
10-90 minutes or 2-36 hours
36+ hours
PHASE VERSUS PERIOD FOR HOLLISTER
CHAPTER 5:
The
MODELLING AND INTERPRETATION
in a ppendix 4.
Palmdale are
given
of less than
about 20
used.
is
It
coherencies,
and
a pparent
t he Zh estimates for both Hollis ter and
resistivities for all
be
p arameters,
eigenstate
The
ninutes are
more
very erratic
difficult
periods for which the
estimates for
to
and w ill
determine
data are reliable.
periods
the
not
longest
For Palmda le,
the
apparent resitivity beg ins to increase with increasing period
Thi s goes against our
at about 60 hours.
apparent
resistivities
period
increases
mantle
which
should
the
and
EM waves
more
grows
continue
keeping
resistivity
from
in
conductive
mind
two
to
that
three
to
the
with
as
long,
and we
have
chosen
48
increase
hours
a
have
72 hours for
in
be
as
apparent
real .
Hollister, the data segments used for the 36+ hour
not
the
into
We
depth.
not
as
deeper
period of
days n ay
t hat the
decrease
penetrate
somewhat arbitrarily chosen a longest
Palmdale,
intuition
For
data were
the
longest
period.
The
1wav e
ellipticity
Nearly
all
is
the values of
el ec tr ic field, are
and Ho llister
ellipticity
.001
between
studied
here.
of the pol arization
the
E,
and
This
(see appendix 4).
the electric fields are
periods
a measure
.04
elli pticity
for
both
of
of
of the magnetic field,
-
58
the
a
the
Palmdale
finding indicates that
close to linear polarization for
Most
of
values
are between
for
(h,
.02 and .4
the
the
for
the magnetic fields
are
the electric
fields.
This
magnetic
source
f iel d
i ster and Palmdale, meaning that
Hol
f its
the
insensitive
struc ture
conduct iv ity
local
the
to
a
of
assumption
standard
relat ively
than
polarized
elliptically
more
and a n electric field distorted by loc al features.
of
the
the pri ncipal
re,
Palmdale
'e-s for
angles
to
relative
are
are
be tween
the
position
d irection
current
gives
a preferred
which
is roughly perpendicula r
strike for the Palmdale
geological
The values
pol e A is
Hollister's
direction
80 south
about
of
the
to
perpendicular
be tweer
is
Ithe
in
coastli ne
(Los Angeles
the
and
-20
-50.
gi vi ng a preferred
whi ch
west
of
south
of
west of south.
area as 300
50 south of west,
-200
estimates
(1981)
fall
f or Hol 1 ister
1e
west
350
of
is
D which
dipo le
the coastlin e
to
LaTorraca
expect.
we
as
These
Taking a n average value of
oriented 350 south of west.
area)
-250.
and
-150
of
wh
Nearly all of
gives the preferred direction of current flow.
the
direct
e igenvector
electri c
the
of
eigenstate
larger
is
parameter
Another useful
approximately
(San
Hol l ister
Francisco) area.
Based
upon
appendix
4
the
a nd
logarithmically
we have estimated the
averages plotted in figures 4.1 to 4.4
resistivities
apparent
frequencies
fit
by
table
5.1
to
in table
forward
is
the
5.1.
Fphases
and
Thi S will
The
modelling.
similarity
-
(using
be the
most
be twe en
59 -
spaced
data we
obvious
the
for
Zh)
six
attempt
feature
Hollister
of
and
Palmdale
data.
features do not have a significant
are near
the ocean so
the
Both stations
influence.
ocean-continent
geological
local
the
that
suggests
Th i s
could be
contrast
important.
APPARENT
TABLE 5.1:
RESISTIVITY AND PHASE
I
Palmdale
Per i od
pA (ohm-m)
:20 mins.
2500-3000
-17
-
1 hour
4800-5300
-16
3 hours
5000-7000
9 hours
8 (deq),
Hollister
8 (deq)
1
PA (ohm-m)
-21
I
2800-3200
-10
-
-23
-
-20
I
5800-7000
-17
-
-19
-22
-
-30
I
6000-7500
-25
-
-36
10000-13000
-40
-
-50
I 11000-16000 -29
-
-47
1 day
7000-8500
-44
-
-47
I
9000-12000 -38
-
-45
2 days
3 days
1 10000-11000 -60
-
-78
7500-11500
-75
-
-84
Reddy et
Gabr i e l s.
to
al.
conducted
found apparent
They
strike)
(1977)
about
of
1000
resi
ohm-m
at
MT
survey in the
San
(perpendic
1ar
ivities
a
one
second
increasing to about 3000 ohm-m at 1000 seconds.
give
any
seconds
The fact
phase
agrees
information.
Their
20
rminute
that PA is
casts doubt upon
phase
of
-300
our
with
to
estimate
(1200
period,
They did not
of
pA at
second)
1000
estimate.
slowly inc reasing from 1 to 1000 seconds
our
-400
value of
would
-200 for 9 at
be more
minimum phase.
-
60
-
20 minutes.
appropriate
A
based upon
We wrote
our Apollo 320 computer.
of
a
mode 1
2-D
forward modelling program on
a two dimensional
the
in
input
The
form
program consists
to the
The program
des ired conduct ivities and a set of frequencies.
use s
transmi ssion
a
In
str icture.
this scheme, the electric field is represented
eac h frequency
relaxation until
as c onjugate gradient
above
E/H using
it is equal
We
program.
10
km
layer
will
apparent
is
strike
to
used;
example
1000
with
The
ohm-m
of
ohm-m
10
resistivities at
It
consists of a
a
50
,
(representiing
material
the
calcul ated
The results are given
.1
second
resistive
the
10 periods rangi ng from
-
km
(represent ing the conductive
program
modelling
material
a
modelling
forward
is shown is figure 5.1.
layer
seconds (3.2 years).
the
using
concepts
important
crust), and a 1 ohm-m half-space
mantle).
in the data
of pA coul d have been
some
illustrate
The model
surface
of
with
to twice the phase of E/H.
one-dimensional
simple
phase
apparent
calculated
is
the E field perpen dicular
The
eigenstate).
(larger
block
below the
is
the
of
magnitude
surface
each
the error
The phase corresponding to 81
equation 1.26.
the phase of
the
Then,
level.
resistivity
iterates using a technique known
program
the
At
field becomes a current.
by a voltage ar d the magnetic
desired
conductivity
the
represent
to
network
the
of
blocks
rectangular
of
-
10
surface
to
in table 5.2.
108
RESULTS FOR 1-D EXAMPLE
TABLE 5.2:
10
12.3
-45.9
100
14.7
-22.1
300
36.8
-21.8
1000
68.2
-45.3
3000
42.3
-70.4
104
14.2
-80.7
105
2.3
-67.5
106
1.3
-51.9
107
1.1
-47.0
108
1.0
-45.5
and imaginary parts of an
The real
are
Phase (degrees)
(ohm-m)
Res.
App.
Period (sec)
not
(1981)
Kaufmann and Keller
independent.
relationship
electromagnetic wave
the
between
and
amplitude
phase
phase
or
amplitude
other can be calculated.
"minimum
phase"
theory.
For
spectrum,
known
is
we
but we can still
If either
frequencies,
all
the
The EM waves are said to behave the
term
a
criterion,
MT
for
the
EM wave
of an
propagating through a horizontally-layered medium.
the
derive
never
have
used
the
in
digital
complete
filter
frequency
make some predictions of the phase
-
62
-
a
For
vice-versa.
or
resistivity
apparent
the
given
homogeneous earth, we can use equation 1.23 to obtain:
[4Kaufmann
treat
(1981)
Keller
and
1ayer over a half-space.
resistivity
of the half-space
If
the
shift
is
-900.
shift
than
less
be
will
for
a
the
if
the phase shift is
the
conductor,
phase
the phase
of
resistivity
apparent
for
450
increasing with
increasing with
that
the absolute value
general,
In
They show
perfect
a
is
half-space
00.
cases
infinite,
is
-450.
be
limiting
the
homogeneous
(5.1)
will
H
and
E
between
shift
phase
the
Hence,
1 2
Gr
than
450
illustrated by
the
greater
period and
for decreasing apparent resistivity.
The minimum phase relationships are
-460,
indicating
the
At
results.
1-D model
apparent
the
that
constant.
The skin depth for
is 5 km.
Since
the
should primarily see
of
12 ohm-m
top
is
thick,
10 km
10 seconds
At
the
a period of
100 seconds,
the
layer,
the
wave begins to see more of the second (resistive)
apparent
resistivity
drops to -220,
indicating an
At 300 seconds,
the
phase
increases
increases
ohm-m,
at
at
1000,
The
-220.
but
-
the
and
phase
increasing apparent resistivity.
increases
the apparent resistivity
remains
to 68
15
to
EM wave
the value
Hence,
Just the first layer.
is
almost
is
resistivity
10 ohm-m material at
layer
is reasonable.
phase
the
period
second
10
63
the
-
apparent
phase
to 37 and
resistivity
increases
to
-450,
data at
3000
seconds
indeed the case.
the
more
(42
apparent
and -700)
half-space
the wave
of
resistivity
drops
(14,
For
and
periods
almost
107
of
no
seconds,
the
on
the
apparent
resi stivities
the apparent resistivity versus frequency
In
is small
our
(increasing
e xamp 1e ,
The
seconds.
section
(decreasi ng PA
foll ow
and
the
the data
phase
pA.
would
knowledge,
no
and
100
phase
The phase
increases
is
At periods of 2 and
The
the
300
angles
has
at
clearly
and
2
proven
-
(table
3
that
64
do
-
20
branch.
1 day
3 days pA levels off
large
nc t behave
day
for
period
crustal
small
is
a period of
the phase shifts are
data
predict
one
T his
with
begins t o drop at
increases, but
a falling
branch.
Pa lmdal e and Hollister
1 hou r, and 3 hours.
for both stat i C ns.
even
the
this case.
for
resistivity
The appar ent re sistivity
or
in
the minimum phase cri ter i on.
appare nt
minutes,
in which
of
large
and
region of
the crustal
periods
have
is referred to as the mantle branch--periods
gener al
5.1)
The
(1.1
The
curve
the cur ve with
of
of 3000 s econds and larger
In
cal led
inclu de
would
this
is
pA)
the
layers
upper
108
1.0 ohm-m) and the phases (-47.00 and -45. 50).
phase
and
-680, and -520).
and
influence
106
1.3 ohm-m).
phase shift remains greater than -450 (-81 0,
At
to
104
the mantle
into
2.3,
is
is beginning to see
(mantle).
penetrates
this
that
show
At this point, the wave
conductive
seconds more
ohm-m
The
is turning over.
meaning the apparent resistivity curve
periods.
indicating
as
minimum
To
3-D structures must
our
obey
the minimum phase criterion.
2
and
3
earth,
data
day
it is possible
Hence,
represent
accurately
the
but we bel ieve that pA and/or 8 are
trust the
tend to
We
per iods.
resistivity because
apparent
that
the
of
the
response
in
error at
these
than
phase estimate more
the
branch should give a
the mantle
falling pA with increasing period.
Our results are very different
IMT
both
on
the
land
and
in
the
typically begins at periods of
on
old
modelling program.
resulting
phase
apparent
His
was
We used Oldenburg's model
for
in
structure
our
in figure 5.2 and the
resistivity
are
plotted
The mantle
between 24 and 72 hours.
begin until
branch
both Palmdale and Hollister beg ins at about 9 hours.
data
forward
can
be
thought
continent and ocean cases.
as
of
The
a
compromise
between
resistive zone in
We shall
show
is only 200 ohm-m.
about
three orders of magnitude too low to fit our data.
try
are many possible 2-D models that we could use
to fit our
where
model.
to
data.
begin
We
looking
discussed
Fortunately, we
in parameter
previous
-
65
do have
space
studies
for
of
the
Oldenburg's
this value
that
for
Hence,
model
There
in
The mantle branch for Oldenburg's model does not
figure 5.3.
our
branch
data
i s shown
The model
and
mantle
Pacific.
oc ean
years)
million
(72
The
less than an hour for surveys
the
in
analyzed by Oldenburg (1981).
an
ocean.
few ocea n MT surveys was conducted by
1980)
and
(1977
Filloux
the
of
One
land.
than other studies using
some
is
to
idea of
a
suitable
the
earth's
model
starting
by
given
on
Herman ce
information for a starting
geology also prov.ides some useful
model
is
conducti ve
very
.3
average value of
to
compared
the ocean.
rock
and soil.
star t i n i
Our
is
ocean
the
t he
mod el s of
Our
sediments.
is
for Pal mdal e
model
Immediatel yb el ow
5.4.
The
ocean
direction)
current
resistivity of
the
is
an
the ocean
for
in
shown
in
located
layer
surface
figure
conductive
layer of
a
only
and sedimenti s are
to
closest
oriented
is
(which
Palmdale
used
We
Electrode
approximate but are satisfactory for our purposes.
D at
resis-
We used bathymetric c harts of the
ohm-m.
Cal iforn i a coasti ine to get a staircase model
depth.
Ocean water
salinity.
and
temperature
varies wi th
tivity
is
obvious feature
most
The
.
local
The
suggested for the Palmdale area.
LaTorraca (1981)
model
the
and
1.4
figure
in
(1973)
structure
general
the
of
combination
a
We based our
chapter.
first
the
in
conductivity structure
hence,
granite;
should be
preferred
the
the
on
order
the
of
the 1000 ohm-m which we have used in our starting model.
Many
Palmdale.
of
the
finding
on
concentrated
We
should
results
A
is
also
apply
located
Hollister's
electrode
Hollister is
about 75 km from the edge of
to 110 km for Palmdale.
to 36
tensors
km
long.
represent
We
the
to
in
granite.
the ocean compared
of
response
-
in
the dipoles themselves are from
interpreting
are
for
Hollister.
These distances can only be used
an approximate sense because
11
models
acceptable
66
-
the
the data
earth
at
as
a
if
the
single
poi nt ;
this
of
the
of
the
is
not
dipoles.
There
Hollister
difference
is
sedimentary
mentioned
true because of
exactly
and
the
Palmdale
Los
regions.
Angeles
area
between
earlier,
the
Basin,
Palmdale
we
chose not
model
for Palmdale,
There
is
Humphreys,
to
include
but we
in
the
local
geol ogy
The
most
obvious
a
the
the
( ~'15
deep
ocean.
data
al.,
for
the LA Basin
velocity zone)
is
for
we
Palmdal e
features are not important.
include
1984)
km)
As
it
in
in
our
starting
a later mode 1.
seismic evidence (Hadley and Kanamori,
et
This slab
and
similarity
and Holl ister suggests that local
Thus,
in
differences
are
the finite length
a
down-going
cool
1977 and
sl.i ab
(high
in the regions of both Hollister and P almdale.
believed
expect
the
mantle
material
slab
to
to
be
due
be
a
more
its
include a resistive slab
subducting
resistive
lower
plate.
than
We
the
temperature.
su rrounding
We
in the starting model,
would
did
not
but we study
its effects later.
The
apparent resistivities
and phases for
our
model
and Palmdale data are plotted in figure 5.5.
this
model
does
not
give
a
good
fit
apparent resistivities for the model
The
periods.
phases are
about 300
to
our
at
Clearly,
da ta.
a t all
are too small
too large
starting
The
six
th e shorter
periods.
The
conductive
Gabriel
location
oceanic
Mountains
and
conductivity
sediments
were
the
and
only
-
67
-
of
the
model
the
ocean
presence
of
parameters
and
the
the
San
wh i ch
we
and
thickness of
the
apparent
of
change,
too much.
pA's)
the San
re sistivi ty of
the ocean mantle more
We made
Gabriels.
hence
the
to decrease
To compensate we had
turnover
This
hours.
(and
vol tages
the
incr eased
howe ver,
9
at
curve
resistivity
resistivity
desi red
the
to give
crust
the
the
We had to increase
to be fixed.
cons idered
than the
ie
conductiv,
cor.tinental mantle, although this was not really necessary as
is
resulting model
The
show.
we shall
in
shown
fiqure 5.6.
The apparent resistivity and phase are pl otted in figure 5.7.
large
the
is
is
resistivity
Ithis
for
need
The
resistivity.
crustal
model
this
feature of
important
The most
illustrated by table 5.3 which shows the phases and apparent
cal culates
model 1 ing program
the model
(continent and ocean).
for
ocean
the
gre.ater
with
ocean
hours).
72
than
period
highly
the
600,
from -140
as
we
resistive
ocean
distance
to
changes
Ranganayaki,
1980)
expect
would
crust
it
phases,
apparen t
the
and
from
ocean
phases
are
at 20 minutes to
however,
minimum
creates
crustal
the
high
resi st i v i t i es
a
takes for crustal
in
of
the
r eflecting
The
itself.
end
each
at
ap parent resistivities
1ow,
very
continent
The
distance (the
readjust
The
to our data (increasing
comparable
at
are
of
conductivity
-720
edge
so lu tion
a 1-D
forward
The
model.
the
of
surface
resistivities across the
are
decrease
phase.
large
all
The
adjustment
current levels to
conductance,
see
which brings the ocean phases to Palmdale.
-
68
-
TABLE 5.11
SURFACE APPARENT RESISTIVITIES AND PHASES ACROSS MODEL 5.6
The apparent resistivities are in ohm-m and the phases are in degrees.
The first entry for each period gives the apparent resistivity and phase
for the 1-D continent solution; the last entry (#33) is the 1-D ocean
solution; the other entries scan across the model and should be read
left-to-right and then top-to-bottom. The table at the bottom gives
the widths of the blocks and also should be read left-to-right and then
top-to-bottom.
419.51
2422.91
2948.27
3417.68
2565.27
0.40
0.10
0.11
0.59
-82.2
-47.0
-45.2
-44.0
-42.8
-44.9
-61.8
-58.8
-14.4
796.98
2646.32
3057.98
3548.93
0.38
0.15
0.10
0.14
20 Minutes
-62.9
1485.60
-46.2
2742.68
-44.9
3172.45
-43.7
3686.50
-45.6
0.40
-51.0
0.16
-61.5
0.10
-54.8
0.23
-52.5
-45.8
-44.6
-43.4
-45.3
-50.7
-61.2
-44.7
2042.01
2843.32
3292.38
3840.14
0.41
0.15
0.11
0.50
-48.7
-45.5
-44.3<---Palmdale
-43.2
-45.0
-51.7
-60.4
-25.2
146.53
2754.49
3533.95
4241.98
3298.49
0.49
0.07
0.09
1.54
-87.1
-33.8
-32.5
-31.6
-30.7
-31.9
-46.3
-43.1
-13.2
522.32
3084.19
3698.77
4441.24
0.46
0.16
0.08
0.13
1 Hour
-50.1
1415.98
-33.2
3227.09
-32.2
3871.20
-31.4
4650.52
-32.4
0.49
-36.2
0.17
-46.0
0.08
-39.2
0.29
-38.6
-32.9
-32.0
-31.2
-32.2
-35.9
-45.6
-31.0
2200.42
3377.14
4052.18
4882.75
0.51
0.15
0.08
1.04
-35.2
-32.7
-31.8<---Palmdale
-31.0
-32.0
-36.8
-44.7
-18.9
50.59
4929.99
6457.67
7852.44
6184.63
0.91
0.11
0.14
3.60
-86.4
-32.5
-31.9
-31.5
-31.1
-31.6
-38.6
-36.9
-22.5
667.75
5574.30
6782.08
8246.94
0.85
0.28
0.11
0.22
3 Hours
-41.1
2338.86
-32.2
5855.62
-31.7
7121.65
-31.4
8660.90
-31.8
0.90
-33.5
0.29
-38.4
0.11
-34.9
0.56
-34.7
-32.1
-31.6
-31.3
-31.7
-33.4
-38.2
-31.0
3851.09
6149.26
7477.83
9119.12
0.94
0.26
0.12
2.33
-33.1
-32.0
-31.6<---Palmdale
-31.2
-31.6
-33.7
-37.7
-25.6
17.81
6623.42
8720.70
10637.10
8405.48
1.23
0.13
0.19
5.43
-84.1
-43.7
-43.5
-43.3
-43.1
-43.3
-46.4
-45.7
-39.7
818.09
7508.10
9165.69
11179.46
1.15
0.37
0.14
0.28
9 Hours
-47.6
3080.82
-43.6
7892.10
-43.4
9632.58
-43.3
11749.68
-43.4
1.22
-44.2
0.39
-46.4
0.14
-44.8
0.77
-44.7
-43.6
-43.4
-43.2
-43.4
-44.1
-46.3
-43.0
5145.03
8295.94
10124.20
12380.39
1.28
0.35
0.16
3.33
-44.0
-43.5
-43.3<---Palmdale
-43.2
-43.4
-44.3
-46.1
-40.6
7.38
5348.13
7051.29
8611.38
6810.23
-78.2
-58.6
-58.5
-58.4
-58.3
644.89
6066.26
7414.21
9051.89
0.93
24 Hours
-60.4
2473.37
-58.5
6378.44
-58.5
7793.98
-58.4
9514.70
-58.4
0.99
-59.0
-58.5
-58.4
-58.4
-58.4
4148.00
6707.88
8192.15
10028.47
1.03
-58.7
-58.5
-58.4<---Palmdale
-58.3
-58.4
1.00
0.11
0.15
4.70
-58.4
-60.0
-59.6
-54.0
0.30
0.11
' 0.23
-58.8
-59.9
-59.1
0.31
0.11
0.62
-58.8
-59.9
-58.2
0.28
0.12
2.74
3.39
2668.49
3518.79
4294.86
3397.19
0.50
0.05
0.07
2.50
-62.3
-72.7
-72.8
-72.8
-72.7
-72.8
-73.5
-73.4
-71.9
322.23
3026.70
3696.72
4515.55
0.46
0.15
0.05
0.11
72 Hours
-72.7
1235.85
-72.8
3183.49
-72.7
3886.65
-72.8
4745.61
-72.8
0.49
-73.1
0.15
-73.7
0.06
-73.2
0.31
-72.7
-72.8
-72.8
-72.8
-72.8
-73.2
-73.5
-72.8
2070.63
3346.07
4080.21
5002.48
0.52
0.14
0.06
1.34
Block Widths (kilometers):
1000.000 500.000 200.000
100.000
20.000
20.000
20.000
20.000
20.000
20.000
20.000
30.000
20.000
20.000
50.000
100.000
-58.9
-59.8
-56.9
-72.8
-72.8
-72.7<---Palmdale
-72.7
-72.8
-73.3
-73.5
-74.5
50.000
20.000
20.000
20.000
20.000
20.000
20.000
30.000
20.000
20.000
20.000
20.000
300.000 1000.000 3000.000 3000.000
-
69
-
150 ohm-m resistivity for
The
the San Gabriels in model
5.6 is not geologically reasonable (a more reasonable granite
resistance
of
is
the current
the
in
km)
3
(upper
layer
surface
the San
Gabriels.
probably bypassing the San
Gabriels,
area with conductive paths around
Palmdale
Much
the
modelled
(1981)
LaTorraca
effects.
three-dimensional
to
this
attribute
We
ohm-m).
2000
and
300
between
be
would
resulting in the low apparent resistivities there.
We
tried
increasing the conductivity of the
from
.1 to
(all
other model
expected,
periods.
the
The
change
pA at
had
no
almost
figure
5.8
5.6).
As
120 at 24 and 72
the
longer matches
no
hours
72
to fitting the
This model comes closer
72 hours but
at
resistivity
apparent
The
shorter
the
at
effect
phases were decreased 70 and
increased about 20%.
Palmdale
in
shown
parameters were the same as model
respectively.
hours
results are
The
ohm-m.
1.0
half-space
Palmdale
phase.
our data with a one-dimensional mantle.
We tried fitting
We
used layers of
600 ohm-m
the continent mantle used
1 ohm-m.
increased
The
the
compensate, we
to 110 ohm-m.
increase
in
if
and 200
model
ohm-m,
resistivities
decrease
the resistivity of
-
70
at
all
the
of
periods.
San
To
Gabriels
is given in figure 5.9 and
in figure 5.10.
-
as for
of the ocean mantle
apparent
the plots of pA and 8 are shown
same
5. 6 , and a half-space
the resistivity
The resulting model
the
We added a 10,000 ohm-m resistive zone
represent
figure
a
and
5.11
plotted
in
5.12.
higher
than
for
Thus,
our
slab.
subducting
The
model
the
apparent
resistivity
The
apparent
resistivities
model
5.6;
to model
is
data allows for but does not
phase
are
about
10%/
are
about
require a
to
in
shown
and
the phases are
5.6
the
same.
subducting
slab in the area.
Our
ocean
includes 20 ohm-m material
next model
to represent
at all frequencies by about 50%X.
resistivity
Apparently,
current
the
of
the
presence
to stay near
conductive mantle.
the
of
Gabriels
the
basin
surface rather
is
shown
data.
the
resistivity
Model
5.15
of
is the
the ocean
200,000 to 20,000 ohm-m.
this
does
not
resistivity
come
causes
more
than going
in
crust
ohm-m.
of
the
into
the
figure 5.13 and the
to
the
is
for
in
that
from
the
The
location
the ocean.
a loss of current
resistivity curve
figure 5.16 decreases with period for all
71
data.
enough by
The apparent
-
decreased
our
small
distan ce results
phases.
except
in figure 5.16 show that
matching
too
5.6
has been
i nfluenced
to be
The smaller adjustment
in
130
same as model
thickness product
in
to
that clearly does not fit
The plots
close
representing Palmdale
and a change
of
and phases are plotted in 5.14.
We conclude by showing a model
the
addition
To compensate, we decreased
San
Our model
apparent resistivities
the
to
increased the apparent resistivities
this conductive material
the
The
Los Angeles Basin.
the
next
periods from 20
minutes
to
72
apparent resistivities by
San
Gabriels,
curve (i.e.
but
only
not
resolve
the
the
change
Hence,
the phase structure).
is
compensate
increasing
this would
very resistive crust
can
could
We
hours.
required to fit
for
resistivity
the
small
the
shape
of
the
of
the
we conclude that a
our data.
resistivity-thickness
We
really
product;
a
400,000 ohm-m, 50 km thick crust would also approximately fit
our data.
-
72
-
10
km
10 ohm-m
1000 ohm-m
50 km
1 ohm-m
Hal f-space
FIGURE 5.1:
THREE-LAYER MODEL
-
73
-
3 km
Ocean
.3 ohm-m
50 km
200 ohm-m
50 km
150 ohm-m
50 km
50 ohm-m
150 km
20 ohm-m
100 km
40 ohm-m
200 km
30 ohm-m
Half-space
10 ohm-m
FIGURE 5.2:
OLDENBURG MODEL FOR OLD OCEAN
-
74J
-
T
71
101
100
10
104'0
3~
PERIOD (seconds)
-10
-1
-2C
-25
-3
-
-35
-4C
rv
-4-E
105
FIGURE
5.3:
T04
PERIOD (seconds)
105
APPARENT RESISTIVITY AND PHASE FOR OLDENBURG MODEL
-
75
-
Palmdal e
110 km
Ocean
1000 ohm-m
.3
ohm-m
5 km
San Gabriel Mountains
30 km
3 ohm-m
I
10,000 ohm-m
(Crust)
500 ohm-m
(Man t 1e)
400 km
1.0 ohm-m
(Man t 1e)
Half-space
FIGURE 5.4:
STARTING MODEL FOR PALMDALE
-
76
-
3 km
CLC
<
ca.
10'
EL
PERIOD (seconds)
-20
-a
-30
-
-40
-70-
i03
105
PERIOD (seconds)
FIGURE 5.5:
MODEL 5.4 (U)
AND PALMDALE (9)
- 77 -
Palmdale
~
110 km
I
_
5 km
150
Ocean
_
I
3
ohm-m
I
I
ohm-m
_.3
3
I
I
San Gabriel
Mountains
3
150 ohm-m
I
200,000 ohm-m
100 km
Crust
50 km
600 ohm-m
6 ohm-m
100 km
200 ohm-m
2 ohm-m
Half-space
. 1 ohm-m
FIGURE 5.6:
ACCEPTABLE MODEL FOR PALMDALE AREA
-
78 -
I
3-1
0'
O
Q
3
0D
110
PERFOD (seconds)
5
-20
-30-
ED
Fn
I-
-50
-
LL~
-70
-
10C4
105
PERIOD ,seconds)
FIGURE
5.7:
MODEL 5.6 (C)
AND PALMDALE (*)
. 79 -
7-
zH - 5 -
10)5
10104
FERIOD (seconds)
L
<-
-4 -
-45
-75'
-65
-70103
o5
10 4
PERIOD (seconds)
FIGURE 5.8:
MODEL 5.6 WITH 1 OHM-M HALF-SPACE
-
80
-
V1)
AND MODEL 5.6
(U)
Palmdale
110 km
I _Ocean
I
5 km
3
110 ohm-m
I
I
ohm-m
_.3
3
I_
1
_
_
3
110 ohm-m
San Gabriel Mountains
200,000 ohm-m
100 km
Crust
50 km
600 ohm-m
100 km
200 ohm-m
Half-space
1.0 ohm-m
FIGURE 5.9:
MODEL WITH ONE-DIMENSIONAL MANTLE
-
81
-
I
I
3
I
£
:2
E
L
11
-i105
4
PERIOD (seconds)
-20'
-30-
-40'50
4' -60,
IL
-70
,
-R0',',
03
10
104
PERIOD (seconds)
FIGURE 5.10:
MODEL 5.9 (N)
-
AND PALMDALE
82 -
(0)
Palmdal e
45-
110 km
Ocean
I
1
5 km
150
3
ohm-m
I
I
.3
3
I
I
ohm-m
3
150 ohm-m
San Gabriel Mountains
200,000 ohm-m
100
km
40 km
<------ >
Crust
I
50 km
600 ohm-m
110000
I ohm-m
100 km
200 ohm-m
I
1
I
I
I
600
I
200
I
I
I
I
6 ohm-m
2 ohm-m
90 km
Half-space
.1 ohm-m
FIGURE 5.11:
MODEL WITH RESISTIVE SLAB
-
83 -
I
1
_
3
1Gt ~i1
9F
V)
7
m
6
LJ
5L
z
iv
4
104
103
105
PERIOD (seconds)
-3
V
V
-35
-40
-am
Q
C5
5l
-6
Q-
-7
1O
10 5
PERIOD (seconds)
FIGURE 5.12:
MODEL 5.11 (.) AND MODEL 5.6 (N)
-
84 -
Palmdal e
110 km
I
5 km
I
130 ohm-m
I _Ocean
I
20 ohm-m
3
1
I
.3
3
I
San Gabriel
Mountains
I
ohm-m
I
I
3
<--------->
70 km
200,000 ohm-m
Crust
100 km
50 km
600 ohm-m
6 ohm-m
100 km
200 ohm-m
2 ohm-m
.1 ohm-m
Half-space
FIGURE 5.13:
MODEL WITH LOS ANGELES BASIN
-
85
-
I_
I
LA Basin
_
3
I
z
03
10
FERIOD (seconds)
5
-204*
-30Cn
-40'
0
c.
-50
-60
-70
-50
p
S
-
104
105
PERIOD (seconds)
FIGURE 5.14:
MODEL 5.13
-
(5)
86 -
AND PALMDALE
(0)
Pal mdal e
110 km
---------
>
Ocean
I
5 km
3
150 ohm-m
San Gabriel Mountains
100 km
600 ohm-m
100 km
200 ohm-m
Half-space
ohm-m
_.3
3
I
I
_
3
150 ohm-n
Continental Crust
200,000 ohm-m
50 km
I
I
1_
I_
I
_
3
Oceanic Crust
20,000 ohm-m
6 ohm-m
I
2 ohm-m
.1 ohm-m
FIGURE 5.15:
MODEL WITH MORE CONDUCTIVE OCEANIC CRUST
-
87
-
L
1031
uJ-
1035
104
103
PERIOD (seconds)
n
Q.
-20
-30
e
-
-
6.
nH
0
N
7(
.1m
i05
j04
PERIOD (secords)
FIGURE 5.16:
MODEL
5.15
-
88
(11) AND PALMDALE (@)
CHAPTER 6:
We
found
reasonably
well.
period
of
20
several
models
We were
min utes or
simul taneo usly at
CONCLUSIONS
that
abl e to
never
the
apparent
72 hours.
most
fit
of
the
fit
resistivity
our
data
phase at
and
a
phase
We were able to fit most of our
data with or without ocean-continent con trasts in the ma n tle.
Hence,
we
cannot
make
ocean-edge effect
the
conti nent
and
the
toward
models
acceptable
any
with
definitive statements
path
of
the
ocean.
and
without
resenting a cool subducting slab.
data were
similar,
important
for
the
indicating
periods we
+ , LOs Angeles Basin (a local
no counterpart
of another model
Our
have
a
a
resistive
km
rep-
The P almdale and Holl
ster
i
not
local
have used
here.
Inc 1us i o n of
required
a slight
high
the
causing it
adjustment
parameter to compensate.
thick
resistivities
depress
geology
feature near Palmdale but with
200,000
the
give
ohm-m
crust
current
current
a
large
al though
adjustment
Smaller
levels.
levels
to be closer
Our models
we
resistivity thickness product.
causes the Palmdale phases to be similar
with
f ound
we
zone
data requires a highly resistive crust.
100
the
flowing f rom
Similarly,
that the
near Hollister)
really only resolve
high
current
the
abou t
and
to the
change
distance
can
The
which
to the ocean phases
crustal
the
resistivities
phase
1-D continental
structure,
solution.
We
can compensate for the lower current levels by increasing the
-
89
-
resistivity of
Palmdale),
the
but
surface
this
observed values.
nental
will
not
data
Our
(San
Gabriel
bring
does not
and oceanic crust must be
the
Mountains
for
back
to
phases
that
prove
identical
in
the
conti-
thickness and
but we have found that the ocean models proposed
resistivity,
ohm-m,
by Oldenburg (200
Our
layer
are
values
closer
50
km crust)
will not
to Kasameyer's
our
fit
data.
estimate
(1974)
of
a
30,000 ohm-m, 40 km crust based upon surveys in New England.
inversion of
the
data was needed since we only have data at one point for
the
did not
initially
We
Holl i ster
and Palmdale
Afte r working with
areas.
mode l s and
struggling to separate
parameters
(about
of
5 thicknesses
our mod els) , we
Other
inverted.
include
the use
The
apparen t
too
biased
data,
the data
for
this
the
data
useful.
to
this
The
the
minimum
but
would
not
make
be
study
strike.
probably
the
phase
phase and apparent
probably
to
are
strike
most
should
augmenting
effects,
phase
criterion
resistivity
any
major
our data except at 72 hours where the data did not
come cl ose to obeying minimum phase.
n ice to
the various
for E and H parallel
three-dimensional
be
that
parallel
to smooth
alth ough
changes in
of
the forward
and 8 resistivities on
possibilities
could
u sed
could be
the effects of
concluded
resistivities
by
information
have
that an
believe
hav e longer period data.
the magnetic
observatory
It
would,
We were
data from Tucson
would probabl y be sufficient
-
to use either
90
-
of course,
be
limited by gaps in
and Boulder.
It
Tucson or Boulder
directly,
study.
without
the
prediction
scheme
we
used
in
this
In that case, Boulder could be used whenever there
is
a gap in the Tucson data or vice-versa.
We have also heard
that
opened
a
new
California.
magnetic
The
data
observatory
from
has
it could be useful.
in
The
Fresno,
use of
the multi-channel maximum entropy technique might be superior
to fourier transforms for the long period data.
-
91
-
MAGNETIC FIELD PREDICTION
APPENDIX 1:
to predic t the three magnetic
We developed a technique
components,
the
observations
magnetic
these
methods
to
from
data
magnetic
hourly
and
minute
5
We applied
the prediction methods.
January, 1974 to develop
from
data
minute
2.5
used
We
observatories.
on
Boulder
and
Tucson
the
at
D
and
H
of
based
California
Castlerock,
at
(Z),
intensity
vertical
and
(D)
declination
(H),
intensity
horizontal
various time segments, 1-3 days for shor t period data and 1-3
months
operated).
observatory
Castlerock
(the
in 1974
data,
period
long
for
This
yielded
the
year
last
time-domain
operators to predict Castlerock given Tucson a nd Boulder.
We
Tucson
and
of
the
applied
these
Boulder
for
to
We
f or
data
magnetic
to
1980
and
1979
Castlerock.
at
fields
operators
generate
an
performed
all
e stimate
the
predic t i on
operations in the time domain.
We
found
that
simultaneous measurements
Victoria
was
Tucson,
at
Boulder,
Operators
adequate.
not
us ing
observed
D, or
fields
increments
each
at
way
same
the
time,
92
time
and
(future
-
To predict
time and memory.
Z at a single
-
past,
the
past).
one
and
the
uses the
the ope rator
and
and
results without
error, an operator was found which gave good
value of H,
and
Honolulu,
After some trial
present, and future signals were tried.
requiring too much computer
upon
b ased only
Castlerock
predicting
two
Akverages
of
time
the
observed values for 3 to 22 time
included.
The operator can be represented as:
-22d
The
increments each way are also
operator
has
a
o
-2st
-3at
-12t
total
of
station and component used.
7A
7A
11
terms
1W4f
for
f
2
each
magnetic
In the case of five minute data,
it samples data over a 220-minute range.
A
useful
operators
is
measure
the
the
coherency
signals for Castlerock.
and B,
of
of
the
predicted
prediction
and
two time
observed
series, A
is:
coherency
A-
measures
signals
Identical
the
have
a
random signals, each with
of
the
of
The coherency of
CAA6)6 C
The
quality
(A1.1)
correlation
coherency
of
of
two
exactly
100 data points, have
signals.
one.
Two
a coherency
.08.
We
four
found
magnetic
that prediction
stations did not produce
coherencies
than
Figure A1.1
shows the
Castlerock.
operators using
The
operators
H components of
Tucson
and
significantly
only
using
three
Boulder
Tucson,
Castlerock
and
signals are
1966).
is
possibly a result of
The
D
components
-
the
for
93
-
"island
the
same
effect"
three
all
larger
Tucson.
Honolulu,
more strongly correlated with each other than with
This
or
and
clearly
Honululu.
(Rikitake,
stations
are
in Figure
plotted
Tucson
There
and
alike
and Boulder
the
again,
are
plotted
of
signal.
Castlerock/Tucson
shift between
c omponents
and
Castlerock
Honolulu
the
than
H
The
Vict oria,
Castlerock,
in figure Al .3.
first
The
gives the coherencies of Castlerock versus
part of Table A1.1
ot her
the
raw data from
1974.
more
to be a ph ase
Honolulu.
Tucson,
the
Once
are
signals
appears
A1.2.
stations for
four
to 03 Jan
01
Castlerock is most strongly correlated with Tucson and
The
Boulder.
coherencies of
second
the
of
section
table
shows
the
the observ ed Castlerock H component versus the
Castlerock H component pr edicted from only the H component of
one
magnetic
other
Cas tlerock
of
(.8590)
coherency
entry
next
The
sta tion.
versus
observed
gives
Castlerock
predicted from both Bould er's and Tucson's H components.
this point,
we
could depend not
but
also
on
inhomogeneities
and
the
simple
only on
the
D
in the
magnetic latitudes.
H component
condouctivity structure of
the
are
stations
At
Castlerock
stations
from
resul ts
This
component.
at
other
at
the H component
that
fact
the
that
realized
the
the
at
earth
different
Similarly, the D component at Castlerock
should be considered to be a function of H and D at the other
observatories.
this idea.
Prediction
operators
were
The final entry in Table A1.1
generated
using
is the coherency of
Castlerock observed versus Castlerock predicted from H and D
at Tucson
The result,
and Boulder.
improvement over the
.9177,
is
a substantial
.8590 using only H components.
-
94
-
Similar
improvements were
the coherency of Castlerock's
observed for
D component.
minute magneti c
(CO=Castlerock
TABLE A1.1:
Coherencies of 2.5
1974,
H
component
01-03
Jan
CP=Castlerock Predicted)
COHERENCY
SIGNALS
CO and
CO-and
CO and
CO and
data for
Observed,
.7977
.7750
.4185
.5442
Tucson
Boulder
Victoria
Honolulu
CO and CP (based upon Tucson H)
CO and CP (based upon Boulder H)
CO and CP (based upon Victoria H)
.8358
.8193
.7174
CO and CP (based upon Tsn & Bld H)
.8590
CO and CP (based upon Tsn & Bld H & D)
.9177
above
The
prediction
operators
same
operator
set
a
true
prediction
operator
test
data
of
is
to
16
and apply
it
to
The results of such a test are given
to
an
another
in Table
The operators used were again based upon the 01-03 Jan
Jan
1974
and
25
coherencies
are
other cases
they were
lower
the coherencies are
A1.5,
was
generate
1974 data but were applied not only to that segment
to
the
of
test
Jan 1974 data and applied
be?tter
A
segment
is not
the
the 01-03
data.
from one
data segment.
A1.2.
of
.9177
because
generated based upon
the
of
value
and
A1.6,
1974.
Jan
for
the
higher.
acceptable
show
the
-
16th
The
in
all
observed
95
-
In
three
and
25th
important
cases.
and
but also
cases,
in
but
thing
the
three
is
that
Figures A1.4,
predicted
Castlrock
the predicted data go to
The plots of
16 Jan 1974.
data for
zero on both ends because the prediction operator relies upon
the past and future measurements.
predicted
versus
observed
of
Coherencies
A1.2
TABLE
Castirock magnetic data (periods of 10 to 90 minutes)
01-03 Jan 1974
Compon
25 Jan 1974
.9242
.8954
.9058
.9521
.8481
.7955
.9177
.9039
.8549
H
D
Z
Three months of data,
were
16 Jan 1974
to generate
used
January, February, and June, 1974,
and
the hourly data (periods of 2
the
larger).
to
36 hours, and 36 hours
of
months
twelve
operators for
prediction
the
test
obtained
data
large
Boulder
data
for
that
ustng
this was
the
both
resulting
coherencies
the
produced
larger
al 1
to
operators
did
better.
operators
did
slightly
in
fi
Ir
Ove ral 1
better
-
96
we
-
so
we
they
were
of
The
In
some
February
data
the
June
cases,
found
set
data.
of
the
other
operators
A1.3.
table
rom
indicate
Each
data.
months
th re e
gener ated
coherencies.
ne
JL
gi ven
are
operators
the
and
applied
were
cases,
We gene ral ed prediction
February
operators
resu lt ing coherencies
The
adequate.
so
of
data based only upon the D and
predicted the hourly magnetic
H components of Tucson.
se gments
missi ng
al so
w ere
1980
and
1979
Large
data.
mi ssi ng
of
sections
f rom the
the only o nes
magnetic observatories, these three months were
without
and
the
used
February
in
the
prediction of the
show
the
Figures Al. 7 to A1.9
1979 and 1980 data.
predicted
versus
observed
data
Castlerock
for
January, 1974 (using operators based upon February, 1974).
predicted
observed
versus
Coherencies
of
Table
A1.3
Castlerock magnetic data (periods of 2 to 36 hours)
Coherency
Month Predicted
Comp
Operator
Based Upon
H
H
H
H
H
H
Feb
Feb
Feb
June
June
June
Jan
Feb
June
Jan
Feb
June
.9550
.9683
.8555
.9204
.9382
.9199
D
D
D
D
D
D
Feb
Feb
Feb
June
June
June
Jan
Feb
June
Jan
Feb
June
.8984
.9384
.9471
.8561
.9032
.9643
Z
Z
Z
Z
Z
Z
Feb
Feb
Feb
June
June
June
Jan
Feb
June
Jan
Feb
June
.8092
.9186
.7905
.7154
.7640
.9292
the
With
of
exception
the
table A1.3 are greater
coherencies in
Z
component,
than
.85.
all
In general,
we found that we could not predict the Z component as well
H
and
This
D.
sensitivity of
was
only
used
Z to
is
probably
local
indirectly
a
result
inhomogeneities.
in
computing
the
of
The
the
97
-
as
greater
Z component
magnetotelluric
tensors (for the Park-Chave method, see chapter 4).
-
the
The
prediction
operators
for
the
long
period
data
(36+ hours) were also generated from the February, 1974 data.
The
resulting
observed
June,
are
coherencies
versus
given
Castlerock
predicted
in
table
The
A1.4.
long-period
for
data
1974 are shown in figures A1.10 to 12.
predicted
versus
A1.4
Coherencies
of
observed
Table
Castlerock magnetic data (periods of 36 hours and larger)
Comp
Month (1974)
Coherency
H
H
H
D
D
D
Z
Z
Z
Jan
Feb
June
Jan
Feb
June
Jan
Feb
June
.9862
.9908
.9565
.9096
.9288
.9359
.8387
.9357
.7627
The prediction operators are given in tables A1.5, A1.6,
and A1.7.
time
The
extreme
For
segments.
column
left
in each
table
"-22 Ot-->-13jt"
example,
the data points from 22
the past.
Positive values of t represent the future.
the case of 5 minute
same
to be
should only be
operator;
larger
than
increment s
that
in A1.6
T hus,
the magnetic
to the
the values
is merely
other values
in
table A1.5
a result
of
un i ts in the 2.5 minute and hourly magnetic data.
-
in
In
data
The numerical coefficients in each
compared
the fact
the
in the future.
increments
this would mean
data,
10 minutes in the future.
operator
time
means
average of
+24t means the data at 2 time
to 13
the
gives
98
-
in
the
tend
different
Table A1.5
data
Prediction operators for 10 to 90 minute magnetic
Operator to Predict H Component of Castlerock
-22at-->-13 at
-12at-->-8at
-7zt-->-34t
-2 at
-13t
Oat
+1 4t
+24t
+3at-->+7at
+8 t-->+12at
+1I3,at-->+22at
Boulder-H
.071
.262
-. 190
-1.213
.515
6.590
9.128
Tucson-H
-. 073
.213
-.
398
1.643
-1.291
5.910
-3.320
5.068
.350
.295
-.
764
-. 089
-. 147
.228
-. 277
Tucson-D
-
-.
Boulder-D
.496
271
1.441
3.763
-4.011
14.431
-8.349
6.610
-1.188
1.061
-. 007
-.
473
.009
.771
3.418
-2.083
8.485
1.272
4.121
-. 856
.486
.095
Operator to Predict D Component of Castlerock
Tucson-H
-22 &t-->-13at
-12,ot-->-8at
-7zt-->-3 At
-2at
-1 At
0 at
+2&t
+3 ot-->+7,t
+8t-->+122t
+13at-->+22&t
-.
Boulder-H
Tucson-D
Boul der-D
.269
-. 011
1. 398
-1. 780
1. 672
.800
-. 946
.812
2. 319
219
6. 471
689
12. 218
1. 308
090
632
-. 157
-1.693
-3.673
-13.659
2.893
.400
-. 229
.472
547
.375
229
-. 144
-4.610
6.466
-9.427
5.553
-7.368
.147
.750
1.220
2.112
-.
-.
-. 788
7.011
.515
.136
-. 001
-. 070
804
Operator to Predict Z Component
-1 2At-->-8At
-7 t-->-3At
-2,at
-1 at
OAt
+14t
+2at
+3 it-->+7At
+83 t-->+12at
+ 13 at-->+22 at
of Castlerock
Tucson-H
Boulder-H
Tucson-D
Boul der-D
-. 214
.162
-. 101
.460
.207
1.353
-1.997
1.601
.094
.084
-. 070
.215
.171
-. 419
-. 457
1.161
2.683
2.146
.214
.164
.157
-. 111
-. 019
-. 017
-. 453
.714
-
99
-
-. 875
1.202
1.622
-. 679
6.643
-2.364
9.487
-. 540
-. 809
1.460
2.581
-2.480
3.069
-4.965
3.681
-. 298
-. 654
1.058
Table A1.6
Prediction operators for 2 to 36 hour magnetic data
Operator to Predict H Component of Castlerock
-22bt-->-13at
-12 at -- >-80t
Tucson-H
Tucson-D
.015
.015
-. 001
.023
.010
.197
-. 106
.092
-. 040
.008
.037
-.
.017
-74t-->-34t
-24t
-1 at
Oat
+1 at
+2at
+3at-->+7&t
+8 At-->+ 12at
+13at-->+22&t
025
-.
020
.048
.970
-. 003
-. 011
.004
.014
-. 021
-. 020
Operator to Predict D Component of Castlerock
Tucson-H
Tucson-D
-. 024
-22at-->-13at
-12at-->-84t
-7 at-->-3at
-2at
-1 at
-.
.080
.003
.313
-. 111
0ot
+1 At
.170
-. 080
-. 060
-. 187
-. 097
008
.041
-.
+2at
+34t-->+7at
+8 at-->+ 12,at
+13at-->+22at
023
-. 020
-.
039
.039
-.
004
-. 027
.920
.001
-. 064
.011
Operator to Predict Z Component of Castlerock
Tucson-H
-12 6t-->-8at
.008
.025
-76t-->-3at
-. 026
-24t
-1 4t
Oat
- lat
-. 137
-. 101
.257
.025
-22,6t-->-13,at
+ 1,At
+2at
.003
+3at-->+7&t
+ 8at--> + 12 at
+ 13 at-->+22 at
-.
003
.076
-.
-
084
100
Tucson-D
035
011
003
159
155
213
096
017
003
030
018
Table
data
operators
Prediction
A1.7
for
Operator to Predict H Component
Tucson-H
-
2 2
.002
t-->-13at
8
-12 t-->- zt
-7t-->-3 at
-2,t
-1 dt
0 Ait
+1 4t
+2at
-. 002
-. 011
-. 092
.136
.827
.168
-. 148
.016
+3at-->+7At
-. 029
+8at-->+12bt
+1 3At-->+22At
.024
36+
hour
magnetic
of Castlerock
Tucson-D
-. 008
.009
.007
-. 166
.439
-. 084
-. 157
.141
-. 008
-. 003
-. 006
Operator to Predict D Component of Castlerock
Tucson-H
-22At-->-13at
-12zt-->-8at
-7 6t-->-3at
-. 011
.043
-2ot
-.
- 1 Ibt
0 at
+1 At
+2At
+3 At-->+7 6t
+8at-->+12At
-. 087
465
.919
-1.034
.846
-. 702
.054
-. 045
.045
+ 1 3,t-->+224t
Tucson-D
.004
-. 002
.025
1.021
-1.599
2.856
-1.666
.568
-.
-.
002
044
.025
Operator to Predict Z Component of Castlerock
Tucson-H
-22At-->-l13at
-12at-->-
8
,At
-7 t-->-3at
-26t
-1at
0 at
+14t
+2At
+3 1t-->+7At
+8t-->+12t
+13At-->+22,at
-. 007
.056
-. 152
.005
.023
-. 016
-.
-.
929
1.016
-1.330
1.434
-1.012
.112
-. 001
-. 010
-
Tucson-D
101
328
.127
1.084
-1.189
.691
-. 009
.002
.010
In all
or
near
several
that
04t;
time
the
is,
increments
nature
awa>y
table
A1.5
Tucson's
for
the
H are
-2at,
the
to
values
for
-4.610,
is
smaller
were concerned
that such
the best (least
squares)
generated,
might
Castlerock
Based
on
that we
data
when
previous
than
fields
at
to
, -9.427, 5.553,
and +2,t,
and
applie d
to
experienc e
from
-7.368
respecti vely.
We
although providing
desired
other
(Madden,
time
1983)
the oscillations and
it
was
predicted
segments.
we
thought
i nprove
the
applied to a ti me segment
was generated)
by damping
the prediction operator.
the smallest eigenvalues of
least squares solution to Ax=b is:
(Al .2)
x = (ATA)~1ATb
where A
D
to the data from wh ich it
the
in
e xample,
predi :t
yie ld
could eliminate
, there is
operator
other than the one from which
The
at
For
coherencies (when an operator is
out
fields
In some cases
an operator,
fit
not
the
operators.
6.46
-1t, Ot, +13t,
of
influence
nearby times as we would expe ct.
a oscillatory
at
largest coefficients are
three tables, the
is
eigenvalues
a matrix
in
ATA
and
b a vector.
can
to
lead
In
practice,
unstable
small
solutions.
Eigenvalues smaller than some epsilon can be damped out by
using:
x =
-
(ATA
102
+
-
E21)-1ATb
(Al .3)
where I is the
identity matrix.
In many applications, we
have found such damping
improves the solutions
We
value decomposition
performed
ATA for
the
a singular
10
immensely.
(SVD)
H field prediction
to 90 minute
on
our
operator,
where A is a (N-44) by 44 matrix of the form:
2 Tcs9V
Zs,
0
C,
2411
H
Ovader9P
(A1 .4)
I
h-e 3
even column section consti sts of
where eac
the
of
form
about
operator
data points
the
on
93,
p.
with
indicated on the
eac h
lef
data in the
row
centered
The
t.
number
of data points in the time series is N.
The
44
eigenvalues
of
ATA
.00650.
The singular values of A are the
roots of
the
the
eigenvalues of ATA.
condition
largest
to
of
a
300.
is
1234.
We
as
the
(1961)
ratio
the
to
defines
of
the
The condi- ion number for
tried values of
As expected,
9893.7
ositive square
Lanczos
matrix
to smallest eigenvalue.
this matrix
.007
number
rom
range
$ 2 ranging from
coherency
decreased when
predict i ig the data from wh ich the operator was generated
(this
is
equivalent
to
-
saying
103
-
that
the
best
fitting
solution
is
the
however,
surprise,
when
amounts)
squares
least
the
solution,
coherency
generated
operators
To
f=0).
by
the
small
(by
decreased
01-03
our
Jan
1974
data were applied to the 16 Jan 1974 and 25 Jan 1974 data.
We do not understand why the damping failed to
improve the
Perhaps, the data segments were
long enough
coh-erenc ies.
that the magnification
factor
of
of
1200 was not
noise
in
important.
the
eigenvectors by a
Looking
back, we
now
realize that we couldn't have hoped to improve coherencies
by
a large
not decrease
amount
because
the
coherencies
generally
too much when operators are applied
to data
sets other than the ones from which they were generated.
-
104
-
do
Cast1er-ock
Homo i ua u
Tuscoom
f
I'
2 daye
Fig ur-e A1
1
Magneti c
Fi
H
at
Thr-ee
Stations
ltered for 36+ Hour-s
June,
7
1974
Coa stierock
Hn
or--,,
u
I U .
2 daye
Fi gure A1.2
Magnetic
Filtered
June
1974
at
For
Three
Stations
36-+ Hours
V i ctoruscoo
i a
Boul derCast 1 er-ock
p
"AA
V.*j
Figure A1.3
1
Magnetic
at
F i 1tered
for- 10
16
Jan
1974
Four- Stations
to
90 Minutes
hour
Observed
1 hour
Figure A 1.4
Predicted
Filtered
16
Jan
and
for-
1974
Observed
10
to
Castlerook
90 Minutes
Obser-ved
Precicted
1 hourV,
Figure
A1.
Pr-e dicted
and
Obser-ved
Castlerock
Filtered for- 10 to 90 Minutes
16
Jan
1974
Obser-ved
Predc iotI..edI
I'
I'
3
A
3'
II!"'
/\JVXA
1k
1
Figure
A1.6
Predicted and Observed
Fi itered for
16 Jan
1974
10
to
Cast1er-ock
90 Minutes
hour-
Obser-ved
Prected
1 day
Figur-e Al. 7
Predicted and Obser-ved Cast1erock H
Fi1ter-ed
January
for
1974
to 36 Hours
Ob ser-ved
Pr
edctCedO
A.
A
AA
1
Figure
Al. 8
Pr-ed i cted
Filtered
JanuarX
and
for
1974
Obser-ved
Cast 1 erock
2 to 36 Hours
day
Obser-ved
PrediCtea
1 day
Figur-e A1.9
Predicted
Fi1ter-ed
Januarny
and
for1974
Observed Castler-ock
to
36
Hours
Ubserved
-Prec i creC
2 dazye
Figur-e
A1. 10
Predicted and Observed Castler-ock H
Fi1ter-ed
June
1974
for
36+
Hours
Observed
2 days
Figure
A.
11
Predicted
Fi1ter-ed
June
1974
and
Obser-ved
for- 36+
Hour-s
Castler-ock D
Observed
Predzioted
Z dayZ
Figur-e
Al. 12
Predicted
Fi 1ter-ed
June
1974
and Obser-ved
for
36+- Hour-s
Castler-ock
MT TENSOR ROTATION
APPENDIX 2:
As
discussed
dipoles used
the
north
t he magnetic
tensc r
illustration,
bL t
Palmdale array.
with
a
the
of
was
technique
used
in
tensor along the st ruc tural
some
MT
and
array
also
geometry
for
to
the
applied
analyses
orient
to
the
are
rotations
shown
in
Dipole A at Hollister poin ts five degrees south
geographic west.
Dipole
B
is
magnetic declination for the area is
are
the
stri ke by minimizing Z 1 and Z2 2 '
1
dipo le or entat ions
figure A2.1.
if
This tensor rotation should not be confu sed
techniqu e
The
Hollister
the
use
We
wh i ch
tensor
obtained
In
and coincident with the magne tic
dipoles had been orthogonal
measurements.
not
and did
the MT
been
have
would
which
of
electrical
components.
east
and
rotat i on
a
we der i ve
appendix
gives
The
in this study were not orthogonal
coincide with
this
components.
field
magnetic
and
electric
orthogonal
of
the measurement
survey consists of
totel 1-uric
magne-
a conventional
one,
in chapter
equivalent
to dipoles
250
16
south
of
east.
so the magnetic data
of geographic
160
east
the
magnetic
The
north
and
that
the
160 south of east.
First,
we
rotate
magnetic-north component coincides with
fields
so
electrical
dipole A.
This requires a rotation through an angl e of 90-16-5=690.
-
117
-
Geographic
North
Magnetic
North
HMN
w
EA
HMN
B =150*
T=69*
EB
Figure A 2.1:
Rotation of Measured E and H Fields to an Orthogonal System
(for Hollister, California).
-
118
-
rotation matrix except we
We apply a standard 2-D
signs of
row to switch
first
the
direction
the
change the
of
the
Hmn
We have:
component.
sT
-co
HN
-s i nT
HMN
(A2. 1)
HM
-sir
or
with
nT cosT
HME
(A2.2)
= RHH
H'
T=69 0 for Hollister.
Next we
rotate only the B
L
Lt=
it
angl e C to make
the rotation is
Hme'.
coincide wi
dipole through
lectrical
If
we
let B=C+90
an
0
,
given by:
EA
cosB
0
EB
( A2.3)
sinB
RE
E'
or
(A2.4)
= REE
with B=150 0 for Hol Ii ster.
The
MT
tensor
Z
is
defined
by
the
relation E=ZH.
Substituting for E and H we have:
RE~IE'
or
E'
= ZRH~ 1 H'
= REZRH~H'
-
119
-
(A2.5)
(A2.6)
This is equivalent to:
where
E'
= Z'H'
(A2.7)
2'
= REZRH-1
(A2.8)
Substituting A2.1 and A2.3 into A2.8:
1
-sinT
-cosT
212
211
cosB
(A2. 9)
-sinT cosT
Z22
0sinB 221
Simpl ifying:
Z'
=
1 + Z2 1 cosB Z 1 2 +
-sinT
(A2. 10)
-sinT
222sinB
221si nB
Mul tipl ying gives the elements of
'-11
1-cosT
22cosB
= -cosT(Zi 1
'-12 = -sinT(Zi
Z21 = -(cosT)Z
1
2 1
cosT
the rotated tensor:
sinT( 212 + Z 2 2 cosB)
+ Z2 1 cosB) -
+ Z 2 1 cosB) + cosT( Z
cosB)
1 2 + Z2 2
(sinT)Z
sinB -
22
(A2.1 1)
si nB
Z22 = -(sinT)Z 2 1 sinB + (cosT)Z 2 2 si nB
Equation (A2. 11) was used to con vert the measured ratios
of E and H fields to
standard MT ten sors.
array dipole A (se e figure A2-1)
C, T=44
0
, and B=12 20.
-
120
-
For
the Palmdale
bec omes dipole D, B becomes
APPENDIX 3:
COMPLEX SINGULAR VALUE DECOMPOSITION
Golub and Reinsch (1970) give an efficient algorithm for
the
This
singular
value
appendix
gives
complex matrices.
compute
decomposition
a
We
simple
our HP computer
real
extension
developed
eigenvalues and
of
M
of
X
N
matrices.
their
method
to
the method so that we could
eigenvectors of complex matrices
(which does
not
have a built-in
for complex numbers and functions).
on
capability
We applied the method to
decompose M X 5 (M ranged from 5 to 42) complex matrices
in
the Park-Chave method of tensor calculation and to decompose
the
2
X
2
com"iex
tensors
eigenstate analysis.
used
to keep
track
the
for
principal
direction
In both cases, the complex numbers are
of
the relative
phases
of
the
E and
H
fields.
First, we
express a complex matrix A as the sum of
two
real matrices:
A = A,
Expressing
the
eigenvectors,
(A3. 1)
+ A2i
v
and
u,
as
sums
of
real
eigenvectors, the standard eigenvalue equation becomes:
[A1 + A2iJ
[21 + -2
where the eigenvalues,
=J ')\l
, are real.
-
121
-
+ U2
iI]
(A3.2)
By multiplying out the
AK
-A2
Viu
left-hand-side
separating
and
can express A3.2
real
and
imaginary
parts,
as:
---
A2
u2
V2
Al
(A3.3)
Hence, an M X N complex matrix can be decomposed by
the
Only
real
half
and
of
imaginary
the
eigenvalues will
we
parts
resulting
into a
complex
be unique.
-
122
-
2M
X
2N
real
eigenvectors
imbedding
matrix.
and
real
APPENDIX 4: DATA (IMPEDANCE EIGENSTATE PARAMETERS)
In this appendix, we present the MT impedance eigenstate
parameters for the Zh estimates as a function of period.
The
parameters are
give
the
and
two
apparent
defined
resistivity
parameters
in chapter
as
defined
called coherency
are somewhat analogous to
in
are
coherency at
form
a
vector
by
equation
and
equation A1.1.
consisting
Also, we
1.26
parameters
These
two.
the standard coherency of
series defined
defining a
one
four.
of
In
a single
the
this case,
however,
frequency.
observed
E
two time
First,
fields
at
we
we
one
dipole for a single frequency and n data segments:
EO = (E 0, E ,
where
the
superscript
0
En")
...
indicates
the
(A4.1)
observed
E
field.
Next, we use equation 1.28 to calculate the predicted E field
for each data segment at a single frequency:
0
+ 21H
12 iME
=IiMN
Z1 1 H,
E
where the superscript P indicates the
subscript
indicates
subscripts MN
and ME
east,
respectively.
the
ith
predicted E field, the
data
represent magnetic
For convenience,
-
123 -
(A4.2)
segment,
and
north
magnetic
and
we are using
the
Ex;
should be replaced by Z2
ffor Ey, Z,1
1
, and Z 1 2
by Z22
is given by:
The vector EP
EP =
(E
1', E,2'
(A4.3)
EP)
n
...
We defince the coherency as:
(0"
perfect,
were
data
would
fields
E
observed
and
predicted
the
our
If
multiplication.
represents
*
the
where
(A4. 4)
be
identica I and the coherency would be exactly one.
to
refers
Coher
follow,
that
tables
the
In
the
coherenc y for
the dipole oriented closest to the direction of
the prin cipal
axis of
predicte d and measured
(B
Hollister
for
degrees.
in
are
long-per iod data
minutes
for
and
coherency
of
fields at
the other
dipoles
the
(tables
The
period
A4.1,
A4.2,
short-period
data
A4.4,
3
82,
hours
in
is
apparent
The
Palmdale).
for
C
to
in ohm-meters and the angles (81,
resistiv ies are
th)
electric
the
the
refers
Coher2
P almdale).
D for
Hollister and
the tensor (dipole A for
for
and
and A4.5)
(tables
A4.3
e,
and
and
the
in
A4.6).
The sign of the ellipticity is sometimes used to indicate the
handedness of
values of
the ellipticities.
2-36 hours, or
table.
the field, but
here we
just give
of
the
(36+ hours,
the
top of each
tables data for
-
absolute
The filtering band
10-90 minutes) is indicated at
In some
:he
124
-
periods outside
the
filter
are
cutoff
The
included.
of
the
we
filter
digital
used is not sharp so data for periods near a cutoff have some
meaning.
the data.
We emphasize that these tables include all
mentioned in chapter five,
abou t 20 minutes or
the data with periods shorter than
than a few days
longer
Logarithmically-spaced
averages
of
the
and phase (weighted by the coherency)
4.1
for
and 4.4.
the
six
The average
As
apparent
periods
evenly-spaced
modelling are given in table 5.1.
-
125
-
is
not
reliable.
resistivity
apparent
are plotted
in
resistivities and
which
were
used
figures
phases
in
the
Taole A41.1:
Period
Palmdale, ')6+
Hours
App. Res.
Theta 1
1416.29
-80.1
113.78
-77.1
Lambda1
Lambda2
Coherl
Coher2
Theta 2
EpsilonE EpsilonH
Ga mmaH
GammaE
16014
0.7711
0.8213
-39.2
2G.7
0.3899
115.1
0.0040
0.G17
0.004
17137
0.4574
0.0044
0.9504
0.9574
-31.4
0.008
-22.0
111.6
0.002
0.9/142
93.09
0.0153
13496
0.4487
0.9354
G.031
-75.6
0.020
-74.7
105.3
2G.2
78.77
-75.9
11451
0.9673
-77.4
0.9802
-20.7
0.4493
0.0161
0.027
0.068
101.9
68.27
-84.1
9897
0.0195
0.9786
0.9896
0.4487
0.016
-76.4
102.2
0.222
-2G.4
60.24
7405
0.9790
0.9813
-77.1
-21.3
0.0128
0.4132
0.128
0.010
92.5
53.89
-80.2
6994
0.4245
0.0179
0.189
96.3
0.015
48.76
-77.1
6443
0.9552
0.9533
-87.5
-21.3
0.0211
0.4284
90.9
0.014
0.239
44.52
5873
0.2059
0.8963
-66.6
-21.0
97.3
-75.3
-74.1
40.96
-74.1
0.9427
-80.4
7939
0.9646
-60.3
0.9F98
-21.2
0.9899
-19.6
37.93
- -75.0
8661
0.8689
0.920
-57.5
-19.7
35.31
7039
-77.0
33.03
-75.5
0.4280
0.0255
0.016
0.060
0.0303
0.5188
0.047
0.007
106.2
0.5632
0.0298
0.054
0.001
102.2
0.7341
0.7221
0.0363
0.5262
0.002
0.029
-75.4
102.3
-19.9
7773
0.4323
0.3823
-63.2
-20.1
- 126
-
0.0336
0.5717
0.087
0.024
93.2
Table A4.2:
Period
o 3
PaI mdale.. 2 2to
ar
Lambda2
Lambda1
Coher2
Coher 1
EpsilonH
i lonE
Eps
GammaH
Ilhet=2
m
aE
Gam
App. Res.
Theta 1
73.14
-34.7
56.89
-64.8
11522
0.9069
-66.6
0 . 4678
0.9486
1G7.8
-20.9
0.0196
0.020
0.501
5568
0.9109
0,9257
-78.8
-20.
0.0269
0.3687
0.126
0.033
95.6
0. 9078
-20.7
0.0319
0.3667
0.079
0.037
95.4
0.E200
46.55
-66.0
4507
39.38
-65.6
0.8162
0.0433
0.4473
0.7770
5674
0.034
0.034
103.6
-18.6
-74.7
34.13
-58.6
0.0445
0.4948
0.6234
0.5407
6017
0.028
0.039
1C7.7
-18.7
-77.3
30.12
-47.2
0.0494
7111
0.8054
0.6906
0.5727
0.053
0.027
111.9
-72.8
-18.9
26.95
-45.6
0,
7162 10.9317
-19.2
-71.8
24.38
-44.2
0.0547
0.7008
0.9R97
0.9690
R620
-74.1
0.164
-19.4
0.006
104.8
22.26
8041
-44.0
20.48
-42. 1
18.96
-43.4
17.66
-36.0
-82.0
0.8877
-74.2
0 . 6076
9218
1C9.3
0.7019
-73,6
9634
0.8354
0.092
0.0560
0.7083
0.161
0. 0 4
164.4
0.9202
-19.4
0.7108
7451
0.9115
0.9197
19.4
-73.8
7128
0.0512
0.021
105.3
0.0572
0.173
0.001
0.0603
0.7226
0.145
0.0G3
162.7
0.7151
-19.8
0.8706
0 .815
86.2
-26.8
0.0575
6.032
0.c00
0.5833
0.4583
11218
16.52
-0.5
-69.7
-39.6
0.0641
0.9713
0.016
0.007
89.8
0.9141
0.8811
11873
15.52
-26.1
-36.3
-70.4
97.6
-
127
1.0310
-
0.0668
0 . G10
C.013
Table A4.2:
Period
Palmdale, 2 to 36 Hours
App. Res.
Thetal
Coher 1
Coher2
Lambda1 Lambda2
Theta2
GammaE
Ga mmaH
EpsilonE EpsilonH
14.63
12348
0.7115
0.7097
1.0828
0.0665
-60.0
-68.5
-19.6
103.8
0.011
0.089
13.84
-69.6
12805
0.6252
0.5778
1.1337
0.0796
-66.6
-19.4
103.0
0.026
0.051
13.13
-60.3
14592
0.6351
0.6161
1.2425
0.0813
-69.8
-19.0
105.5
0.017
0.094
12.49
13193
0.9087
0.8806
1.2113
0.0861
-60.1
-71.8
-19.0
106.0
0.014
0.073
11.91
-60.7
12895
0.9541
0.9427
1.2264
0.0874
-71.1
-19.1
104.4
0.014
0.073
11.38
-62.8
12637
0.9388
0.9353
1.2420
0.0881
-70.2
-19.4
101.6
0.014
0.061
10.89
120142
0.9367
0.9384
1.2391
0.0863
-57.4
-69.5
-19.0
106.9
0.013
0.114
10.45
-47.8
0.9101
0.8869
1.4962
0.0856
-67. 0
-19.0
101.1
0.004
16843
0.333
10.04
12534
0.9708
0.9729
1.3168
0.0874
-45.7
-69.4
-19.2
-98.8
0.004
0.221
9.66
-47.0
13242
0.8528
0.84106
1.3798
0.0921
-71.7
-19.0
100.7
0.009
0.222
9.31
11621
0.8829
0.8925
-6815
-18.7
.-45.5
1.3168
0.0965
99.2
0.012
0.223
8.98
12183
0.8586
0.8947
1.3725
0.1042
-41.0
-68.1
-18.7
100.6
0.020
0.156
8.68
-41.0
10328
0.9129
0.8915
-65.7
-19.2
1.2857
0.1132
95.1
0.020
0.047
8.39
10733
0.9255
0.9320
-43.8
-63.8
-19.8
1.3327
0.1183
92.5
0.C20
0.016
- 128 -
Table A4.2:
Period
Palmdale, 2 to 36 Hours
Lambda1 Lambda2
Coherl
Coher2
EpsilonE Epsi lonH
GamimaH
Theta2
GammaE
App. Res.
Thetal
8.13
-43.2
7.88
-44.2
0.9927
10296
0.9892
-63.4
-19.8
9635
0.9074
0.9274
-62.3
-19.9
0.1193
1.3265
C .018
0.G20
93.2
0.1204
1.3034
0.005
0.023
93.5
7.64
-43.2
7.42
-42.5
0.9155
9537
0.9091
-19.9
-63.1
10205
0.9210
0.9"16
-62.0
-20.1
0.1235
1.3166
G.013
0.018
93.3
0.1227
1.3821
0.034
91.0
0.017
7.21
-41.2
12210
0.8789
0.8926
-19.2
-60.4
0.1288
1.5335
0.101
0.C08
97.5
7.01
-43.8
11230
0.8948
0.9008
-64.2
-19.1
0.1252
1.4913
97.6
0.079
0.016
6. 83
0.8575
10410
0.8498
-19.3
-67.5
0.1197
1.4553
G.139
0.G13
97.2
6.65
-45.6
0.9270
0.8895
9773
-18.9
-69.3
0.1243
1.4287
0.138
0.006
98.5
8.48
-38.6
0.1320
1.4094
0.9606
9269
0.9690
c.009
0.019
100.7
-18.6
-68.2
6.32
-38.3
0.9688
8953
0.9687
-18.6
-64.6
0.1374
1.4025
0.022
0.020
99.1
6.17
38.8
0.9815
0.9880
8912
-19.0
-63.3
1.4165
0.1422
0.041
0.022
97.4
6.02
-38.1
0.9831
0.9923
9212
-63.4
-19.0
0.1409
1.4574
0.020
0.019
97.2
5.89
-39.2
0.9462
0.9210
9216
-19.1
-62.6
0.1430
1.4748
0.042
0.020
96.0
5.75
-41.0
0.9357
9547
0.9424
-19.5
-60.6
0.1428
1.5182
0.052
0.022
94.7
5.63
-42.2
0.9572
9471
0.9567
-81.4
-19.5
0.1426
1.5290
0.029
0.018
94.7
-47.0
-
129
-
Table A4.2:
Period
Palmdale. 2 to 36 Hours
App. Res. Coherl
Coher2
Lambda1 Lambda2
Theta2
GammaE
GammaH
EpsilonE EpsilonH
Thetal
5.51
-48.3
11299
0.8713
0.9162
-67.1
-19.8
0.1291
1.6884
0.095
0.011
96.1
5.39
-54.4
13736
0.9223
0.9374
0.1147
1.8815
-19.8
0.146
-68.3
102.4
0.012
5.28
-58.9
12384
0.7286
0.7908
1.8052
0.1249
-19.8
-66.3
102.7
0.149
0.008
5.17
-54.3
9934
0.8684
0.9096
-65.2
-19.5
1.6334
0.1317
99.4
0.115
0.005
5.07
-37.4
8853
0.9675
0.9677
-18.7
-64.6
0.1624
1.5575
98.1
0.028
0.117
-33.9
8123
0.8949
0.9003
-18.4
-66.3
1.5065
0.1671
99.9
0.151
0.036
4.88
-33.9
4.79
-32.6
8239
0.9580
0.9396
-64.2
-18.3
R658
0.8570
0.8297
-63.9
-18.5
1.5319
0.1680
0.136
99.4
0.034
1.5853
0.1695
99.0
0.034
0.128
4.70
-28.8
9226
0.9522
0.9242
-18.3
-63.2
1.6517
0.1669
0.075
99.2
0.032
4.61
-27.0
9831
0.8757
0.8803
-61.7
-18.4
1.7206
0.1722
0.G33
C.063
99.5
4.53
-34.1
10138
0.9580
0.9598
-60.0
-18.5
0.1646
1.7629
0.066
99.4
0.016
4.45
-37.7
12454
0.1571
0.7771
1.9711
0.8395
0.089
100.5
0.011
-60.2
-19.0
4.38
-39.0
15082
0.9322
0.9586
-81.9
-19.1
4.30
0.1546
16161
0.9522
0.9662
2.2841
0.110
0.009
-60.8
-19.1
104.2
4.
97
-39.5
4.23
-39.1
2.1879
103.3
0.1485
0.013
0.120
0.1634
16739
0.9289
2.3440
0.9258
0.099
0.008
-58.7
-18.7
104.6
-
130
Table A4.2:
Period
App.
Theta1
2 to 36 Hours
Pa IlaIe.
Res.
Coher 1
Theta2
Lambdal Lambda2
Coher2
EpsilonE Epsi lonH
GammaE
GammaH
0.9613
11732
0.9489
4.16
-53.9
-18.8
-33. 1
0.1681
1 .9785
c.012
99.3
0.006
4.10
-31.6
11860
0.9719
0.9806
-53.6
-18.8
0.1696
2.0054
0.036
0.007
99.0
4.03
-31.6
0.9458
10651
0.9433
-18.5
-54 .9
0.1767
1.9156
0.041
0.010
98.4
3.97
-30.7
0.9729
0.9696
10359
-18.3
-53.8
0.1817
1.9039
0.050
97.9
0.008
3.91
-29.1
0.9391
9462
0.9219
-53.2
-18.2
0.1821
1.8336
0.070
0.011
97.1
3.85
-27.8
0.8600
R456
0.8535
-18.2
-53.1
1.7466
96.4
3.79
-31.0
0.9323
0.9116
10330
-18.4
-54.9
3.74
-30.9
0.9610
0.9198
9803
-54.4
-18.9
-
3.68
-28.8
9148
0.9519
0.9740
-19.3
-50.8
0.1685
1.8573
G.068
0.001
93.2
3.63
-26.6
0.9701
0.9434
9078
-19.8
-49.1
0.1675
1.8634
0.111
0.067
92.1
3.58.
-25.0
0.9232 - 0.9388
8646
-20.3
-47.8
0.1549
1.8313
0.132
0.008
90.2
3.53
-26.9
0;8798
0.8323
8204
-20.5
-43.0
0.1663
1.7963
0.143
0.008
86.1
3.482
-26.6
0.9175
0.8656
7793
-20.5
-44.2
88.8
- 131 w
0.1750
0.076
0.010
0.1704
1.9450
0.001
0.009
97.5
1.9087
95.8
1. 7628
0.1737
0.019
0.010
0.1784
0.203
0.015
Table A4.2:
Period
Palmdale, 2 to 36 Hnurs
Coher2
Lambdal Lambda2
Coherl
EpsilcnE -EpsilonH
GammaH
GammaE
Theta2
App. Res.
Theta1
3.44
-24.9
3.39
0.8778
7467
0.8545
-44.8
-20.5
8075
0.9094
0.9221
-46.1
-20.1
0.17217
1.7373
G.227
0.016
90.8
0.1682
1.8187
0.195
0.017
93.8
3.35
-22.4
-24.0
7818
0.9645
0.9701
-20.5
-46.0
7944
0.9747
0.9681
-43.6
-20.2
0.1654
1.8014
0.249
0.C20
91.6
0.1916
1.8276
0.201
0.013
91.5
3.26
-19.3
0.9567
0.9153
8288
-20.1
-44.3
0.1975
1.8788
0.243
0.018
94.4
3.22
-20.6
0.9261
0.8973
8427
-19.9
-42.9
0.1943
1.9065
0.240
0.013
93.9
0.8604
0.8728
8222
-2G.0
-43.2
0.1976
1.8950
0.243
0.G15
92.9
0.9668
0.9372
6962
-20.4
-42.4
0.2089
1.7545
0.296
0.016
91.8
3.10
-19.4
0.8842
0.8920
6421
-20.4
-41.8
0.2165
1.6953
C.309
0.017
91.4
3.07
-14.3
0.8682
0.8511
5759
-19.7
-46.2
0.2011
1.6153
0.414
0.030
97.2
3.03
-18.0
0.8882
0.8637
5728
-42.8
-20.0
0.1961
1.6204
0.363
0.021
91.6
0.9004
0.8998
-199. 5394
- 19.0
-20.8
-37.3
0.1981
1.5818
0.376
0.019
87.4
-22.3
3.30
-21.8
-1.7
8
-21.7
-
132
-
Table A4.2:
Palmdale. 2 to 36 Hours
Period App. Res. Coherl
Lambda1 Lambda2
Coher2
EpsilonE EpsilonH
Thetal
Theta2
GammaH
GammaE
2.96
-22.1
5303
0.6645
0.7965
-21.2
-31.3
1.5776
0.1909
0.362
0.017
81.8
2.93
-24.5
4625
0.9009
0.9502
-28.2
-21.9
0.1829
1.4817
0.4A51
0.027
77.0
2.89
-30.0
4483
0.8202
0.8580
-29.3
-21.6
0.1708
1.4671
0.349
0.019
79.5
2.86
-31.0
4382
0.8249
0.8595
-26.1
-22.6
0.1558
1.4587
0.374
74.6
0.021
2.83
-29.1
0.9573
0,9657
4471
-22.4
-28.2
1.4816
0.1649
0.353
0.020
78.3
2.80
-26.5
0.9252
0.9326
4894
-31.6
-21.6
0.1676
1.5586
0.332
81.9
0.023
2.77
-27.9
4745
0.9116
0.9174
-21.9-30.8
1.5431
0.1735
0.348
0.021
79.9
2.74
-25.0
0.9781
0.9742
4794
-21.8
-30.4
0.1770
1.5595
0.281
0.011
79.1
2.71
-27.1
0.9449
4493
0.9231
-22.3
-23.9
0.1832
1.5178
0.315
0.068
74.6
2.68
-27.7
2.65
-26.6
0.9481
0.9208
4380
-22.1
-25.9
0.9217
0.9247
4150
-26.6
-22.1
0.1766
1.5064
C.292
0.608
75.7
2.63
-29.2
0.8633
0.7958
3765
-31.2
-22.6
0.1722
1.4112
G.256
0.602
72.4
2.60
-30.0
0.9364
0.9256
3959
-22.5
-36.6
72.7
- 133 -
0.1761
1.4740
0.340
0.013
76.2
1.4546
0.1692
0.001
0.175
Table A4.2:
Palmdale, 2 to 36 Hours
Period
Res.
Coher1
Coh e r2
Lambda1 Lambda2
Theta2
Gamm aH
EpsilonE EpsilonH
GammaE
App.
Thetal
2.57
-29.5
3616
0.8285
0.8733
-37.8
-22.2
1.3971
0.1771
77.0
0.0G7
0.209
2.55
-26.9
3582
0.9033
0.9350
-39.4
-22.2
78.3
-24.9
4387
0.9331
0.9430
-39.6
-22.3
0.1750
1.5542
0.05
%
0.042
76.4
2.50
-25.6
4404
0.8238
0.8262
-39.0
-22.5
0.1735
1.5650
0.041
74.4
0.004
2.47
-25.2
0.9179
4339
0.8874
-31.8
-22.3
0.1660
1.5608
0.069
75.2
0.004
2.45
-22.5
3762
0.9457
0.9337
-26.8
-22.3
0.1807
1.4604
0.158
76.1
0.008
2.43
-22.1
4008
0.9147
0.9522
-26.6
-22.9
0.1762
1.5145
0.233
72.2
0.021
2.40
-21.3
3987
0.7539
0.8749
-27.0
-23.1
0.1738
1.5177
0.193
72.2
0.018
2.38
-16.5
3532
0.1625
0.8538
0.88411.4352
0.310
0.038
-31.7
-23.1
68.0
2.36
-17.6
3389
0.9043
0.9139
-31.5
-23.1
0.1524
1.4125
G.31G
0.033
65.5
2.34
-19.8
3288
0.9087
0.9378
-33.1
-23.6
0.1687
1.3976
0.289
65.1
0.025
2.32
-26.2
3509
0.9364
0.9286
-25.8
-23.1
0.1615
1.4503
G.169
0.007
67.2
2.52
-
134 -
1.3975
0.1681
0.017
0.192
Table A4.2:
Palmdale,
2 to 36 Hours
Period App. Res.
Lambda2
Coher 1
Lambda1
Coher2
Thetal
Theta2
EpsilonE Epsi lonH
GammaE
GammaH
2.30
-26.9
3763
0.8519
-30.5
0,8735
-23.0
1.5087
63.9
0.1461
0.098
0.005
-23.3
3978
0.9149
0.9322
-27.0
-23.0
0.1403
1.5582
0.070
0.011
62.8
2.26
-25.3
3680
0.9273
0.9727
-24.6
-23.5
0.1380
1.5054
0.066
0.011
63.6
2.24
-26.7
3645
0.1577
1.5047
64.6
0.005
0.013
2.22
3806
0.9556
0.9627
-24.4
-27.5
2.28
-25.6
0.8714
-23.3
0.8600
-24.0
1.5443
61.4
0.1402
0. 006
0.005
0.1134
0.046
0.017
2.20
-22.6
3674
2.18
3774
0.9151
0.9570
-28.7
-23.1
1.5511
0.1135
0.172
0.020
63.2
3567
0.9304
0.9362
-23.2
-23.0
2857
0.7503
0.8391
-28.0
-23.0
1.5144
0.1120
0.056
0.007
68.7
0.1160
1.3610
0.201
0.028
68.5
2.12
3238
0.8824
0.9053
-26.5
-22.8
1.4548
62.3
2.11
2914
0.1145
1.3860
0.040
0.002
65.5
-17.7
2.16
-21.5
2.14
-18.6
-17.9
-26.4
0.7872
--24.2
0.9105
-37.7
0.8774
-23.7
1.5239
60.0
0.8976
-22.7
0.0964
G.029
0.009
2.09
-10.0
0.8797
0.8879
3391
-40.7
-23.2
0.1222
1.5013
0.177
0.017
62.3
2.07
-21.8
3070
0.9326
0.9073
-33.4
-23.6
64.7
2.06
-23.7
2505
0.7297
0.7594
-34.1
-23.0
0.0992
1.3008
0.010
0.017
73.7
-
135
1.4342
0.1233
0.094
0.012
Table A4.3:
Palmdale,
10 to 90 Minutes
Coherl
Coher2
Lambdal Lambda2
Period App. Res.
EpsilonE EpsilonH
Theta2
GammaE
GammaH
Theta1
91.43
-20.7
71.11
-19.6
0.2902
0.9019
0.8988
6247
0.136
0.G36
107.5
-18.0
-49.5
0.3350
2.4874
0.7458
0.8699
5280
0.108
0.038
109.3
-17.3
-48.9
58.18
-1S.0
0.3790
2.7186
0.8547
0.8458
5160
0.020
0.022
108.7
-16.4
-44.3
49.23
-16.1
0.4249
0.94,1
2.9155
0.9080
5022
0.071
0.008
107.6
-16.3
-39.4
42.67
-18.1
0.4525
3.0708
0.9549
0.9563
4828
G.056
0.008
113.6
-15.0
-33.6
37.65
-18.0
0.4876
3.1723
0.8993
0.9575
4546
0.019
0.013
112.0
-15.0
-36.2
33 .6Ge
4478
-18.0
2.
0.9248
-28.S
0.9263
-13.7
3861
0.5485
3.3286
0.082
0.008
114.7
30.48
-21.1
0.5623
3.5429
0.6385
0.6907
4590
0.108
0.008
121.8
-12.0
-23.5
27.83
-13.7
0.5439
3.5910
0.8076
0.8304
4306
0.167
0.035
122.9
-11.2
-23.8
-13.9
0.5991
3.4822
0.7919
0.8655
3725
0.181
0.055
120.9
-10.5
-26.6
23.70
-20.7
0.6298
2.9515
0.6996
0.8198
2478
0.013
0.018
120.7
-8.4
-26.2
22.07
-17.0
0.7283
3.3612
0.8327
0.8697
2992
0.126
0.023
108.0
-12.5
-18.3
20.65
-12.9
0.6689
3.2442
0.6206
0.5727
2607
0.064
0.020
113.6
-11.5
-17.4
25.G0
- 136
-
Table A4.3:
Period
App.
Thetal
Palmdale, 10
to 90 Minutes
Res. Coher 1
Lambda2
Coher2
Lambda1
Theta2
EpsilonE EpsilonH
GammaE
GammaH
19.39
-12.3
2474
18.29
3067
0.5806
0.7047
0.7630
3.7387
-18.7
0.050
0.205
-12.0
120.2
3.0
17.30
3519
-31.1
0.9221
0.6740
0.8094
3.2606
-8.8
0.100
0.022
-11.0
115.3
4.1177
0.8492
0.4787
0.7256
0.079
C.264
15.8
128.4
-13.2
17.7
0.4704
4532
4.7972
0.8837
0.8664
-15.9
0.183
0.018
-15.3
117.6
15.6
4431
0.7529
0.4878
0.7350
4.8636
C.177
-12.7
0.G06
114.7
-15.9
16.41
15.61
4923
14.88
12.9
14.22
0.7673
0.4043
0.7371
5.2500
0.002
0.248
-9.8
-16.6
115.1
3767
10.1
13. G2
29.0
13.06
0.5603
2.9788
0.4346
0.5762
0.075
0.214
36.2
-15.4
119.6
1197
0.4271
0.7393
2.8191
0.528
0.348
9.7
129.1
0.083
-13.7
1119
0.3981
0.5221
2.7785
0.3610
59.9
-11.8
140.1
0.099
0.286
521
0.3154
0.4996
0.5399
1.9322
0.446
62.7
-11.0
0.109
131.9
45.7
11.23
0.6705
397
48.4
4.6979
0.3691
0.006
G.136
114.9
1391
19.6
11.64
. --
0.8694
3.5691
0.4322
0.762
14.8
0.037
0.126
-16.1
112.7
42.6
12.08
0.G379
-16.4
2082
14.8
12.55
0.8524
12.0
61.0
0.1777
0.6307
1.7165
136.2
0.087
0.508
-13.0
- 137 -
Table A4.4:
Period
App.
Thetal
Hollister, 36+ Hours
Res.
Coherl
The ta2
Cchor2
GammaE
Lambda1 Lambda2
EpsilonE EpsilonH
GammaH
73.14
-78.0
0.4492
0.0053
10626
0.9328
0.8766
0.006
0.023
-3.4
-106.5
132.0
56.89
-78.2
0.0124
9848
0.4903
0.8819
0.8407
0.104
0.007
-74.0
-2.5
127.9
0.0119
46.55
11154
0.7547
0.5769
0.8568
G.022
126.3
0.G11
-2.68
-70. 7
-92.7
39.38
-67.2
10074
0.5575
-106.1
0.30'8
0.0086
0.5960
0.035
0.016
123.2
0.7175
0.0071
0.5981
C.169
0.020
123.4
-3.1
34.13
-53.3
8790
0.7128
-101.6
30.12
-44.6
0.0118
0.6404
8894
0.8769
0.9169
0.011
0.040
-78.5
-4.1
126.5
26.95
-42.5
0.0149
0.9287
0.7132
9870
0.9277
G.036
-4.0
0.005
125.G
-78.0
24.38
0.0126
0.9819
0.7434
0.9775
9702
0.058
124.5
0.008
-4.1
-77.8
22.268
-42.5
0.0130
0 9745
0.7891
9979
0.9435
G.098
122. 2
0.007
-4.2
-75.4
20.48
-38.4
0=6741
0.82868
0.0160
10123
0.7010
-68.5
0.135
0.000
-4.2
124.4
-41.8
0.9462?
12224
0.0161
0.9263
0.8993
18.96
0.225
0.,02
122.4
-4.0
-37.8
-76.3
14232
0.0151
1.0581
0.9428
0.9248
17.66
0.026
0.004
121.3
-32.3
-59.6
-3.9
16.52
-34.9
0.0071
1.0207
12388
0.8726
0.8760
0.226
0.006
118.7
-71.7
-4.0
-
138
-
Table A4.5:
Hollister,
2 to 36Hours
Period App. Res. Coher1
Lambda1 Lambda2
C her2
EpsilonE EpsilonH
The ta2
Gamm aH
Theta1
GammaE
0.0036
0.8861
14632
73.14
0.5271
0.7941
0.433
0.069
-49.6
-145.0
-3.9
122.8
56.89
770.7
0.0137
0.4644
8834
0.896R
0.8676
0.040
-71.1
0.008
-2.4
127.2
46.55
-60.0
0.0100
10739
0.8077
0 . 9050
0.5661
0.106
0.011
-87.1
-2.9
121.8
39.38
-62.6
0.0087
9257
0.5753
0.3109
0.5713
0.025
-111.2
-3.4
128.3
0.019
34.13
-49.8
8560
0.7398
0,7407
0.0080
0.5902
0.164
-91.2
127.8
0.020
-3.8
30.12
-39.6
0.7002
0.0135
10632
0.8888
0.9222
0.031
0.008
-75.4
-4.0
131.2
26.95
-40.7
0.0141
0.7799
11800
0.9204
0,9181
0.072
0.066
-4.0
127.5
-75.7
24.38
-40.0
0.0135
0.807Ai
11443
0.9805
0.9836
0.091
0.006
127.0
-76.1
-4.0
22.26
-41.2
0.0133
0.9374
0.9627
11648
0.8525
0.120
0.006
124.9
-73.9
-4.1
20.48
0.0157
0.9008
11964
0.7187
0.6495
G.143
0.600
126.2
-68.8
-4.1
18.96
--36.6
0.0166
0.9995
13640
0.9068
0,9300
0.209
0.002
125.7
-74.8
-4.0
17.66
-28.0
0.0162
17190
1.1629
0.8632
0.9026
6.017
0.004
123.5
-61.2
-3.9
16.52
-28.9
0.0109
1.1566
0.861 0
15909
0.8579
0.094
0.004
118.0
-4.0
-70.5
0.0130
0,9153
1.3910
0.8897
15.52
21615
G.067
0.001
120.4
-4.1
-36.5
-78 .2
m
139
-
Table A4.5:
4
Hollister, ? to 36 Hours
Period App. Res. Coher 1
Lambda1 Lambda2
Coher?
Theta1
Theta2
GammaH
EpsilonE EpsilonH
GammaE
14.63
-46.1
0.0230
25193
1.5466
0.6579
0.756;3
-55.7f
G.056
0.601
116.3
-4.0
13.84
12687
-51.1
0.7536
0.8019
0.0221
1.1285
8 0. 8
-3.7
127.7
0.396
0.009
-53.7
15405
0.6685
0.6191
1.2766
0.0180
-74.9
-3.7
120.8
G.121
0.007
12.49
-60.7
14626
0.8552
0.8404
1.2754
0.0185
-70.6
-3.8
114.3
0.007
0.169
11.91
-56.3
14627
0.8652
0.8511
1.3062
0.0193
-73.8
-3.8
117.8
0.006
G.107
11.38
-57.3
13542
10.89
-46.8
10338
0.8788
0.8680
1.1481
0.0146
-89.8
C.213
-3.6
0. c 11
129.5
13.113
0.9203
-74.5
0.8997
1.2857
0.0188
-3.8
0.006
117.7
0.130
10.45
20642
0.9166
0. 9241
1.6564
0.0160
-39.2
-60.6
-3.7
0.277
118.4
0.005
10.04
-41.3
15352
0.8511
0.9075
1.4574
0.0154
-68.8
G.183
-3.7
122.8
0.003
9.66
-42.4
15955
0.7173
0.0186
0.6121
1.5145
-69.1
0.207
-3.6
0.002
123.6
9.31
-39.4
13063
0.8996
0.8096
1.3960
0.0193
-58:7
-3.4
0.156
0.003
118.8
8.98
-29.0
13355
8.68
-26.0
11444
0.4024
0.0898
1.3533
0.0273
-66.4
-3.8
0.081
120.1
0.007
8.39
-34.8
13690
0.9733
0.0328
0.9589
1.5051
-61.4
0.141
0.003
-4.1
11 0.2
-69.4
0.90G7
0.9176
0.0206
1.4370
0.116
0.065
-3.6
120.8
- 140 -
Table A4.5:
Hollister, 2 to 36 Flours
Period App. Res.
Coherl
Cohor2
Lambda1 Lambda2
Thetal
Theta2
GammaE
GammaH
EpsilonE EpsilonH
8.13
-36.1
12419
0.9950
-64.S5
7.88
12212
0.8888
0.8870
1.4674
0.0314
-62.1
109.3
-4.1
0.005
0.209
7.64
-37.7
12117
0.6752
0.8190
1.4840
0.0316
-63.6
-4.1
110.2
0.005
G.183
7.42
-37.1
12385
0.9179
0.8993
1.5225
0.0318
-59.2
-4.1
108.8
0.005
0.163
7.21
-44.5
11926
0.8244
1.5155
0.0318
0.8256
-57.7
-3.9
118.0
0.601
C.112
7.01
-44.6
8600
0.8617
0.7893
1.3050
0.0287
-60.8
-3.7
125.4
0.003
0.025
6.83
-42.9
9343
6.65
G577
6.48
-20.9
6794
0.9625
0.9476
1.2066
0.0293
-70.8
-3.4
139.5
0.612
G.258
6.32
-22.6
7002
0.7988
0.7316
1.2403
0.0328
-71.0
134.8
0.013
-3.5
0.367
6.17
7530
-39.5
0.7608
-61.6
0.9945
1.4569
0.0319
111.2
0. 604
G. 171
0.8154
1.3787
0.0262
-3.7
0.004
129.9
G.035
0.5582
0.6631
1.1721
0.0267
-64.4
-3.4
133.2
0.002
0.024
- 35'.1
0.9662
-66.5
0.9504
1.3021
0.0352
-3.8
122. 3
0.012
0.520
6.02
-31.6
7974
0.9859
0.
-66.4
-3.7
5.89
35.3
8249
0.6783
0.7961
1.3953
0.0352
-63.1
-3.8
120.8
0.467
0.011
5.75
-48.0
10853
0.8150
0.7r13
1.6187
0.0346
-52.5
-4.0
168.7
0.010
0.406
9760
- 141 -
1.3560
0.0350
124.1
0.011
0.419
Hollister. 2 to 36 Hours
Table A4.5:
Period
App.
Theta1
Res.
Coher1
Theta2
Lambda1
Coher2
GammaE
GammaH
Lambda2
EpsilonE
EpsilonH
5.63
-48.1
1.5G92
0.0356
0.8724
0.8780
9975
C.321
0.608
111.1
-3.9
-55.1
5.51
-66.2
0.0297
2.0331
0.9681
0.9577
16385
0.006
0.002
123.0
-62.0
-3.8
5.39
-64.2
0.0248
0.8255
2.4463
0.8615
23221
G.048
0.603
-3.7
134.5
-65.9
5.28
70.3
0.0273
2.6067
0.7935
0.8273
25824
0.075
0.002
135.0
-3.8
-66.8
76.4
0.0244
2.4366
0.9086
0.9009
22107
C.157
0.000
133.6
-3.8
-66.6
5.17
5.07
-39.6
0.0351
1.6378
0.9521
0.9510
9791
0.124
122.5
0.001
-3.5
-58.9
1.758
0.7286
0.7263
10051
4.97
-3.5
124.6
-60.8
-32.8
0.0374
0.G03
G.177
0.0374
1.7092
0.9436
0.9580
4.88
10256
0.189
0.004
127.3
-3.4
-62.8
-28.2
4.79
-23.0
4.70
-12.7
4.61
-13.5
4.53
-31.1
1.7011
0.8013
0.7759
9969
128.4
-3.3
-64.3
0.0384
6.143
0.G04
0.0348
1.7426
0.9317
0.9590
10270
0.049
0.067
C
133.9
-3.1
-67.2
0.4416
9632
-68.8
0.0371
1.7030
0.139
0.008
134.4
0.3311
-3.1
0.0342
1.8430
0.7914
0.8855
11081
0.010
0.062
11.9
-3.2
-64.4
0.0320
2.1155
0.9307
0.8900
14346
4.45
0.063
0.001
-62.2
131.7
-3.4
-45.9
4.387
-47.0
0.0321
0.9213
2.2194
0.8905
15520
0.062
0.001
130.8
-3.5
-62.4
-
142
-
Table A4.5:
Hollister, 2 to 36 Holtrs
Period App.
Theta1
Lambda2
Res.
Lambda1
Coherl
Coher2
EpsilonE EpsilonH
GammaH
Theta2
GammaE
0.0318
2.3722
C.019
0.001
132.4
4.30
-44.9
17433
4.23
-46.7
0.0318
2.4175
0.9506; 0.9328,
17806
0.073
0.000
-61.5
-3.5
129.5
0.8921
0.8838
-65.3
-3.6.
0.4817
4.16
0.4897
12459
-33.5S
-53.0
-3.4
4.10
-29.8
0.0334
2.0389
0.007
0.001
123.6
0.0349
2.1092
0.9260
0.9009
13120
0.010
0.000
123.4
-52.7
-3.4
0.0374
0.9146
0.9031
1.9236
4.03
10741
C.066
0.001
122.6
-28.2
-57.8
-3.3
3.97
-25.3
3.91
-25.1
3.85
-21.4
9925
0.9297
0.9246
-56.7
10111
0.8862
-51.4
1.8636
122.8
-3.2
0.8949
-3.3
0.0378
0.107
0.003
0.0387
1.8955
G.146
0.002
121.0
0.4954
0.0397
1 8048
9028
0.3207
0.258
0.002
119.7
-3.5
-45.1
2.2623
0.0351
0.004
0.000
3.79
-36.1
13976
0.7965
-54.2
3.74
0.0333
0.9767
2.3849
0.9716
15305
0.100
0.003
123.4
-3.9
-61.7
-32.2
0.8263
122.6
0.0306
3.68
0.9953
2.2587
135 30
0.9773
-26.8
0.227
0.001
-47.1
119.0
-4.0
3.63
-28.3
0.0268
12230
0.9503
2.1629
0. 9594
0.267
0.001
113.2
-42.5
-4.2
-
143 -
Table A4.5:
Period
Hollister, 2 to 36 Hours
App. Res.
The.tal
3.58
Coher 1
Theta2
Coher2
Lambdal Lambda2
GammaE
GammaH
EpsilonE Epsi lonH
-31.5
12911
0.8260
0.8683
2.2379
0.0250
-35.5
-4.2
116.2 0.001
C.12C
3.53
-34.9
10574
0.7230
0.0299
0.7697
2.0394
-44.3
-4.1
109.8
0.001
0.110
3.48
-28.2
11121
0.8003
0.0304
2.1059
0.8413
-45.4
C.236
-4.0
117.7
0.001
3.44
-18.0
11806
0.4557
0.0325
0.6007
2.1845
0.268
-42.0
-3.9
122.9
0.001
14502
3.39
0.9138
0.90?6
2.4372
0.0310
G. 228
-15.6
-47.6
0.003
-3.9
126.4
3.35
- 13.9
14984
0.0319
0.9659
2.4938
0.9631
0.250
125.4
0.003
-52.5
-3.9
14811
0.0355
0.9475
2.4955
0.9418
3.30
C .288
0.C03
-2C.9
-50.5
-4.0
120.5
0.0365
2.8274
0.9200
18771
0.8583
0.266
0.004
125.4
-45.9
-3.9
3.26
-17.3
19103
0.9679
3.22
-51.2
-15.6
0.
1
0.9549
0.0388
2.8704
C.332
0.Cos
126.2
0.8874
0.0358
2.7271
0.270
0.0C6
123.9
0.9358
0.0380
2.4036
0.434
0.007
124.2
-3.8
.
3.18
-23.8
17028
3.14
-18.7
13066
3.10
0.0396
0.7486
2.2411
11221
0.7790
0.539
131.1
0.0 C08
-50.2
-4.0
-6.5
3.07
0.9088
-5 3.3
0.9352
-49.8
-3.9
-4.0
20.3
0.9907
9860
0.0364
0.9940
2.1134
-70.5
0.561
-3.9
157.0
0.013
22.1
8697
0.9194
0(.9223
-66.1
-4.0
3.03
- 144 -
1.9968
0.0404
0'. 574
153.7
0.012
Table A4.5:
Period
App.
Theta 1
2.99
2.96
2.93
Hollister. ? to 36 Hours
Res.
Coherl
The t 2
Coher2
GammaE
Lambda1
Lambda2
GammaH
EpsilonE EpsilonH
22.7
7815
0.8987
0.9194
0.0383
1.9040
0.559
-66.9
154.5
0.012
-4.0
34.2
9447
0.6966
0.78G
-73.2
-4.0
34.3
8154
0.7917
0.0371
1.9675
0.8341
-80.9
0.795
-4.0
169.1
0.012
0.0372
2. 1055
0.646
0.01 2
162.9
2.89
-18.1
7779
0.9050
0.8931
1.9327
0.0342
-45.4
-4.0
0.657
0.009
124.7
2.86
-24.5
6531
0.9266
0.9428
1 .7807
-39.0
-4.1
119.1
0.0313
0.574
0.008
283
-22.7
7182
0.9899
0.9927
1.8779
0.0305
-43.9
-4.1
123.1
0.492
0.009
80
-18.9
7588
0.7971
0.8010
1.9409
0.0331
0.440
-47.1
125.8
0.0 C9
-4.0
2.77
-26.5
7373
0.8927
0.8789
1.92368
0.0367
-44.6
-4.1
118.0
0.009
0.447
2.74
-26.2
7054
2.71
-28.1
0.9110
7144
0.9211
-36.4
-4.4
2.8
7138
-18.8
-40.5
0.9483
0.9532
1.8916
-4.2
1-11.8
0.7429
0. 8099
-4.3
-35.3
0.0346
0.422
0.008
0.0358
1,9139
G.500
0.009
97.9
0.0333
1.9231
0.563
101.9
0.011
2.65
6631
0.8920
0.8953
1,8632
0.0322
G.711
0. G11
-25.7
111.1
-4.2
2.83
-17.6
5934
-21.1
-30.3
0.9252
0.9238
-33.2
-4.4
0.0329
1.7717
0.574
107.4
0.009
6231
0.0346
0.9105
0.920A1
1.8247
0.G10
-30.C
110.9
-4.3
-
145 -
Table A4.5:
Hollister. 2 to 3E H-ours
Period App.
Theta1
Lambda2
Lambda1
Coher2
Coher 1
Res.
EpsilonE EpsilonH
GammaH
GammaE
Theta2
2.57 ~
-26.0
0.0389
1.9009
f.9448
0.8735
6694
0.487
0.012
120.5
-4.1
-38.1
2.55
-21.1
0.0396
1.8874
0.9668
0.9474
6533
0.406
0.010
126.9
-38.1
-4.0
2.52
6958
-22.7
0.9650
0.9511
-4.0
-41.0
0.0458
1.9574
0.308
0.008
123.9
0.0480
1.9137
0.F969
0.305
0.008
117.2
-4.1
2.50
-27.2
6586
2.47
-26.6
0.0489
1.9277
6618
0.8406
0.87?8
0.305
0.007
114.9
-34.7
-4.1
2.45
5724
- 22.7
0.9127
-35.6
0.8883
-34.8
0.862?
-4.0
0.0494
1.8015
0.007
0.354
117.7
2.43
-21.9
0.0426
1.8786
6166
0.9205
0.9146
0.520
0.010
109.3
-30.7
-4.1
2.40
5652
-23.8
0.9109
-32.1
0.9548
0.0448
1.8071
0.9327
0.378
0.009
107.2
-4.2
0.941 ?
1 .7360
1-C9.2
0.0403
0.396
0.009
2.38
5167
2.36
0.0367
1.6995
0.8858
4907
0.9169
G.452
0.010
110.2
-4.1
-26.3
2.34
-25.9
4499
2.32
-24.8
3757
2.30
3712
-24.4
-26.2
-26.0
2.28.
-21.9
-29.6
0.9855
-30.5
0.9717
-27.3
0.9237
-32.2
-4.1
0.985
-4.2
0.97?1
-4.2
0.0394
1.6348
0.481
0.012
107.7
0.0401
1.5008
G.286
0.008
109.4
0.0443
1.4985
0.9220
0.214
0.004
107.8
-4.2
0.0427
1.5686
0.9191
4021
0.9379
G.26C
108.3
0.004
-4.3
-30.4
m
146 -
Table A4.5:
Hollister. 2 to 36 Hours
Period
Res. Coherl
Coher2
Lambdal Lambda2
Theta2
GammaE
GammrraH
EpsilonE EpsilonH
App.
Theta1
2.26
-26.5
4003
0.9921
0.9810
1.5700
-21.4
-4.5
100.6
0.0400
G.257
0.C03
2.24
-30.3
3753
0.0404
0.010
2.22
-30.8
3494
2.20
-26.4
2791
0.8523
0.8455
0.0400
1.3282
-36.5
-4.3
108.7
0.077
0.001
2.18
-23.6
2968
0.9259
0.9576
1.3755
0.0346
-4.3
-25.8
107.6
0.002
G.021
2.16
-28.7
3190
0.8663
0.8236
1.4321
0.0313
-21.8
-3.9
127.1
0.003
0.049
2.14
-24.3
2734
0.6537
0.7297
0.0312
1.3313
0.002
G.022
-25.7
131.6
-3.5
2.12
-30.9
2635
0.9281
1.3126
0.0292
0,9619
-33.3
-4.1
0.235
109.3
0.009
2.11
-45.5
2225
0.9151
0.9063
0.0324
1.2112
-26.5
C.074
0.601
-4.5
102.2
2.09
-42.9
4305
0.9588
0c9259
0.9683
-26.9
1.5269
113.3
-4.1
-25.3
0.9693
-4.5
1.4796
0.0452
103.1
0.608
C.321
0.8956
-4.4
0.0302
1.6915
0.309
0.062
87.9
-30.9
3726
0.8689
0.8892
-29.1
-4.3
0.0180
1.5800
91.4
0.006
0.031
2.06
-23.6
3685
0.7101
0.7730
-44.3
-4.3
0.0140
1.5777
0.006
0.110
90.1
2.07
0.9291
-1.9
-
147
-
Table A4.6:
Hollister. 10 to 90 Minutes
Period App. Res. Coher 1
CobPr.?
Lambdal Lambda2
Theta 1'
Theta2
GammaE
EpsilonE EpsilonH
GammaH
91.43
-19.3
7874
0.8804
-56.2
-3.6
71.11
-17.5
0.8518
7047
0.0691
0.7362
2.8737
-58. 0
0.148
0.009
-3.5
137.9
58.18
-17.6
6545
0.8472
0.P71 1
3.0617
-3.3
-56.7
137.1
0.0797
0.026
0.007
49.23
-17.0
6214
0.8824
-53.6
-3.3
0.0911
0.012
0.004
42.67
-19.3
0.1011
5828
0.9573
0,9589
3.3739
0.020
-52.0
-3.1
0.0 cs
138.1
37.65
-19.9
3.4148
0.1106
5268
0.906
0.8986
-56.0
-3.1
0.077
137.4
0.008
33.68
-19.4
0.1242
5026
0.9116
0.8947
3.5262
0.032
-51.5
0.0 G9
-2.8
139.9
30.48
-23.3
5080
0.4219
3.7271
0.1256
0.4L08
-47.8
0.024
-2.5
145.6
0.G09
27.83
-21.9
4347
0.8701
0.8198
0.1230
3.6079
-44.1
0.032
-2.1
145.6
0.006
25.60
3185
0.7627
0.6690
0.1365
3.2202
0.C07
C.026
-45.2
-1.7
145.0
-22.5
23.70
-15.2
,
2.6790
134.8
9?Z'
3.2432
134.5
0.0592
- 0.0G7
0.178
2310
0.6528
0.1220
0.F507
2.8497
-52.5
0.141
-1.5
153.6
0.025
-11.5
0.1524
3215
0.7302
0.5195
3.4841
G.009
0.011
-42.6
-2.5
138.7
20.65
-10.5
0.1311
2798
0.5526
0.6590
3.3605
144.5
-34.3
-2.4
0.055
0.008
22.07
-
148 -
Table A4.6:
Period
App.
Theta1
19.39
Hollister, 10 to 90 MinUtes
Res. Coher1
Coher?
Lambdal Lambda2
Theta2
GammaE
GammaH
EpsilonE EpsilonI
4.5
3289
0.8915
0.94
clg
3.7591
0.1252
-30.9
-2.5
0.614
6.01 8
150.3
7.9
5523
0.4861
0.1942
5.0170
0.1039
-33.1
-2.8
154.1
0.053
0.009
18.29
17.30
16.7
7636
0.8780
0.7715
8.0651
0.0843
-42.3
-3.3
159.7
0 . G11
20.0
7679
0.7441
0,8180
6.244L
-44.6
-3.3
150.9
18.4
5857
0.6168
0.5771
5.5917
0.0848
-45.9
-3.0
145.7
0.601
6.037
16.41
15.61
14.88
7648
17.1
14.22
8.8
13.62
0.7638
-3 .)
6.5437
141.8
0.0960
0.004
0.044
0.0999
0.004
0.147
5774
0.7182
0.4244
0.0860
5.8167
-26.6
-3.4
138.6
0.G02
G.10 1
11.7
2827
0.8920
0.7063
4. 1591
0.1152
-13.6
0.0G1
0.074
-3.3
131.2
18.3
1616
0.5519
-15.3
13.06
12.55
12.08
3.2107
0.1351
0.002
0.028
126.9
0.0439
0.2462
3.1G17
0.1143
1.9
0.297
-2.6
0.064
142.9
1303
0.4150S 0.5184
0.0805
2.9991
32.1
-2.4
0.010
0.389
155.4
20.1
11.64
0.3965
1505
8.0
454
0.287
30.0
0 F,?70
1.8040
0.0789
0.434
117.4
0.019
396
0.7245
11.2
0.F70
1.7138
0.0504
117.2
0.006
0.386
78.8
11.23
0.7169
-39.9
C. 07C
-
149
APPENDIX 5:
DATA PROCESSING STEPS
1. Obtai'n magnetic data for Boulder, Tuscon, Victoria,
(appendix 1)
Honolu'lu, and Castlerock for 1974
2.
Filter magnetic data
(appendix 1)
3. Generate time-domain operators to predict Castlerock's
(appendix 1)
magnetic field based upon the other stations
4. Select electric data sections for 1979 and 1980
(chapter 2)
(chapter 2)
5.
Filter electric data
6.
Predict magnetic data for
7.
Apply window to electic and magnetic data
1979 and 1980
(appendix 1)
(chapter 2)
8. Calculate fast fourier transform of electric and magnetic
(chapters 2 and 3)
data
9. Remove effects of RC filter from electric data
(chapter 2)
10.
Calculate MT tensors (Zh' Ze, and ZpC)
11.
Rotate tensors
(chapter 4)
(appendix 2)
Calculate eigenstates of tensors
12.
appendix 4)
(chapter 4 and
Calculate apparent resistivity in principal direction
13.
(chapter 4)
14. Attempt to fit apparent resistivity and phase data with
(chapter 5)
2-D models
-
150
-
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37,
BIOGRAPHICAL NOTE
He lived the first eighteen
The author was born in 1962.
years of his life in Overland Park (a small Kansas town of
His first
recognizable hobby was disabout 80,000).
After that, he turned to collecting
assembling appliances.
rocks, bottle caps, stamps, gum wrappers, and coins.
In
In junior high, the author discovered that he liked math.
high school,
he conducted some research projects in microHis work was
biology and found that science was fun too.
recognized in several local and national science fairs, and
During his
he was selected as a 1980 Presidential Scholar.
At
senior year, he decided that physics was the way to go.
they
about the same time, he made a deal with the Air Force:
would pay for him to go to college and then he would serve
for four years. He decided he might as well get all he could
out of the government so he selected the most expensive
school in the country, MIT.
He entered MIT in the Fall of 1980 and soon began to wonder
During his second
if physics was all that neat after all.
term, he took a course from Dr. Frank Press entitled "Survey
of Earth Sciences," and decided that geophysics was where it
In his second year, he began working with Ted
was really at.
Madden, conducting experiments on the induced polarization of
minerals.
the author tried to make
During his senior year at MIT,
Force.
Air
He said, "Just forget ab out
the
another deal with
get
go
and
a PhD and then I'll se rve
I
me for 4 years while
but
"
Oh
sure, no problem,"
they said
At first,
my time."
t
Stanford,
hey
a
nd
selected
schools
to
after he was accepted
few
a
decided
He
all."
go
after
can't
you
"Sorry,
said,
years out of school might not be so bad after all and was
especially pleased when they said he could spend his time in
The author is
the laboratory rather than Centra 1 America.
currently a physicist with the Sol id State Sciences Divis ion
of the Rome Air Development Center at Hanscom Air Force Base,
Massachuse t ts.
-
155
-