Seismic moment, stress drop, strain energy, dislocation radius, and location of seismic acoustical
emissions associated with a high alpine snowpack at Berthoud Pass, Colorado
by Charles Cleland Rose
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Earth Science
Montana State University
© Copyright by Charles Cleland Rose (1981)
Abstract:
For many years, Highway and Ski Area managers have sought a qualitative predictive indicator of the
size and timing of snow avalanches. The monitoring of the number of acoustical-seismic impulses
arising from snow instabilities is regarded as a relative indicator of an unstable snow slope but has not
yielded a qualitative predictive indicator. Until now, the source parameters (fracture area and length),
seismic moment, energy released, stress drop, and location of acoustical seismic emissions arising from
the snowpack have been neglected. A comprehension of these parameters leads to a better
understanding of the event and may help in avalanche prediction.
The seismic-event source locations are derived from time differences between P-wave arrivals at four
sensors located at the snow-ground interface. Three location methods confirm acoustical seismic
snow-event locations to within 2-4 cm when an event is internal to seismic net.
Spectral analysis of body waves from seismic snow events yield estimates of source parameters, stress
drop and energy released. Equivalent dislocation surface radii range from 4.8-9.0 cm which give stress
drops of 0,20-0.29 bars with a dissipated energy in the range of 0.205-0.632x10^6 ergs.
Spectral analysis of the acoustical seismic snow event with application of dislocation theory provides
several likely methods to predict climax type avalanches. These techniques could be used jointly or
separately to evaluate snow slope stability. Besides locating individual events, the location technique
indicates a fracture line by means of event accumulation before any surface indication is evident. This
fracture line and the migration rate of events across the starting zone could be used to predict a time
interval until snow-pack failure. Also, when equivalent dislocation radii exceed snow stratigraphic
layer thicknesses, a snowpack failure depth could be predicted. Moreover, the computed stress drop
when compared to Narita's (1980) work, gives a qualitative measure of stability. STATEMENT OF PERMISSION TO COPY
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P?
SEISMIC MOMENT, STRESS DROP, STRAIN ENERGY, DISLOCATION
RADIUS, AND LOCATION OE SEISMIC ACOUSTICAL EMISSIONS
ASSOCIATED WITH A HIGH ALPINE SNOWPACN AT BERTHOUD PASS,
COLORADO
by
Charles Cleland Rose^
A thesis submitted in partial fulfillment
of the requirements for the degree
of
MASTER OF SCIENCE .
in
Earth Science
Approved:
Graduate Deah / /
MONTANA STATE UNIVERSITY
Bozeman, Montana
September, 1981
iii
Acknowledgments
;
I would like to extend a special thanks to Dr. W. Keightly, Civil
Engineering Department, Montana State University, who provided the
main part of the program used and for his time in consultation.
Also,
a special thanks goes to Dr. R. Sommerfeld, Rocky Mountain Forest and
Range Experiment Station, for helping me select the data and for his
patience while this work was being completed.
My thanks goes also to those committee members, Dr. William St.
Lawrence of the CRREL institute, N.H., and Dr. Tony Qamar, University
of Montana, who commented on the technical aspects of this thesis.
The support and efforts of the remaining members of my committee along
with the Department of Earth Sciences, Montana State University, is
also sincerely appreciated.
The work was made possible through a grant from the U.S. Depart­
ment of Agriculture Forest Service, Rocky Mountain Forest and Range
Experiment Station (Agreement No. 16-779-CA).
agency is greatfully acknowledged.
The support by this
iv
Table of Contents
PAGE
V i t a .......................................................... ...
Acknowledgments.........................................
iii
Table of C o n t e n t s .............................................. iv
List of Table and F i g u r e s .......................
v
A b s tract........................................................ vi
Introduction ....................
I
Previous Investigations ......................................
4
Scope and M e t h o d s .............................................. 11
Instrumentation ..........................................
11
Data S e l e c t i o n ............................................ 12
Data R e d u c t i o n .................................
15
Determination of Locations ....................................
20
Spectral Analysis ............................................
23
Discussion................................
32
C o n c l u s i o n s .................................................... 35
References...................................................... 36
Glossary...........................................
39
Appendix A ...................................................... 41
Appendix B ...................................................... 50
Appendix C ...................................................... 59
Appendix D ..........
68
V
List of Table and Figures
PAGE
Figure I: Sketch map of part of the Cliff Avalanche Path,
Colorado showing locations of the sensors, elevation control
points adjusted to an arbitrary datum, and seismic snow
event locations.
............................................... 3
Figure 2: Output from three sensors showing two ultrasonic
pulses, both indicative of an intergranular failure, are
recorded on one trace............
14
Figure 3: Monochromatic signals showing the typical symmetrical
shape with uniform frequency content per sensor and inphase
characteristics between sensors................................ 14
Figure 4. Three velocity geophone records showing a typical
classical seismic snow event (341:18:56:20) with observable
P- and S-wave arrivals.......... , . ........................ 16
Figure 5: A comparison of the converted ground displacement
power spectrum (line) and the averaging operation (dashed)
so that a corner frequency can be easily selected.
.......... 19
Figure 6 : The corner frequency (Wc =2tiF c ) , is an intersection
of a horizontal trend, indicated by the horizontal line, and
a sloping trend, indicated by the sloping line................ 24
Table I: Parameters Related to the Displacement Corner
Frequency.................. ..................... ........... 30
vi
Abstract
For many years, Highway and Ski Area managers have sought a
qualitative predictive indicator of the size and timing of snow ava­
lanches. The monitoring of the number of acoustical-seismic impulses
arising from snow instabilities is regarded as a relative indicator
of an unstable snow slope but has not yielded a qualitative predictive
indicator. Until now, the source parameters (fracture area and
length), seismic moment, energy released, stress drop, and location of
acoustical seismic emissions arising from the snowpack have been ne­
glected. A comprehension of these parameters leads to a better
understanding of the event and may help in avalanche prediction.
The seismic-event source locations are derived from time differ­
ences between P-wave arrivals at four sensors located at the snowground interface. Three location methods confirm acoustical seismic
snow-event locations to within 2-4 cm when an event is internal to
seismic net.
Spectral analysis of body waves from seismic snow events yield
estimates of source parameters, stress drop and energy released.
Equivalent dislocation surface radii range from 4.8-9.0 cm which give
stress drops of 0,20-0.29 bars with a dissipated energy in the range
of 0.205-0.632x10 ergs.
Spectral analysis of the acoustical seismic snow event with
application of dislocation theory provides several likely methods to
predict climax type avalanches. These techniques could be used
jointly or separately to evaluate snow slope stability. Besides lo­
cating individual events, the location technique indicates a fracture
line by means of event accumulation before any surface indication is
evident. This fracture line and the migration rate of events across
the starting zone could be used to predict a time interval until snowpack failure. Also, when equivalent dislocation radii exceed snow
stratigraphic layer thicknesses, a snowpack failure depth could be
predicted. Moreover, the computed stress drop when compared to
Narita's (1980) work, gives a qualitative measure of stability.
Introduction
Increased back-country and downhill ski area use, as well as safe
maintainence of high mountain roads, has required an improvement over
current predictive methods for snow slope stability evaluation.
Slope
stability evaluation is especially needed in remote areas where
inaccessibility makes routine field evaluation cost-preventative.
In
order to predict stability, a wide range of indirect physical proper­
ties have been investigated by previous researchers for use in the
field (eg. see Mellor, 1968).
Investigated properties range from snow
strength measurements to crystal analysis.
In the wake of this work,
a direct method for gaging snowpack stability has been adopted which
involves the monitoring of acoustical emissions from the snowpack (St.
Lawrence and Bradley, 1977).
It has been known since 1973 that snow
emits seismic and ultrasonic signals (St. Lawrence and Bradley, 1973).
Seismic signals have frequency components well below I KHz, while
ultrasonic signals are greater than I KHz.
A real-time display of a
seismic signal on a slow speed recorder exhibits a "spike like" record
on a seismograph.
These seismic signals are referred to as spike
impulses because of this display, even though the pulse is a complex
wave form.
Another property of the seismic events is that they tend
to swarm during periods of snowpack instability.
These seismic
signals, occurring within the snowpack, represent a nonobservable
2
fracturing of the snowpack and are probably the precursers to a cata­
strophic failure of the snow slab (St. Lawrence and Williams, 1976).
The development of a numerical criterion based on these seismic emis­
sions for stability evaluation is the purpose of this investigation.
This investigation is an extension of previous work on seismic
emissions arising from the snowpack with dislocation theory applied to
seismic snow events.
The investigation is concerned with the location
of the event and the estimation of fracture size, stress drop, seismic
moment, and the amount of energy released from these seismic signals
from Berthoud Pass, Colorado (Figure I).
Thus, the foundation for a
direct predictive theoretical method for forecasting potential slab
avalanches from spectral analysis of seismic events with known foci
has been laid.
The material presented is narrow in scope but has potential
pratical application possiblities.
To aid the reader, whose back­
ground maybe unfamilar with the dialogue presented, a glossary of
terms is included at the end of this investigation.
3
LOCATION
CLIFF
SKETCH
AVALANCHE
BEFITHOUD
LEGEND
PATH
PASS, COLORADO
GEOPHONE
ANALYZED
OTHER
SPIKES
SPIKES
ELEVATION
RELATIVE
POINT
CONTOUR
341 O O 30 58
341 OO 50 20
3 3 6 21 22 4 0 O
BERTHOUD
PASS'
DENVER
SCALE
COLORADO
METER
(A rb itra ry
Datum)
Figure I: Sketch map of part of the Cliff Avalanche Path, Colorado
showing locations of the sensors, elevation control points adjusted
to an arbitrary datum, and seismic snow event locations. The accuracy
of the events and sensor locations are to within 4 cm (to the scale of
their symbols). Topographic contours are sketched relative to the
elevation control points and the relative elevations of the sensors.
The data for the elevations and spacing was provided by the Rocky
Mountain Forest and Range Experiment Station, Fort Collins, Colorado.
Previous Investigations
Previous work on acoustical signals from snow has been semiquantitative in that the monitoring of the number of events per unit
time has been used as an indicator of snow slope stability.
Moni­
toring events has led to a constitutive deformation theory (St.
Lawrence and Lang, 1977) based upon an interpretation of acoustical
emission activity occurring from stressed laboratory snow samples and
previous heuristic deformation theories (St. Lawrence and Bradley,
1975 and 1977).
Also, the interpretation of event activity has gaged
snow slope stability by analyzing the gross frequency component of the
snow event and the collating events into a frequency number of event
diagram (Sommerfeld, 1977 and 1980).
Thus, there have been two previ­
ous directions of work on seismic snow.events: that of developing a
deformation theory and that of monitoring distinct frequency bands.
Two conclusions have been drawn with regard to slab stability
evaluation from monitoring acoustical seismic events arising from
snowpacks.
The first is that the number of spontaneous acoustic
emissions rises as the snowpack approaches a condition of instability
or fails (St. Lawrence and Bradley, 1975 and Sommerfeld, 1977).
The
second is that these acoustical seismic events are associated with a
local fracture which might possess sufficient energy to cause a major
rift, thereby resulting in failure of the snowpack (St. Lawrence and
Williams, 1976).
5
Frequency content of emissions from fracturing of snow-grains and
snow-grain-bonds can be used to develop a concise deformation theory.
A separation of frequency bands made it possible for intergranular and
intragranular events to be differentiated (St. Lawrence and Bradley,
1977).
This separation has also been used by St. Lawrence and Bradley
(1975) to formulate a heuristic deformation theory.
Intergranular
emissions, resulting from the fracturing of several snow grain bonds,
are thought to be associated with a nonobservable rift within the
snowpack which gives rise to the seismic activity.
Narita (1980),
when doing tensile failure tests on snow samples, may have seen such
rifts or more likely seen rifts whose displacements have been enhanced
by a separation due to the testing procedure.
On the other hand, the
ultrasonic emissions are believed to originate at both a granular (St.
Lawrence and Bradley, 1977) and intergranular level (St. Lawrence and
Bradley, 1975).
Ultrasonic pulses, a probable result of basal-glide
slip planes being formed within the snow crystal, are interpreted as
signifying a change in stress states and not an instability (St.
Lawrence and Bradley^ 1975).
Hence, the ultrasonic emissions arising
from the snowpack are not considered to correlate closely with snow
slope stability (St. Lawrence and Bradley, 1977).
Deformation theory
concludes, that regardless of the mode of deformation (tension or
compression) intergranular flow is the principal mechanism of defor­
mation (St. Lawrence and Bradley, 1975).
Deformation theory also .
6
concludes that regardless of the mode of deformation, the greater the
load the greater the number of emissions, although the emission level
associated with compression was an order of magnitude less than for
tension tests.
Previous load histories of the snow has also been investigated
with respect to the level of ultrasonic acoustical emissions.
During
testing of a material, a phenomenon often occurs which indicates
former stress states.
When a material is subjected to a stress beyond
its elastic limit, allowed to relax, and then is restressed while
acoustical emissions are being monitored, there is no acoustical ac­
tivity until the orginal stress is reached.
In the field of Engi­
neering Mechanics this phenomenon is often called "memory" or the
"Kaiser Effect".
Bradley and St. Lawrence (1975) found that snow
possesses a memory to a degree.
It was found that, when compression
and tension emission activity were contrasted, the results of the
processes of compression (pressure melting, refreezing, and pore col­
lapse) contributed to a better memory of previous loadings than did,
tension cycles.
Tension cycles were found to give a more erratic and
less definite pattern of acoustical emissions due to previous unhealed
fractures.
Therefore tensile loading and reloadings led to a brittle
nature and a poorer memory.
Bradley arid St. Lawrence (1974) concluded
that the memory property of snow is related to the number of unhealed
fractures between ice grains.
Compression tested samples having the
\
7
least number of fractures, therefore, have the better memory.
But.
with both modes of deformation the snow will return to an equilibrium
position with time; hence, snow possesses a fading memory. The Bradley
and St. Lawrence (1977) longevity tests, on snow samples which have
undergone previous compression cycles, indicated that memory decay is
very rapid within the first six hours but could last up to fifteen
hours. No longevity tests were run on tensile tested snow samples.
Sommerfeld (1977 and 1980) has examined acoustical events within
the_seismic range using frequency analysis in conjunction with event
density per unit time of the seismic signals from snow to investigate
slope stability.
Four frequency peaks were discerned at at approxi­
mately 3, 30, 60 and 120 Hz based upon voltage distributions of the
seismic events (Sommerfeld, 1977).
The peak at 3 Hz was weak while
the 30 Hz peak coincided with the geophohe resonance; the higher peaks
were, discounted as powerline noise.
Using a geophone resonant fre­
quency of 30 Hz to count events, per unit time, the data indicated that
emission activity rose before a natural or artifical avalanche re­
leased (Sommerfeld, 1977).
Sommerfeld (1977) also observed that there
seemed to be no threshold count level that corresponded to ava­
lanching .
Sommerfeld (1980) has stated that his 1977 results contained cer­
tain ambiguities that could not be fully explained.
These ambiguities
pertained to a threshold count level of activity and the frequency
8
content of the seismic signal.
Other properties, such as the failure
pattern of the seismic event, are also ambiguous since there has been
no previous investigations to locate snow events.
Microearthquake
concepts make it possible for snow events to be located and to have
their corner frequency identified (corner frequency concept is fully
developed by figure 6 , page 24).
These two properties were relayed to
Sommerfeld by the author in 1977 in conjunction with this investi­
gation.
It was hoped that locating seismic events and using corner
relationships could remove these ambiguities.
Sommerfeld (1980) at­
tempted to resolve these ambiguities in a direct manner by using
dislocation theory relationships which were not adjusted for a slowly
rupturing source and by directly solving for epicenter locations.
When attempting to solve directly for seismic event locations,
Sommerfeld (1980) correctly stated that a snow velocity of 200 m/s
with a time accuracy of 5.0x10
racy of 0.1 m.
-4
s would give an event location accu­
With this type of accuracy an exact type of failure
pattern can not be rectified.
This location process can be improved,
however, by using time differences between P-wave arrivals which be­
come ratios between first arrivals of an event at the sensors. The
inaccuracies incurred by using this method can be reduced to the error
of the sensor location.
Also, it will be shown that Sommerfeld (1980)
has misconstrued the corner frequency-fracture radius relationship by
using a shear wave velocity instead of a rupture velocity.
This
9
relationship, in a more correct form, will be stated in the section on
spectral analysis herein.
The dislocation theory method (Dahlen, 1974), when properly ap­
plied to snow slope stability, contains several aspects which are more
appealing for gaging stability than previous acoustical monitoring
methods.
With this method only the seismic activity need be monitored
because of its previous association with snow slab stability.
It is
possible that only the frequency band between 0-150 Hz need be moni­
tored; this is a result of the attenuation properties of snow
(Sommerfeld, 1980) and the corner frequency relationship discussed
later.
Also, analysis need only be performed on those events which
appear on several sensor recordings when a sensor separation is 3-4 m
apart.
This separation would limit the analysis to those major events
which lead up to climax type slab avalanches, the most destructive and
potentially the most dangerous.
Spectral analysis seems to be the
most feasable method when monitoring is conducted in a "tensional
starting zone" since the St. Lawrence and Bradley studies (1973, 1975,
and 1977) have revealed that tensional activity is the most active,
least predictable, and would possibly last longer than compressive
processes due to its destructive crystal fracturing nature.
Previous
investigations have pointed to another aspect which makes dislocation
theory more appealing: the emission activity rises before development
of slab instability. The count number is an indirect way to estimate
10
stress drop or energy released. These two properties (stress drop and
*
1
energy released) should correlate with the fracture strength of the
snow slab and show an upper limit.
This relation is beyond the scope
of this investigation due to the exiguous amount of data processed but
could easily be extended by the results cited in other investigations,
especially those of Narita (1980) which are discussed in more detail
later.
Scope and Methods
Research Site
Data for this investigation was provided by the U.S. Department
of Agriculture Forest Service, Rocky Mountain Forest and Range Experi­
ment Station, Fort Collins, Colorado. The research site was located
along a known fracture line in part of the Cliffs Avalanche Path at
Berthoud Pass, Colorado (Figure I).
At the site, geophones were
affixed to the ground and transmitted the data 100 m to a hut where it
was recorded by a magnetic tape recorder. .
Five geophones were installed (numbered 5-9) by the Experiment
Station at the recording site.
Four of these formed an approximate
square 3 m on a side in plan pattern. The fifth, 4 m away from its
closest partner, was installed to decipher noise (Figure I).
Relative elevation contours were computed from a plane table
survey of the site made by the Experiment Station. These contours
indicate a uniform slope, the vertical distance between geophones
being about 0.5 m (Figure I). Geophones 7, 8 , and 9 were located along
the same contour, 5 and 6 being located upslope (Figure I).
Data from
geophone 6 , which encountered electrical problems, could not be used.
Instrumentation
GeoSpace model HS-I geophones having a 4.5 Hz natural frequency
were used to detect acoustic signals.
They were installed on the
12
ground mounted to a 30 cm square plate by the Experiment Station.
At
70% critical dampening of the seismometer, a flat frequency response
was obtained from 5-1000 Hz.
Signals were transmitted on a shielded cable to a heated hut.
Here, a slow speed magnetic tape recorder (TeIedyne Geotech Model No.
19429) was run at a tape speed of 0.9375 ips.
Using direct-record
electronics, the recorder had a frequency response of 0.5-125 Hz.
A
time channel was also recorded so that events could be referenced to
Greenwich mean time.
Playback was made on a Honeywell 7600 tape recorder with a tape
speed of 7.5 ips to monitor seismic activity. Two high-frequency
amplifiers with a frequency response of 50-10000 Hz were used to moni­
tor the character of the wave with a tape speed of 1.875 ips.
Further
time expansion of the wave form was made with a Honeywell Model 1858
Graphic Data Acquistion System paper oscilloscope.
McNair and Wolf
(1977), Sommerfeld (1977), Sommerfeld (1980) and St. Lawrence and
Bradley (1977) describe additional instrumentation which has been used
in conjunction with previous studies on acoustical emissions from
snow.
Data Selection
Data selection was based upon emission activity and the frequency
content of the emission.
Two days (336 and 341) indicated a snow slab
13
instability because of a relatively high number of emissions (30100/hr) . Events were also selected because the amplitude of the sig­
nal was at least twice background noise.
This selection was done to
override the background noise which plagued smaller amplitude events.
This process led to a selection of 20 events.
These seismic events, once expanded in time (0.01 s/1.27 cm),
could be divided into three groups.
The highest frequency component
group (greater than 150 Hz) was usually recorded on just one geophone
(Figure 2). This phenomena is most likely due to the attenuation
properties of snow which have been observed by Sommerfeld (1977 and
1980).
These ultrasonic pulses are probably not significant in terms
of energy released because their dislocation radius is so small.
These events were thus not investigated.
Another observed wave group has a monochromatic frequency proper­
ty. These signals are believed to be a resonance in the monitoring
equipment and therefore were not investigated (St. Lawrence, pers.
comm., 1981).
These monochromatic events (approximatly 100 Hz) were
nearly in phase on all traces and had a nearly constant amplitude, and
thus could be easily rejected (Figure 3).
Acoustical seismic events comprise the third grouping and are the
most significant in snow slope stability evaluation.
The wave form is
of the classical seismic shape, a sharp P-wave first arrival and, in
the majority of cases, an identifiable S-wave arrival which is based
14
0.02 s
Figure 2: Output from three sensors showing two ultrasonic pulses,
both indicative of an intergranular failure, are recorded on one
trace. Ultrasonic pulses are usually detected by a single sensor.
I im ii iiiiiiiiiiiiiiiiiin iiiiiiiim iiiiiiiiH iiiii
0.02 s
Figure 3. Monochromatic signals showing the typical symmetrical shape
with uniform frequency content per sensor and inphase characteristics
between sensors. These signals are believed to be a resonance in the
monitoring equipment and are of electronic origin.
15
upon the next major arrival after the quiescence of the P-wave (Figure
4).
These seismic pulses comprised nearly half of the approximately
80 investigated events while the monochromatic resonant signal made up
the majority of the remainder.
The classical seismic pulse readily lends itself to spectral
analysis and the application of dislocation theory because of its
physical properties.
The seismic event is comprised of a suite of
frequencies which theoretically characterizes the physical properties
of the fracture.
The "corner frequency" depicts the size of the
source, due to this frequency-fracture radius relationship, through a
simplistic physical theory developed by Brune (1970).
The corner fre­
quency is ah intersection of two trends; one horizontal and one with a
W
-2
slope.
These trends are formed, under a condition of complete
stress drop (no stresses remain in the area of the fracture after rup­
ture) , when plotted pn a log-log frequency-displacement diagram.
stress drop can easily be computed from the source size.
The
A comparison
of the stress drop and the maximum strength measurements of Narita
(1980), as described later, can be used to formulate an avalanche pre­
dictive theory.
Data Reduction
Frequency content and amplitude of the pre-signal noise deter­
mined the portion of the record of the seismic event suitable for
16
P
V
trace
P
> \c Y
3 jjv
9
S
Il'P^WW
I'
0.1s
P
S
i.
l?
trace
8
trace
5
FIGURE 4. Three velocity geophone records showing a typical classical
seismic snow event (341:18:56:20) with observable P- and S-wave arri­
vals. Note that there is no indication of an amplitude or frequency
difference in the raw records after the arrival of the S-wave, indi­
cating a rupture velocity is 0.6 that of the S-wave snow velocity.
17
analysis.
Records of the seismic events were digitized until trace
amplitudes decayed to the level of the pre-signal noise and were of
similar frequency content.
This digitization method was done to in­
sure that a signal dominant record was present and that the majority
of the event was analyzed.
To increase the signal-to-noise ratio, the
noise (predominately 60 Hz) was also digitized and used as a filter.
These samples were autocorrelated with the event record to find an
overlap point at which the signal and the noise interfaced.
The noise
was then subtracted in the time domain to give a more noise free sig­
nal.
This procedure was done to eliminate any possible interference
with corner frequencies.
A visual comparison of the displacement
spectra, with and without noise, indicated negligible changes at fre­
quencies other than 60 Hz.
The observed data recorded by a velocity geophone was converted
to a ground displacement spectra by a computer algorithm.
The first
step in the conversion process was to obtain ground acceleration
(Appendix A).
A computer program (Keightley, .1970) took the system
amplification and instrument response associated with the observed
spectra into account and converted it to ground acceleration.
The
acceleration spectrum was then divided by the angular frequency to
give a ground velocity spectrum (Appendix B). A ground displacement
spectrum was obtained by repeating the same process but applying it to
the ground velocity spectrum (Appendix C).
These spectra, being in
18
the frequency domain, were transformed
back to their respective time
domains by a fast Fourier algorithm (Borgman, 1973).
No corrections
were made for attenuation, scattering, partitioning at free surfaces,
focusing, or spherical spreading.
The displacement spectra were converted to a log-log plot so that
corner frequencies could be identified (Appendix D).
This information
was enhanced by an averaging process, resulting in a smoothed power
spectrum (Figure 5). All plots were enhanced by retracing computer
output.
19
IE-3-r
E IE -4 - •
POWER
AVE. —
IE-5
i— t— t— »
FREQUENCY
(Hz)
341:18:56:20 CHANNEL 9
Figure 5: A comparison of the converted ground displacement power
spectrum (line) and the averaging operation (dashed) so that a corner
frequency can be easily selected. The plot is of the event which oc­
curred on day 341 at 18 hr 56 min 20 s Greenwich mean time. The
straight line, labled W"2 , represents a frequency slope associated
with a complete stress drop, that is, the stress in the event area has
been totally relieved.
Determination of Locations
Qualitative analysis and evaluation of spectral data with regard
to a seismic snow event requires an accurate location.
Several
microearthquake techniques have been developed to monitor and locate
rock bursts (Blake, Leighton, and Duvall, 1974).
Bath (1973) and Lee
and Lahr (1975) also have presented techniques which are applicable to
locating snow events.
The techniques of Bath (1973), due to their
simple nature, are better adapted to the data frqm four sensors.
The
other procedures use more sophisticated programs requiring multiple
recordings of the event for error checking, velocity profile analysis,
and accurate selection of the first arrivals of the event at each of
the sensors for locating event epicenters.
These qualities required
by the more sophisticated programs were lacking in the data analyzed.
Foci from Berthoud Pass were computed based upon time differences
between first arrivals of the four channels.
Being limited to infor­
mation from four sensors, the focus of each event was assumed to have
a zero depth.
Using time and distance differences between geophones
for each of the events, a velocity of snow was indicated to be between
250-330 m/s.
A fixed wave speed of 300 m/s was selected because the
majority of the events used had this velocity and the error due to
varying the wave speed was less than 5 cm, the same as the error in
locating the sensor.
Using a fixed wave speed of 300 m/s, three lo­
cation methods were contrasted using the first arrivals of the seismic
event at the four sensors.
21
The location of an acoustical seismic event arising from a snow
instability was confirmed by two or more location techniques once the
proper times of the first arrivals were identified.
methods were attempted to locate events.
Three location
These methods included a
direct solution technique (Blake, Leighton and Duvall, 1974), the
Hypo-71 computer routine (Lee and Lahr, 1975), and a hyperbolic
graphical technique (Bath, 1973).
Due to the amplitude of the pre­
signal noise in some cases, the first arrival selection was obscure.
Pre-signal, noise resulted in multiple first arrival possibilities.
This problem existed predominantly on one trace.
The direct solution
method was sensitive to velocity and first arrival selection.
Varying
the wave speed 10-40 m/s caused epicenter locations to move 1-2 m.
First arrival sensitivity was also true of Hypo-71 a computer program
designed to locate earthquake epicenters.
The hyperbolic method
proved to be the most successful for it allowed for one channel to be
errant in the first arrival selection.
Once the first arrival inaccu­
racies were corrected through the hyperbolic method, the direct so­
lution method confirmed the foci locations.
When the first breaks
were not obscure, the three location methods concurred to within 2-4
cm.
The hyperbolic method, as with most methods, is most accurate
when the event is internal to the seismic net.
Inaccuracies of loca­
tions outside the net have been investigated by Blake, Leighton, and
22
Duvall (1974).
The location of eight events whose epicenters corre­
sponded when two or more methods were applied are shown in figure I.
An equal number of events had first arrival differences which indi­
cated that their epicenters were outside the seismic net.
events could not be accurately located.
These
Spectral Analysis
Dislocation theory considers the seismic record as a represen­
tation of a stochastic process which needs to be consolidated to
resemble a singular event for analysis.
The consolidation process is
usually made by competing a displacement spectral density estimate.
This method tends to smooth P- and S-wave frequencies but retain maxiI
mum frequency resolution. A power spectrum and a spectral density
estimate vary in that the latter smooths the peaks and troughs of the
former (Smith and others, 1974).
Both of these consolidation schemes
make use of a fairly small amount of data to obtain a rough estimate
of some interesting properties.
Dislocation theory leads to an estimation of fault area, energy
released, seismic moment, and stress drop by computing the corner fre­
quency, W c , a general feature of a spectral density estimate. Physi­
cally, the corner frequency is an intersection of a horizontal low
frequency trend and a sloping high frequency trend on a log-log
displacement-frequency diagram (Figure 6).
Numerically, the corner.
frequency has been equated to an equivalent dislocation radius, Ro
(Brune, 1970 and Dahlen, 1974).
The general form of the equation
relating the corner frequency to the dislocation radius (Brune, 1970)
is
Ro=CV/Wc
where Ro is the radius of the ruptured area, C is a constant depending
upon mode of failure and assumptions made, V is the velocity of the
I
24
<
IE -S ■
IE -6
50
FREQUENCY
341:18:56:20
100 150
(H z)
CHANNEL
FIGURE 6 . The corner frequency (Wc=27fFc), is an intersection of a
horizontal trend, indicated by the horizontal line, and a sloping
trend, indicated by the sloping line. A fracture will theoretically
propagate distinct frequency components that are related to its size
and shape. These properties are related to the corner frequency. The
trends are indicated on a displacement spectrum for the event which
occured on day 341 at 18 hr 56 min 20 s Greenwich mean time.
25
rupture, and Wc is the corner frequency in radians per second
(Wc=2nFc, Fe in Hz), usually of P- or S-wave spectra.
Independent
estimates for the value of C by Dahlen (1974) and Brune (1970) are in
close agreement when the rupture velocity is near the S-wave velocity.
Dahlen computes a value of 1.697 compared to Brune1s 2.34.
The
difference arises from a basic assumption made in the development of
the corner frequency-dislocation radius equation.
Brune1s concept is
that the stress drop is instantaneous over the dislocation surface.
Dahlen assumes a more realistic mode of rupture, where the rupture
initiates at a single point and spreads elliptically outward to cover
the dislocation surface.
Dahlen's model accomodates a much lower rup­
ture velocity than does Brune1s fixed S-wave rupture velocity model.
When the rupture velocity is much lower than the S-wave velocity,
Brune 1s model will drastically overestimate the size of the dislo­
cation.
This overestimation occurs because the conservative elastic
dislocation theory (Brune, 1970) does not consider surface forces to
be relevant compared to body forces, thus the difference in rupture
models.
For large rupture velocities, near that of the S-wave ve­
locity, there is a pronounced shift increasing the S-wave spectral
amplitude over that of the P-wave (Dahlen, 1974).
The raw seismic
snow record does not indicate any frequency shift nor amplitude
difference (Figure 4) implying that both P- and S-wave spectra are
equivalent in frequency over the focal sphere (Dahlen, 1974).
This
26
equivalence indicates that the rupture velocity is on the order of
one-half that of the S-wave velocity (Dahlen, 1974).
A rupture velo­
city of one-half that of the S-wave velocity has been used previously
for icequakes (Neave and Savage, 1970).
Also brittle fracture theory
seems to confirm that a rupture velocity is normally one-half that of
the S-wave velocity. Yoffe (1951), when theoretically developing the
nature of a stress field in an elastic medium, has predicted that if
the rupture exceeds 0.6 of the S-wave velocity, the rupture would
curve or branch.
Branching is a result of a nearly equivalent stress
field over a wide arc about the head of the fracture.
For snow,
branching of the fracture may effectively stop the rupture.
Thus,
both the works of Dahlen and Yoffe, when applied to snow, indicate
that V should be about 0.6 that of the S-wave velocity.
has also confirmed Yoffe1s relationships.
Sih (1968)
Thus, Dahlen's model is
most applicable to seismic emissions from snow.
An S-wave velocity can be calculated from elasticity theory.
In
high alpine snow packs, snow has an average density of about 300
3
kg/m . With this density the Poisson ratio would be about 0.2
(Mellor, 1974).
With a P-wave velocity of 300 m/s the computed S-wave
velocity is 184 m/s with a computed Youngs modulus of 243 bars (compa­
rable to Mellor, 1974).
An equivalent dislocation surface radius can be computed from a
seismic snow event once the proper values of C and V are found. As
27
has been discussed, Dahlen1s model describes a slowly rupturing dislo
cation surface.
Since snow has a slower rupture velocity than rock,
which Brune's model was formulated for, the Dahlen equation relating
the corner frequency to the fracture radius will be used.
His dislo­
cation radius equation is
Ro'=1.82V/Wc
with V=IlO m/s (Dahlen, 1974, eq. 52).
using this relationship are about 0.3 m.
Equivalent dislocation radii
Comparing these values to
the size of the fractures illustrated in Narita1s (1980) work indi­
cates that these radii (Rot) are an order of magnitude too high.
A
reduced radius size is also confirmed from an energy standpoint dis­
cussed later.
Thus Dahlen1s equation over estimates Ro and the value
of C must be reduced.
There are two probable sources of error in the above dislocation
radius equation.
The effects of scattering are a probable source of
error which have been predicted to effect Wc by a factor of 3-4
(Dahlen, 1974).
Another probable source of error is an assumed uni­
form stress drop made by both Brune (1970) and Dahlen (1974).
Em­
ploying a nonuniform stress drop, Dahlen (1974) predicts that an addi
tional factor of 2-3 raised to the 1/3 power could be incorporated.
Table I restates the fracture radius values when the maximum cor­
rection is used to decrease the size of Rot. These new computed
28
results (Ro") resemble the size of the fractures seen by Narita (1980)
just before tensionsI failure in tested samples of snow.
From an energy standpoint these new computed dislocation radii
results can also be shown to be in close agreement with previous works
on seismic events from snow. St. Lawrence and Bradley's (1977) system
magnification of snow, signals was 32 times greater than that of
Neave
and Savage (1970) using glacier signals. Neave and Savage estimate
energy release from an icequake to be IO^ ergs, indicating that large
snow events should be no more than two orders of magnitude less.
To
compute energy released, the stress drop and the seismic moment first
need to be computed.
The stress drop and the seismic moment are related to the dis­
placement spectrum and are needed to compute energy released.
Under
the condition of complete stress release the displacement spectrum, at
the corner frequency, decays according to W
-2
, a t frequencies higher
than Wc, as illustrated in figure 5 (Brune, 1970).
Each snow event
shows this type of decay (Appendix C) indicating that the accumulated
stress has been released and no fractional relationships need be con­
sidered.
To compute the average stress drop, the seismic moment is
first computed.
The seismic moment is related to the corner frequency
amplitude, Ac, through the relation
Mo=AnGVsAc
(Smith and others, 1974), where Ac is also affected by attenuation,
29
scattering, and focusing effects taken here as unity.
G is the shear
modulus (101.25 bars) and Vs is the S-wave velocity for snow of densi-
2
ty 300 kg/m . Moment values are tabulated in table I.
For a slow
rupture, the seismic moment is related to the stress drop, S, by
S=O.0729Mo(I.82/Ro)3
(Dahlen, 1974, eq. 51).
These stress drop values, table I, are in the
range of those computed by Mellor (1974) from snow failure tests.
They are also on the order of estimated icequake stress drops (Neave
and Savage, 1970).
Having computed both the seismic moment and the
stress drop, the strain energy is calculated by the equation
Es=SMo/G
(Stacey, 1977, eq. 5.27).
Here, the strain energy is indicative of
the total energy because it includes locally dissipated energy which
is important for small shocks (Stacey, 1977).
The strain energy com­
puted for large snow events in the seismic range, table I, are two
orders of magnitude less than icequakes, as had been estimated above.
Thus, the modified dislocation radii for seismic snow events are close
estimates of the actual snow fractures.
Now that the size of the
fracture has been computed, the fracture area, A, is easily computed
through the relation
A=4rtRo^.
Moreover, the amount of the dislocation can be estimated from the
displacement spectra of the seismic snow events.
Brune (1970) has
Table I:
Parameters Related to the Displacement Corner Frequency
EVENT - TRACE
Fe
Ac
Ro'
Ro"
(Hz)(cm -s) (cm)
(cm)
Ron
Mo
Mo
Ave.
Ave.
(cm) (dyne-cm)(dyne-cm)
IxlO™5
341:00:36:58-5
341:00:36:58-8
341:00:36:58-9
341:00:56:20-5
341:00:56:20-8
341:00:56:20-9
341:18:55:15-5
341:18:55:15-8
341:18:55:15-9
341:18:56:20-5
341:18:56:20-8
341:18:56:20-9
160
100
102
102
120
101
150
70
70
67
56
61
0.25
0.50
0.17
0.60
0.20
0.30
0.30
1.00
1.00
1.00
1.50
1.70
IxlO8
19.9
31.8
31.2
31.2
26.5
31.5
21.2
45.5
45.5
47.5
56.9
53.2
3.45
5.51
5.41
5.41
4.59
5.46
3.67
7.89
7.89
8.23
9.86
9.04
4.79
5.15
6.48
9.04
Fe -Corner Frequency (Hz)
Wc -Corner Frequency (Radians)
Ro *-Equivalent Dislocation Radius
Computed from Dahlen (1974, eq 50)
Ron-Equivalent Dislocation Radius
Corrected for Scattering and
Nonuniform Stress Drop
Mo -Seismic Moment
S -Stress Drop
E -Strain Energy Released
0.59
1.17
0.40
1.40
0.47
0.70
0.70
2.34
2.34
2.34
3.51
3.98
S
Ave.
(bar)
IxlO8
E
Ave.
(erg)
IxlO6
0.72
0.29
0.205
0.86
0.28
0.235
1.79
0.29
0.511
3.28
0.20
0.632
31
observed -that the displacement pulse never exceeds one-half the actual
amount of the dislocation at any distance from the rupture, unless
some unusual amplification occurs.
The largest displacement amplitude
for a seismic snow event, observed in this investigation, is 2.5x10 ^
mm.
Doubling this amplitude gives an approximation of the average
size of the displacement at the snow dislocation surface.
The average
amount of the displacement, across the dislocation surface, is on the
order of one micron.
Local displacements may be much larger, but
Narita1s (1980) thin sections which have been subjected to a tensile
stress, indicate a much larger displacement.
indicate local displacements of about 2.5x10
These thin sections
-I
mm; thus, there seems
to be some enhancement of the displacements due to Narita's mode
testing which does not represent the actual displacement at the time
when the seismic event would have occurred.
•Discussion
Dahlen1s (1974) elliptically spreading point-source model ade­
quately describes thp origip of the seismic signals from high alpine
snow fields.
The origin of these seismic signals is best understood
from the standpoint of energy focusing.
The relative amplitudes of
the time and frequency plots (Appendix A-D) of the seismic snow events
and their location (Figure I) gives an indication of the amount of
energy focusing and, hence, the direction of propagation of the frac­
ture.
This type of focusing is especially true of event 341:18:56:20
on channel 9.
Channel 9 has frequency components similar to the other
two channels even after the wave has traveled 6-8 m farther in the
snow.
Brune (1970) has stated
"the effect of a smoothly propagating source is to strongly
focus high frequency energy in the direction of rupture
propagation".
Dahlen (1974) indicates that this type of focusing is stronger for the
S-wave spectra than the P-wave spectra. Since both wave groups were
used to obtain corner frequencies this would be reflected in the data.
The focusing of energy towards channel 9 indicates that fractures were
propagating parallel to elevation contours and that the fractures
orginated from tensional stresses.
An equivalent dislocation radius may correlate with the size of
the slab instabiltiy.
The lower corner frequencies are equated to a
larger dislocation surface through the inverse relation of the corner
33
frequency'•dislocation radius equation.
These larger equivalent dislo­
cation radii may be such that they transect several snow stratigraphic
units and thus indicate a greater likelihood of a large avalanche.
A numerical estimate of snowslope stability is feasible in the
light of this investigation and that of Narita's (1980) fracture
strength measurements.
Narita's tensile strength measurements on snow
of various densities (300-445 kg/m ), when plotted against log strainrate, have a peak in the range of 1x10
-4
to 2x10
-5
/s.
The peaks
associated with each snow density shift toward a lower strain-rate
with an increasing density.
For example, given a density of 300
3
kg/m , there is
a gradual increase in snow strength as the strain-
rate increases to 1x10
-4
/s.
The peak strength value of I bar is
reached at this strain-rate, but is followed by rapid decline in snow
strength.
For a stable snow slope, strain-rates are in the region of
lower values investigated by Narita (1980) (Lang and Sommerfeld,
1977).
Strain-rates near a growing fracture should increase above
these lower strain-rate values and be dependent upon the physical
attributes of the snow and the snow slope.
Thus, for an unstable snow
slope, snow in a starting zone would have to have a stress drop which
corresponded to Narita1s maximum snow strengths for a given density
and a given strain-rate.
Therefore, comparing the results from
Berthoud Pass to those of Narita, the seismic snow events investi­
gated were recorded during a period of stability.
This stability is
34
indicated by the relatively few number of emissions and also by the
stress drop values which are below those critical strength values of
Narita.
Conclusions
Several conclusions can be drawn from a corn.br frequency diagram
which pertain to the dislocation radius, and the stress drop.
The size
of the equivalent dislocation radius (Ro= 4.8-9.I cm) indicates that a
local region within the snowpack was subjected to a tensile stress.
Assuming Dahlen's model is correct for a failure mechanism, this
region failed from a point source and spread elliptically outward,
totally relieving the stressed area.
Since there is an inverse re­
lation between the corner frequency and the dislocation radius, the
major seismic snow events will have a lower corner frequency.
The
major seismic event, due to this lower frequency content, will propa­
gate further and be detected by sensors several meters away from the
source location.
The seismic signals recorded by these sensors can be
used to calculate the dislocation radius, fracture area, displacement,
stress drop, seismic moment, and the strain energy of the fracture
which occurred within the snowpack.
Once the strain-rate is known for
a given snowpack, the computed stress drop will give a qualitative
measure of snowpack stability when compared to Narita1s work.
Several
events with stress drop values in the critical range of Narita's work
would mean an unstable slope has been reached.
References
Bath, M., 1973, Introduction to Seismology. John Wiley and Sons, New
York, N.Y., 395 p.
Blake, W., Leighton, F., and Duvall, W. I., 1974, Microseismic Tech­
niques for Monitoring the Behavior of Rock Structures. U.S. Bur.
Mines Bull. 665, 65 p.
Borgman, L. E., 1973, Spectrum Analysis of Random Data. Univ. of
Wyoming. Unpub. class lecture notes.
Bradley, C. C. and St. Lawrence, W., 1974, The Kaiser Effect in Snow.
Snow Mechanics-Symposium (Proceedings of the Gindelwald Symposium
April 1974; IAHS-AISH publ. no. 144, 1975), p. 145-154.
_____, Brown, R. L., Lang, T. E., and St. Lawrence, W., 1975, Acoustic
Emissions in Snow of Constant Rates of Deformation. Unpub.
Brune, J. N., 1970, Tectonic Stress and Spectra of Seismic Shear waves
from Earthquakes. Jour. Geophys. Res. 75, p. 4997-5007.
Brune, J. N., 1971, Correction to Brune, 1970. Jour. Geophys. Res. 76,
p. 5002.
Dahlen, F. A., 1974, On the Ratio of P-wave to S-wave Corner Frequen­
cies for Shallow Earthquake Sources. Bull. Seism. Soc. Am., vol.
64, no. 4, p. 1159-1180.
Douglas, B. M.,and Ryall, A., 1972, Spectral Characteristics and
Stress Drop for Microearthquakes near Fairview Peak, Nevada.
Jour. Geophys. Res., vol. 77, no. 2, p. 351-359.
Hanks, T. C., and Wyss, M., 1972, The use of Body Wave Spectra in the
Determination of Seismic Source Parameters. Bull. Seis. Soc. Am.,
vol. 62, no. 2, p. 561-589.
Keightly, W. D., 1970, Response of Earth Dams to Seismic Disturbances,
Part II, Digital Computer Codes. Engineering Research Labora­
tories, M.S.U. Report to the Lawrence Radiation Laboratories PO
7794903, 79 p.
Lang, T . E . and Sommerfeld, R. A., 1977, The modeling and measurement
of the deformation of a sloping snow-pack. Jour. Glac., vol. 19,
no. 81, p. 153-165.
37
Lee, W. H. K., and Lahr, J. C., 1975, Hypo71(revised). A Computer
Program for Determinating Hypocenters, Magnitude and First Motion
Paterns of Local Earthquakes U. S . Department of the Interior
Geological Survey. National Center for Earthquake Research.
U.S.G.S. open file Report 75-311, 44 p.
Mellor, M., 1968, Avalanches. Cold Reg. Sci. and Eng., U.S. Army
Corps. Eng., Inter. Rep. 352, Cold Reg. Res. and Lab., Hanover,
N.H., 42 p.
_____, 1975, A Review of Basic Snow Mechanics. Snow Mechanics (Pro­
ceedings of the Grindelwald Symposium April 1974; IAHS-AlSH pubI.
no. 114, 1975), p. 1-8.
McNair, D., and Wolfe, F., Jr., 1977, An Acoustical Emission Moni­
toring System for Avalanche Snowpacks. U.S.D.A. For. Serv. Res.
note Rm-340, April, 4 p.
Narita, H., 1980, Mechanical Behavior and Structure of Snow under
Uniaxial Tensile Stress. Jour, of Glac., vol. 26, no. 94, p. 275282.
Neave, K. C. and Savage, J. C., 1970, Icequakes on the Athabasca
Glacier. Jour. Geophys. Res., vol.75, no. 8, p. 1351-1362.
Sih, G. C . 1968, Some Elastodynamic Problems of Cracks. In-tern. Jour,
of Fracture Mech., vol. 4, no. I, p. 51-67.
Sommerfeld, R. A., 1977, Preliminary Observation of Acoustic Emissions
Preceding Avalanches. Jour, of Glac., vol. 19, no. 81, p. 399409.
_____, 1980, Acoustical Emissions from Unstable Snow Slopes. Sec.
Conf. on Acoustic Emissions. Microseismic Activity in Geologic
Structures and Materials- The Pennsylvania State Univ. November.
13-15, 1978. Trans. Tech. Pub. Clausthal, Germany, p. 320-329.
Smith, R. A., Winkler, P. L., Anderson, J. G., and Scholz, C. H.,
1974, Source Mechanisms of Microearthquakes Associated with
Underground Mines in Eastern Utah. Bull. Seism. Soc. Am., vol.
64, no. 4, p. 1295-1317.
Staqey, F. D., 1977, Physics of the Earth. Sec. Ed., New York, N.Y.,
John Wiley and Sons. 414 p.
38
St. Lawrence, W., and Bradley, C. C., 1973, Ultrasonic Emissions in
Snow. U. S. Dept, of Agriculture, For. Serv.. General Tech. Rep.
RM-3, p. 1-6.
_____ 1975, The Deformation of Snow in terms of a Structural Mecha­
nism. Snow Mechanics-Symposium (Proceedings of the Grindelwald
Symposium April 1974; IAHS-AISH publ. no. 114, 1975), p. 155-170
_____ 1977, Spontaneous Fracture Initiation in Mountain Snow Packs.
Jour, of Glac., vol. 19, no. 81, p. 411-417.
_____ and Lang, T. E., 1977, A Constitutive Relation for the Defor­
mation of Snow, Ph.D. Thesis unpub. Montana State University, 37
P_____ and Williams, T. R., 1976, Seismic Signals Associated with
Avalanches. Jour, of Glac., vol. 17, no. 77, p. 521-526.
Yoffe, E. H., 1951, LXXV. The Moving Griffith Crack. Phil. Mag., vol.
42, p. 739-750.
Glossary
Acoustic Seismic Impulse (Event)- An intergranular fracture within the
snowpack causing a seismic wave whose frequency components are
much less than I KHz.
Corner Frequency- A fracture, due to its physical properties of size
and shape, will theoretically propagate distinct frequency com­
ponents. Once the maximum component characterizing the fracture
size is reached the higher frequency components will decay in
amplitude towards zero from the previous lower-frequency hori­
zontal trend. This decay will proceed at a w
slope if the
stress causing the fracture is totally released. The frequency
at the junction of these twti slopes is the corner frequency.
Dislocation Theory- The theoretical developement describing, quali­
tatively the properties of a fracture.
First Arrival- The first evidence that an event has occurred on a
seismic record, usually of a P-wave.
Focal Sphere- A representation of the event pulse on a hemispherical
plot.
Geophone- A sensor which is designed to detect either acceleration,
velocity, or displacement movements of a surface.
Intergranular Fracture-
A fracture which happens between snow grains.
Intragranular Fracture- A fracture which occurs within the snow grain
structure.
Memory (Kaiser Effect)- A phenomenon associated with a material which
has been strained beyond its elastic limit. This strained materi­
al will not emit any type of signal until the prior strain has
been surpassed.
Monotonic Event- An event comprised of
a
single frequency component.
P-wave- A particular wave form which has a unique motion (compressional) and is associated with the first portion of a monitored
wave.
Power Spectrum- The Fourier amplitude components squared and then
summed and square rooted and represented on a amplitude-frequency
diagram.
40
Realtime- The monitoring equipments original speed of recording a
signal. Relative Elevation Contours- A set of contours which is not referenced
to sealevel.
Rift- A fracture or separation within a material.
Seismic Moment- A .quantity, in dislocation theory, which has been
related to a number of properties, such as strain energy and
stress drop.
Source Parameters- The fracture radius and area.
Spectral Analysis- The analysis of a wave form through its spectral
characteristics.
Spectral Density Estimate- A log-log displacement amplitude-frequency
diagram which has been adjusted for spherical spreading, fo­
cusing, and attenuation effects of an event.
Stress Drop- The amount of stress released as energy due to fracturing
of a material.
S-wave- A particular wave motion which has a unique motion (shearing)
and is associated with the second portion of a monitored wave.
Ultrasonic Event- A wave form which contains frequency components that
are above I KHZ.
Appendix A
Ground Acceleration: Time and frequency analysis of the seismic snow
events which underwent dislocation theory analysis. Ground acceler­
ation records are computed from the raw geophone velocity records.
42
N
A m p litu d e («10 m m /
<T
do ' di
do ' o!i
S PIKE
A m plitud e (.10 m m /s 2 1
Channel
do ' di
5
S A I i OO136-58
Three time domain ground
acceleration records for
the seismic snow event
which occurred on day 341
at 00 hr, 36 min, 58 sec
Greenwich mean time.
A m p litu d e
(.1 0 mm
43
oSo ' o!i
do ' o!i
S P IK E
A m plitud e M O m m /s 2 )
Channel
do ' oil
S
Scale <e>
6
341>00'S 6<20
Three time domain ground
acceleration records for
the seismic snow event
which occurred on day 341
at OO hr, 56 min, 20 sec
Greenwich mean time.
44
9
A m plitud e
(»10 mm
Channel
do ' di
do ’ d!i
S P IK E
A m plitud e M O m m Z s 2 I
Channel
S
Seale la)
5
341i18-5S -15
Three time domain ground
acceleration records for
the seismic snow event
which occurred on day 341
at 18 hr, 55 min, 15 sec
Greenwich mean time.
45
6
C hannel
9
A m p litu d e
(«10 mm
C henoel
do ' di
do ' Oil
S cale (•)
S P IK E
3 4 1 1 8 5 6 ,2 0
A m p litu d e
M O m m /s 2)
Three time domain ground
acceleration records for
the seismic snow event
which occurred on day 341
at 18 hr, 56 min, 20 sec
Greenwich mean time.
do ' oli
Scale lei
46
C hennel
0
100
Frequ ency
200
300
400
8
C hannel 9
SOO
F requ ency
Ihzl
Ihzl
S P IK E
2.5 0T
5
1.26
A cceleration
I
C hannel
500
F requ ency
Ihzl
3 4 1 .0 0 -3 6 -5 8
Three frequency domain
ground acceleration
records for the seismic
snow event which occurred
on day 341 at OO hr, 36
min, 58 sec Greenwich
mean time.
Al
8
A ccele
C han nel
0
IOO
F requ ency
200
300
400
600
O
100
F requ ency
(hz)
20
(h zi
S P IK E
0
100
F requ ency
200
Ih z l
300
C hannel
5
400
600
3 4 1 .0 0 '5 6 '2 0
Three frequency domain
ground acceleration
records for the seismic
snow event which occurred
on day 341 at OO hr, 56
min, 20 sec Greenwich
mean time.
48
8
400
SOO
C hannel
9
A c c e le r a tio n
1*1 m m /a '
C han nel
0
XX)
F requ ency
200
Ih z I
300
0
XX)
Frequ ency
20 0
S P IK E
5
A ccelera tion
M m m /s 2 )
C hannel
0
KHD
F re q u e n c y
200
(hz)
300
400
500
300
400
Ihzi
341i18>55>15
Three frequency domain
ground acceleration
records for the seismic
snow event which occurred
on day 341 at 18 hr, 55
min, 15 sec Greenwich
mean time.
49
C han nel
0
XX)
F requ ency
200
300
400
500
O
100
Frequ ency
(h z l
200
"ioo
F requ ency
Mo'
(h z l
300
400
5
400
500
Ih z l
SPIKE
C han nel
300
9
341 i18.56 i20
Three frequency domain
ground acceleration
records for the seismic
snow event which occurred
on day 341 at 18 hr, 56
min, 20 sec Greenwich
mean time.
Appendix B
Ground Velocity: Time and frequency analysis of the seismic snow
events which underwent dislocation theory analysis. Ground velocity
records are computed from the ground acceleration records.
51
do ' oli
do ' di
S P IK E
341<00<36<S8
Three time domain ground
velocity records for the
seismic snow event which
occurred on day 341 at
00 hr, 36 min, 58 sec
Greenwich mean time.
do ' di
S c a t* (si
52
8
A m plitud e
I *1 E-0 4 m m /i
Channel
do ' di
do ' oli
A m p litu d e
I * 1 E-04 mm / s )
S P IK E
341<00<56<20
Three time domain ground
velocity records for the
seismic snow event which
occurred on day 341 at
OO hr, 56 min, 20 sec
Greenwich mean time.
Am pHtude
M E - O A m m /,
53
do ' oil
olo ' oli
SPIKE
3A1>ie>55<15
AmpH tuda
( -IE -O A m m /,)
Three time domain ground
velocity records for the
seismic snow event which
occurred on day 341 at
18 hr, 55 min, 15 sec
Greenwich mean time.
do ' oli
A m p litu d e
C 1E -04 m m /i
54
do
1olt
Scale (•)
S P IK E
341.18 -S 6 '2 0
A m p litu d e
I *1 E-04 m m /s )
Three time domain ground
velocity records for the
seismic snow event which
occurred on day 341 at
18 hr, 56 min, 20 sec
Greenwich mean time.
do ' di
55
OSOt
S P IK E
3 4 M ) 0 - 3 6 'S 6
Three frequency domain
ground velocity records
for the seismic snow
event which occurred on
day 341 at OO hr, 36
min, 58 sec Greenwich
mean time.
V e lo c ity
I- I E - 0 3 m m /i
56
V e lo c ity
I-IE -O a m m Z s I
S P IK E
3 4 1 - 0 0 - 5 6 .2 0
Three frequency domain
ground velocity records
for the seismic snow
event which occurred on
day 341 at 00 hr, 56
min, 20 sec Greenwich
mean time.
57
S P IK E
3 4 1 '1 8 '5 5 '1 6
Three frequency domain
ground velocity records
for the seismic snow
event which occurred on
day 341 at 18 hr, 55
min, 15 sec Greenwich
mean time.
58
Channel
0
100
Frequency
200
300
400
8
OSOt
600
Ihz)
S P IK E
341 i1B'56i20
Three frequency domain
ground velocity records
for the seismic snow
event which occurred on
day 341 at 18 hr, 56
min, 20 sec Greenwich
mean time.
Appendix C
Ground Displacement: Time and frequency analysis of the seismic snow
events which underwent dislocation theory analysis. Ground displace­
ment records are computed from the ground velocity records.
Amplitude
I -IE -03 mm)
60
oio ' o!i
Scale (a)
SPIKE
341-00i36'58
Amplitude
I IE -0 3 mm)
Three time domain ground
displacement records for
the seismic snow event
which occurred on day
341 at 00 hr, 36 min, 58
sec Greenwich mean time.
do ' dli
Scale (a)
61
9
Amplitude
I IE-03 mml
Channel
do ' oli
do ' o!i
SPIKE
341>00'56>20
Amplitude
(*1E-03 mm)
Three time domain ground
displacement records for
the seismic snow event
which occurred on day
341 at 00 hr, 56 min, 20
sec Greenwich mean time.
o!o ' Oil
Amplitude
( -IE -08 mm)
62
do ' di
do ' olt
SPIKE
341-18'55'15
Amplitude
M E -O S m n )
Three time domain ground
displacement records for
the seismic snow event
which occurred on day
341 at 18 hr, 55 min, 15
sec Greenwich mean time.
do ' di
Scale (•)
A m plitud e
I "IE -0 3 mm)
63
o!o ' oil
Scale (•)
SPIKE
341'18'56'20
Three time domain ground
displacement records for
the seismic snow event
which occurred on day
341 at 18 hr, 56 min, 20
sec Greenwich mean time.
OlO ' di
S
Scale lei
64
Channel
9
D ls p la c e m e
W 0.25
0
IOO
200
Frequency Ihz)
300
400
500
Frequency (hzl
SPIKE
Channel
341'00'36>58
5
em ent
M E -0 4 mm l
Three frequency domain
ground displacement
records for the seismic
snow event which occurred
on day 341 at OO hr, 36
min, 58 sec Greenwich
mean time.
Frequency (hzl
65
C han nel
8
400
500
C hannel
9
ili as
0
100
F requ ency
200
300
Ih z i
O
100
Frequency
200
SPIKE
05 0* •
C han nel
5
400
500
iu 0.25
O
100
200
Frequency Ihzl
300
300
400
500
Ih z l
341'00'56'20
Three frequency domain
ground displacement
records for the seismic
snow event which occurred
on day 341 at OO hr, 56
min, 20 sec Greenwich
mean time.
66
Channel B
D isolacem e
Channel 9
0
100
200
300
400
500
Frequency (hi)
0
100
SPIKE
Channel
5
400
500
0.25
em ent
M E -O S inm I
OSOt
I
O
O
XX)
200
Frequency (hi)
200
300
400
500
Frequency (hi)
300
341<18<55<15
Three frequency domain
ground displacement
records for the seismic
snow event which occurred
on day 341 at 18 hr, 55
min, 15 sec Greenwich
mean time.
67
Channel
8
OSO t
Channel 9
D ls p la c e m e
iu 0.25
0
100
200
300
400
500
Frequency IhzI
,0
100
200
SPIKE
m ent
M E -C M m m I
Channel
0
100
200
Frequency Ihzl
300
400
500
Frequency (hz)
300
400
5
341'18'56<20
Three frequency domain
ground displacement
records for the seismic
snow event which occurred
on day 341 at 18 hr, 56
min, 20 sec Greenwich
mean time.
Appendix D
Corner Frequency: Smoothed log amplitude-log frequency analysis of
the ground displacement seismic snow records. Three time domain ground
acceleration records for the seismic snow event which occurred on day
341 at 00 hr, 36 min, 58 sec Greenwich mean time.
69
Chennel 9
Frequency
Ihzl
Frequency
lh«l
SPIKE
341<00<36<88
Three corner frequency
records for the event
which occurred on day
341 at OO hr, 36 min, 58
sec Greenwich mean time.
Frequency
Ihzl
Ground Displacement
(mm)
70
Frequency
(Iu )
S P IK E
341<00<56<20
Displacement
(mm)
Three corner frequency
records for the event
which occurred on day
341 at 00 hr, 56 min, 20
sec Greenwich mean time.
Frequency
(hi)
71
Ground Displacement
(mm)
Channel 9
F requ ency
(h z)
SPIKE
341 18 55.15
Displacement
(mm)
Three corner frequency
records for the event
which occurred on day
341 at 18 hr, 55 min, 15
sec Greenwich mean time.
Frequency
(hz)
72
C han nel 9
Ground
D isplacem ent
Imm l
- IE-3,
Frequency
Ihz)
Frequency
(hzl
D isplacem ent
(nmn>
SPIKE
341'18i56'20
Three corner frequency
records for the event
which occurred on day
341 at 18 hr, 56 min, 20
sec Greenwich mean time.
MONTANA STATE UNIVERSITY LIBRARIES
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stks N378.R719@Theses
Seismic moment, stress drop, strain ener
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