AN ABSTRACT OF THE THESIS OF
LYNN DALE TREMBLY for the Master of Science in Oceanography
(Name)
(Degree)
(Major)
Date thesis is presented
/f /9V
Title__PRIMARY SEISMIC WAVES NEAR EXPLOSIONS
Abstract approved
Redacted for privacy
V
"
This thesis is concerned with near source primary seismic waves
generated by, the Gnome, Hardhat, Shoal and Haymaker underground
nuclear explosions. Records of ground motion between 0. 3 and ZO. 0
kilometers from the sources were analyzed in terms of displacement
amplitude and energy variations with distance.
The observed data
have been compared to similar data from a theoretical source model
to determine the adequacy of the theoretical model.
The Fourier Integral has been used to obtain frequency analyses
of the first half cycle of the primary displacement waves in the near
source region to the observed and theoretical sources. There is
some evidence that a long period displacement field may exist near
the explosions, as predicted by the theoretical source.
Scatter in the
observed amplitude data makes it difficult to distinguish between the
long period and the radiation fields. The variation with distance of
total energy of the primary seismic waves indicates that the radiation
field becomes representative of the energy beyond a few kilometers
from the sources.
When the conditions are approximated, for which the theoretical
source was developed, the comparison of observed and theoretical
data indicate that the theoretical source approximates the observed
sources. It was found that the waveforms from the theoretical source
did not approximate the waveforms from the Haymaker explosion and
from one quadrant of the Shoal explosion. This is thought to be due
to any combination of the following reasons: (a) the elastic-inelastic
boundaries were not correctly defined for these observed sources,
(b) the media were not elastic and elastic theory did not apply, and
(c) the solution for the theoretical displacement pulses given by the
theoretical model does not apply to all cases.
PRIMARY SEISMIC WAVES NEAR EXPLOSIONS
by
LYNN DALE TREMBLY
A THESIS
submitted to
OREGON STATE UNIVERSITY
in partial fulfillment of
the requirements for the
degree of
MASTER OF SCIENCE
June 1965
APPROVED:
Redacted for privacy
S S C/i
of Geophysica1?'ngraphy
in Charge of Major
Redacted for privacy
hairm
Department of Oceanography
Redacted for privacy
Dean of the Graduate School
Date thesis is presented
Typed by Betty Thornton
/7 /9
ACKNOWLEDGMENTS
The work presented in this thesis was performed under the
direction of Dr. Joseph W. Berg, Jr. , Professor of Oceanography
at Oregon State University.
The author wishes to express his grati-
tude to Dr. Berg for his assistance in selecting this project and for
his many helpful suggestions in analyzing the data and in writing
this thesis.
Appreciation is extended to the U. S. Coast and Geodetic Survey,
to the Sandia Corporation and to Stanford Research Institute for the
seismograms used in this thesis.
This research was supported by the Air Force Office of
Scientific Research under Grant AF-AFOSR-62-376 as part of the
Vela Uniform Program directed by the Advanced Research Projects
Agency of the Department of Defense.
PRIMARY SEISMIC WAVES NEAR EXPLOSIONS
by
LYNN DALE TREMBLY
TABLE OF CONTENTS
Page
Introduction ..............................................
1
Availabledata
............................................
4
...........................................
4
Recordings ...........................................
4
Theoretical source ------------------------------------
11
Explosions
Analysis of the data .......................................
Gnome ................................................
17
20
Hardhat ............................................... 24
Shoal ................................................
26
Haymaker .............................................
35
Attenuation ...........................................
39
Summary and conclusions ..................................
41
Bibliography .............................................
45
Appendices: Appendix 1 ....................................
48
Appendix 2 ..................................
52
Appendix 3 ..................................
55
LIST OF FIGURES
Fig.
1.
2.
3.
4.
Page
Location s of surface strong-motion seismic stations in the
close-in region, Gnome explosion
6
Locations of seismic recording stations in the close-in
region, Hardhat explosion
8
.......................
..............................
Locations of seismic recording stations in the close-in
region, Shoal explosion ................................
10
Locations of seismic recording stations in the close-in
region, Haymaker explosion
13
...........................
5.
Observed and theoretical displacement pulses of the following explosions: a) Gnome, b) Hardhat, and c) Haymaker 15
6.
Observed and theoretical displacement pulses of the Shoal
explosion: a) southwestern quadrant, b) northeastern
quadrant, and c) southeastern quadrant
..................
7.
16
Gnome:
a) Fourier transform of theoretical displacement versus
distance
b) Fourier transform of observed displacement versus
distance
c) Total energy of theoretical and observed displacement
versusdistance .......................................
8.
21
Hardhat:
a) Fourier transform of theoretical displacment versus
distance
b) Fourier transform of observed displacement versus
distance
c) Total energy of theoretical and observed displacement
versus distance .......................................
9.
25
Shoal northeastern quadrant:
a) Fourier transform of theoretical displacement versus
distance
b) Fourier transform of observed displacement versus
distance
c) Total energy of theoretical and observed displacement
versus distance .......................................
28
Fig.
10.
11.
Page
Shoal southeastern quadrant:
a) Fourier transform of theoretical displacement versus
distance
b) Fourier transform of observed displacement versus
distance
c) Total energy of theoretical and observed displacement
versus distance .......................................
30
Shoal southwestern quadrant:
a) Fourier transform of theoretical displacement versus
distance
b) Fourier transform of observed displacement versus
distance
c) Total energy of theoretical and observed displacement
versus distance .......................................
12.
33
Haymaker:
a) Fourier transform of theoretical displacement versus
distance
b) Fourier transform of observed displacement versus
distance
c) Total energy of theoretical and observed displacement
13.
14.
15.
16.
versus distance .......................................
36
a) Waves recorded at subsurface station Z2VR at shot
depth; Hardhat explosion
b) Waves recorded at subsurface station 4-UR at shot
depth; Haymaker explosion ............................
50
Waves recorded at subsurface stations at shot depth, Shoal
explosion: a) southwestern quadrant, b) northeastern
quadrant, and c) southeastern quadrant .................
51
a) Shoal surface station SS-3 vertical and radial displacement traces
b) Hodograph of ground displacement recorded at Shoal
surface stationSS-3 ..................................
53
Travel time curves showing the phase velocities of the
peaks and troughs of the first motion on Shoal surface
stations SS-5, SS-2, and SS-1 .........................
54
Fig.
17.
Page
Geological models of the close-in region of the following
explosions: a) Gnome (Weart 22, p. 982), b) Hardhat,
c) Shoal northeastern quadrant, and d) Haymaker
.......
56
LIST OF TABLES
Table
Page
............................
1.
Source data for explosions
2.
Maximum displacement and Fourier amplitudes at
elastic-inelastic boundary calculated using data obtained
at ranges between 3. 8 and 19. 2 kilometers from the
Haymaker explosion .................................
38
Energy attenuation constants for near source radiation
fields of explosions ..................................
40
3.
4
PRIMARY SEISMIC WAVES NEAR EXPLOSIONS
INTRODUCTION
The purpose of this thesis is to study the variations of amplitudes and energies of near source primary seismic waves generated
by four nuclear explosions (Gnome, Hardhat, Shoal and 1-laymaker).
To do this a comparison between the observed data and those deter-
mined from a theoretical source model was deemed desirable. Math-
ematical descriptions of spherically diverging elastic waves instigated
by pressure functions have been given by Sharpe (21, p. 144), Duvall
and Atchison (11, p. 7) and Blake (6, p. 212).
BlakeTs model was cho-
sen as the theoretical source. Berg and Papageorge (3, p. 947) gave
a detailed analysis of this theoretical source. Berg, Trembly and
Laun (4, p. 1115) compared the seismic waves near the Gnome nuclear
explosion with Blak&s theoretical source. They concluded that the
theoretical model seemed to describe the elastic waves from that explosion, but the data were insufficient to make a detailed comparison.
Thus, another objective of this thesis is to make a detailed comparison
with the source model.
When a nuclear explosive is detonated in the ground, gases of
very high temperature and pressure are produced almost instantaneously.
Johnson, Higgins and Violet (14, p. 1467) gave the temperature
and pressure associated with the Rainier underground nuclear explosion to be about 1 x 10 6o K and 7 x 10 6 atmospheres respectively. The
energy provided by the explosive is expended in forming and enlarging
the initial cavity, in heating and fusing the ground, in crushing and
cracking the ground, and in producing sound waves in the air and
seismic waves in the ground (Berg 2, p.
4).
The region around an
underground explosion can be roughly separated into two zones, In
the zone closest to the point of explosion there is an affected region in
which the pressure wave is propagated as a shock wave, The energy
of the shock wave is propagated and dissipated in a nonlinear manner,
The hypothetical surface bounding the inelastic regi.on has been
termed the Itequivalent cavity,
'
Kis slinger l5, p. 43), The size of
the inelastic zone depends, among other things, on the size and depth
of the explosion and on the medium in which the explosion is buried,
Outside the equivalent cavity the pressure is reduced enough to
fail, on the linear portion of the stress-strain curve of the material,
approximately. Hence, the medium behaves quasi-elastically. Propa-
gation of di.sturbances caused by the prs sure pulse (strains) can be
approximated using infinitesimal strain theory, either purely elasti.c
or allowing for frictional losses, This outer region has been termed
the elastic region. A large number of studies regarding the elastic
waves generated by explosions have been conducted. A summary of
3
the strong-motion measurements of underground nuclear detonations
is given by Adams, Preston, Flanders, Sachs and Perret (1,
p. 903).
Werth and Herbst (24, p. 1587) have studied and compared amplitudes
of seismic waves recorded at ranges beyond 100 kilometers from
nuclear explosions in tuff, salt, granite and alluvium.
The generation of elastic waves from an explosive source in-
volves very complex processes. The complete mathematical formulation of the phenomena is formidable at the present time. However,
much can be learned about the generation of elastic waves through
controlled experimentation such as was used to obtain the data pre-
sented in this thesis where descriptions of ground motion are considered in the elastic region only, from the elastic-inelastic boundary
out to about 20 kilometers from the source. For this "close in
region, amplitudes and energies of seismic waves generated by the
four nuclear explosions will be studied as functions of distance from
the sources. The empirical data will be compared with similar
theoretical data to determine the adequacy of the theoretical model.
The ultimate objective of this thesis is to provide a better understanding of the generation of seismic waves by explosive sources.
4
AVAILABLE DATA
Explosions
Information about the four underground nuclear explosions that
were used in this research is given in Table 1.
Table 1.
Source Data for Explosions
Nuclear
Explosion
Date
Yield
Depth of
Burial
Type
of
of
Time of
Detonation
Name
Explosion
(Kton)*
(Km)
Medium
(GCT)
Salt
Granite
Granite
Alluvium
19:00:00. OC
December 10, 1961
0. 360
3
5
February 15, 1962
0.290
Shoal
October 26, 1963
0. 366
12
Haymaker June 27, 1962
53
0. 410
*1 kiloton is defined as a total energy release of
4. 2 x 1019 ergs (Johnson et al. 14, p. 1458).
Gnome
Hardhat
1012
18:00:00.10
17:00:00. 12
18:00:00. 12
calories
Each of these explosions was recorded by instruments at shot
depth and by strong-motion instruments on the surface of the ground.
Recordings
The subsurface recordings around each explosion measured
parti.cle velocity and acceleration. In each case, these records were
integra±ed in order to obtain the particle displacement of the ground
motion.
For all explosions except Hardhat, the subsurface records
used were obtained from the Sandia Corporation through the courtesy
5
of William Perret and Wendell Weart. The subsurface recordings
for the Hardhat explosion were obtained from the Stanford Research
Institute through the courtesy of Larry Swift.
The U. S. Coast and Geodetic Survey furnished records from
strong-motion instruments which were located on the surface of the
gound around each explosion. These instruments measured particle
displacement and particle acceleration. Simple pendulum amplitude
and phase response curves (Richter, 20, p. 217) were assumed to be
applicable for the surface strong-motion instruments (personal cornmunications with U. S. Coast and Geodetic Survey, Berg et al. 4,
p. 1115).
The natural frequencies of the displacement and accelera-
tion meters were about 0. 25 and 10 cps respectively. In essence, the
amplitude and phase response of the displacement meters are nearly
flat from 10 to about 0. 5 cps. A large phase shift occurs and the
amplitude magnification decreases rapidly below about 0.5 cps.
Figure 1 shows a plan view of the locations of the strong-
motion seismic instruments for the Gnome nuclear explosion. In-
struments located on the surface of the ground were at ranges between 0. 8 and 15 kilometers from the source. The strong-motion
recording stations numbers 1 and 5 at 0. 8 kilometers, number 2 at
1. 6 kilometers and number 8 at 15 kilometers were not used. The
surface of the ground near stations 1 and 5 did not respond elastically
I
I
I
0 KILOMETERS 5
0
22'
I
I
8
9
Ui
I
.
20
I.-
4
0
-J
z
.
N
18
3
0
0
2
0
16'
1056
-
7
G.Z.±0
I
F
I
561
18'
103°W.
I
I
521
0
50'
LONGITUDE
strong-motion station
Surface
Note
I
54'
locations
Data
used
Data
not used
station was located
and is not shown because
One subsurface
0.3 km from
G.Z.
ofscals.
Figure 1
Locations of surface strong-motion seismic stations
in the close-in region, Gnome explosion, Carder (9, 1048).
7
and useable recordings were not obtained, and the recordings at station number 2 were felt to be erroneous due to the wrong polarity of
first motion and inconsistent amplitude results (Carder 9,
p. 1050).
The recording at station 8 was not used because the arrival of the
first seismic energy could not be picked with a high degree of confidence.
There were a total of five subsurface stations at different distances from the Hardhat explosion.
To determine which of the sta-
tions were nearest the equivalent cavity radius a technique used by
Werth and Herbst (23, p. 981) was employed. A reduced displacement potential was calculated from each of the five subsurface par
tide displacement traces. The amplitude of the reduced displacement potential should be independent of distance from the source when
the displacement field is conservative and elastic theory should pertam. it was found that the recording of particle displacement at 0. 305
kilometers was in the elastic region and this station is shown in
Figure 2, ZZVR (The abbreviations, VR, denote radial component
particle velocity meters). This technique was used only on the Hardhat explosion since none of the other explosions were recorded with
subsurface instruments at more than one range.
Figure 2 shows the strong-motion instruments located on the
surface of the ground between 1. 0 and 10. 6 kilometers from the
8
1
101
4
22VR
I4
GZ.
1
-
12'
5
0
Lu
0
II-
-J
to
6
7
z
0
N
8'
8
6'
KILOMETERS
o
-
I
I
6'
Subsurface
I
2'
4'
116°W.
5
0'
LONGITUDE
recording
station location
0
strong-motion station locations
Surface
o
Figure
a.
Data
used
Data
not used
Locations of seismic recording stations in the
close-in region, Hardhat explosion.
Hardhat explosion.
The recordings from the strong-motion stations
2 and 4 were not used in this research. The recording from station 2
at 1. 0 kilometer showed that the recording paper was stopped for an
unknown interval of time during recording and that the base-line of
the instrument shifted. The recording from station 4 at Z. 3 kilome-
ters showed considerable interference on the trace and thus could not
be used quantitatively.
Figure 3 shows a plan view of the seismic instruments that recorded the elastic waves from the Shoal nuclear explosion.
This was
the most extensively instrumented explosion of the four considered.
There were three subsurface recording stations on three different
azimuths all at a range of 0. 59 kilometers from the Shoal epicenter
and all essentially at shot depth. Each of the subsurface stations re-
corded three components of particle acceleration and particle velocity.
Strong-motion surface instruments were located along the same
azimuths as the subsurface instruments. There were some instruments on the surface of the ground which were the same type as the
subsurface instruments. These instruments are denoted by the prefix SS in Figure 3. At most of the strong-motion stations there were
three components of ground displacement measured. At several lo-
cations two sets of strong-motion instruments were located together
(Note stations 3-4, 5-6, 7-8 in Figure 3). At each of these stations
10
0'
0 KILOMETERS
5
16
'4.
SS-43ó4
83-5
12'
7,8
I-
9
2.
0
10'
o'4
6.
8'
I
I
24'
aS'
.1
I
22'
I
I
20
S..
IS"
r
0'
116'W. LONGITUDE
Subsurføc.
rscovdinq
station iocoticns
SIwf000 stvonq-motlon statIon Iocatias
Data ussd
o
Data
not u..d
Figure 3. Locations of seismic recording stations
in the close-in region, Shoal explosion.
both sets of instruments showed very similar motions.
Figure 4 shows a plan view of the seismic instruments that recorded the seismic waves from the Haymaker nuclear explosion. One
subsurface recording station, 4-UR, was located 0. 046 kilometers
above ground zero at a range of 0. 55 kilometers (The abbreviations,
UR, denote radial component particle velocity meters). This instrument provided the only subsurface measurement of particle motion
that was available from the elastic region of the Haymaker explosion.
Strong-motion surface instruments were located at ranges between
1. 8 and 19. 2 kilometers from the epicenter.
Theoretical Source
Berg and Papageorge (3, p. 947) gave a detailed analysis of
Blake's proposed theoretical source. They derived the following ex-
pression for the ground displacement for a driving pressure described
by P =
P(e1T e2T).
prEwo
e
relT (c_- r1 )
P0a
U
0r
rc
+ (c0 _l)21 L
! ( cos
w° T
l
w0
sin
+
T).
+
12
cos wT +
P0
pr [w02+
(o
:0
+
Woz
T(c - r2
r
a
rcj
(c0
e0T
o2
cos W0T
Wo
:o
cos WT+
WOT] -
+o2
+
sinW0T +
sin WOT)
(1)
Where:
Particle Displacement
P = Pressure Pulse Amplitude
a = Radius of Equivalent Cavity
U
=
Density
Range
T = Reduced Time = Time Minus Travel Time
c = Compressional Wave Propagational Velocity
W0 = Natural Frequency of Cavity
p =
r
=
=
2 = Pressure Attenuation Constants
Ground Attenuation Constant
In this research equation 1 has been written expressing c, W0,
and
in terms of the elastic constants
j.
andX
.
The equation was
then programmed for the IBM 1620 and 7090 computers.
meters p., X
,
p, a,
l'
The para-
and r were varied, within limits, for each
source until a theoretical displacement pulse was obtained that ap-
proximated the first observed pulses in the elastic region. For a
given source, the values of the above parameters were kept consistent with observed or reasonable values for the medium under
13
1
8'
I
I
I
I
I
9
-
87
6'
6
w
I-
5
-J
z
0
m
2
.
4
2'
0
-
4-uR
-
G.Z.
0
0'
5
KILOMETERS
L
I
I
4'
6'
I
I
I
2'
C
116°W. LONGITUDE
Subsurface
Surface
recording station location
strong-motion station locations
Figure 4. Locations of seismic recording stations
in the close-in region, Haymaker explosion.
14
consideration.
Ground displacements as measured at shot depth near each of
the four explosions were used as the particle displacement pulse in
the elastic region.of the material around the explosions.
The theo-
retical approximations to the observed data are shown in Figures 5
and 6.
The displacements shown for the observed sources are the
measured particle displacement traces corrected for reflections from
the free surface. These corrections are explained in detail in
Appendix 1.
There were three displacement functions derived for the
Shoal explosion because of the azimuthal asymmetry of the compressional waves generated by the explosion. Figure 6 shows the theo-
retical approximations of the wave forms for the three azimuths.
These will be discussed in more detail in the section on the analysis
of the data and in Appendix
.
15
a.
:
Cs 45 km/s.c
I
.4
*0.25
'\
p:2.7
THEORETICAL
I
2
0'0
0.3
0.2
0.1
b.
o
0.3 km
i' '0.3 km
o' 5.1 km/s.c
,: 0.25
,: 8.0
o : 2.?
tiJ
C)
RETICAL
-J
0
0.3
0.2
0.1
c.
0.5 km
a
v0.55km
c:2.5 km/sic
-
20
THE0RETICAL
1
0.2
I
0.4
I
I
0.8
I
I
0.8
I
i
1.0
RECORD TIME MINUS TRAVEL TIME
i
i
i
1.2
IN SEC
Figure 5. Observed and theoretical displacement pulses of the
following explosions: a) Gnome, b) Hardhat, and c)
Haymaker,
16
4-
a.
': 0.55 km
OBSERVED
-
t
0,59 km
p
2.7 gm/cc
2
as 0.45 km
r:0.59 km
5km /s.c
I,1y'\T0T(
2
:
ii
p:27um/cc
OBSERVED
f
w
c.
0
0.2
0.4
0.6
a0.53 km
j
r = 0.59 km
cs 5.0 km/sec
= 0.25
-
OC1
4
= 2.7 gm/cc
I
4
OBSERVED
I
-
- - -
I
-1
THEORETICAL
21
I
0
I
0
RECORD
Figure
6.
1
0.2
I
I
0.4
I
I
0.6
I
I
0.8
TIME MINUS TRAVEL TIME IN SEC
Observed and theoretical displacernentpuIseS of
the Shoal explosion: a) southwestern quadrant, b)
northeastern quadrant, and c) southwestern quadrant.
17
ANALYSIS OF THE DATA
Recordings of seismic waves used in this research were obtamed from instruments at ranges extending from near the shot point
to over 10 kilometers from each of the nuclear explosions.
The theo-
retical displacement at the elastic -inelastic boundary was calculated
as described in the section of this thesis entitled Theoretical Source,
p. 11 and 12..
Theoretical displacement pulses were calculated for
ranges that were comparable to the recording site ranges and corn-
pared to the recorded particle displacements. Amplitudes of given
frequencies and energy content of the observed and theoretical displacement pulses were plotted against distance and comparisons made
between the resulting data. For Gnome, Shoal and Haymaker there
were useable subsurface recordings at only one range for each explosion, thus, the technique used for Hardhat to determine the location
of the elastic-inelastic boundary could not be used. The subsurface
recording stations were possibly not in the elastic region. If they
were not, the observed data would not be expected to compare satis-
factorily to the data for the theoretical model.
Because of the shape of the theoretical displacement pulse and
1.
The subsurface recording instrumentation differed from the surface recording instruments for all explosions except Shoal. This
may cause confusion in interpretation of the observed data, Berg
et al. (4, p. 112.1).
iIJ
because of interference from other waves it was assumed that the
first half cycle of the recorded displacement on seismograms of surface instrumentation repre sented the primary particle displacement
from the source. This is not completely true due, in part, to instrumentation which did not completely follow the motion of the ground.
The observed displacement pulses were corrected for local
geology which necessarily differed for each explosion. The geological
corrections affect the comparisons between the theoretical and observed waveforrns. The methods used to account for variations in
geology near each explosion are discussed in detail in Appendix 3.
The observed particle displacements were corrected to correspond to
spherically diverging waves, unaltered by local geology. Amplitude
spectra analyses and total energy calculations were made for the
corrected observed measurements and compared to the theoretical
measurements.
Frequency analyses of the theoretical and observed displace-
ment pulses were performed using the Fourier Integral method of
analysis. For all data, observed and theoretical, the Fourier transform amplitudes, g(w)j, are not completely representative at fre-
quencies less than 0. 5 cps because the wave-forms were arbitrarily
truncated. The subsurface displacement pulses for the Gnome,
Hardhat and Shoal explosions were truncated at 1. 0 second, and that
19
for the Haymaker explosion was truncated at 1. 4 seconds. When a
waveform is arbitrarily truncated, the shape of the Fourier spectrum
is affected by the length of the pulse. The Fourier spectrum contains
notches at frequencies that are related to the pulse length. For example, when the Gnome waveform (see Figure 5a) is truncated at 2. 0
seconds a notch occurs in the Fourier spectrum at 0. 5 cps, whereas
when the same pulse is truncated at 1. 0 second, no notch occurs.
Thus, the pulse length is important to the shape of the Fourier spectrum at the lower frequencies when the pulse contains a permanent
displacement. The total effect of truncating the pulses in this work
is not known. However, the general character of the spectra is con-
sidered adequate for the purposes at hand.
The total energy of the first arrival was computed for all observed and theoretical displacement pulses using the method given by
Howell and Budenstein (13, p. 42). The method involves computing
the kinetic energy (1/2 MV2) of the ground during the passage of a
seismic pulse and then doubling it since half of the energy would be
potential energy if the medium were elastic. The particle displace-
ment traces were digitized and differentiated with respect to time.
Energy computations were performed using the digitized velocity
data.
20
Analysis of the data from each explosion will be discussed sep-.
arately in the following order: Gnome; Hardhat; Shoal; and Haymaker.
Gnome
The decrease of the Fourier transform amplitudes is shown for
the Gnome theoretical data by the solid curve A in Figure 7a and for
the Gnome observed data in Figure 7b (Berg et al. 4, p. 1120).
Fourier transform amplitudes at 0. 5, 1. 0 and 3. 0 cps are shown
diminishing with distance from 0. 3 to about 10 kilometers. Between
0. 3 and 3. 0 kilometers the theoretical transform amplitude at 0. 5
cps decreases with approximately the inverse square power of the
distance. This has been termed the long period field. This amplitude
would diminish with the inverse first power of distance at distances
greater than about 10 kilometers.
The field of energy that decreases
as the inverse first power of distance has been termed the "radiation
field.
The Fourier transform amplitudes of the theoretical dis-
placement pulses for 1. 0 and 3. 0 cps diminish by the inverse first
power at all distances. A continuation of Figure 7a to frequencies of
5. 0, 7. 0 and 10 cps shows that the transform amplitudes at these fre-
quencies diminish with approximately the 1. 5 power of distance be-
tween 0. 3 and 3. 0 kilometers, and beyond 3. 0 kilometers the transform amplitudes diminish with approximately the first power of the
a.
c.
b.
I
luIH1
I.Ocp.
'5%
0.5cps
-.
IO
LRADIATION
-p
(I,
o
a
-
FIELD
POSSIBLE LONG
PERIOD FIELD
3.Ocps
a
z
I
7A
-2
10-
0
IO1e.
POSSIBLE
RADIATION
_L
'
_"
D"
-t
POSSI
RAD1ATN FIELD
'
10'
IU
lO
100
10
I0
IV
I0
tOO
101
102
0
2
4
6
8
DISTANCE FROM SOURCE P4 KILOMETERS
Figure 7. Gnome: a) Fourier transform of theoretical displacement versus distance
b) Fourier transform of observed displacement versus distance
c) Total energy of observed and theoretical displacement versus distdnce
t\)
22
distance. Thus, the area immediately around the theoretical source
is acting as a narrow band pass filter in which only the frequencies
between 1. 0 and 3. 0 cps diminish according to spherical spreading
laws at all distances.
The Fourier transform amplitudes of the Gnome observed displacement pulses (see Figure 7b) at 0. 5 and 1. 0 cps decrease as the
inverse 1. 7 power of the distance and those for 3. 0 cps decrease as
the inverse 1. 5 power of distance.
The straight solid lines through
the observed data were obtained by the method of least mean squares
using all data shown on the graph.
The presence of the long period
field and radiation field in the observed data is suggested by the
dashedlines (Berg et al. 4, p. 1120).
Figure 7c shows the total energy of the displacement pulse
versus distance from the source. The energy computed from the displacement pulses of the theoretical source are shown by the dashed
curve A. The radiation field energy would be representative of the
energy from the theoretical source beyond about 6. 0 kilometers.
The energy values obtained for the observed data are also
shown in Figure 7c. The solid line B, connecting the data points of
energy computed using the first half cycle of the observed displace-
ment traces, was fitted by the method of least mean squares to all
data.
The straight line, C, was fitted to double the energy values
23
shown on the graph. If the energy data are representative it can be
seen that the first half cycle of the displacement trace on the seismograms is a good approximation of the primary displacement generated
by the explosion because of the relationship with the energy computed
at the subsurface stations. The dashed line D, connects the two energy values at 6. 4 and 9. 5 kilometers from the source. If the ground
displacements measured near the Gnome source were approximated
by the theoretical source it would be expected that the energy in the
radiation field would be representative of the energy transmitted to
large distances (see Figure 7c, curve D). This is the energy that
would be of interest in determining the relative size of the source
from primary waves at greater distances. It is important to realize
that although straight lines have been used in Figure 7c, the energy
decreases such that the straight line D would be asymptotic to a
second degree curve.
An interesting consequence of this argument is that if the ener-
gy of the possible observed radiation field is extrapolated to the elastic-inelastic boundary, a source efficiency of about 1. 3 percent is obtamed. Thus, about l.3 percent of the total source energy (3 kilotons
= 12. 6 x i019 ergs) is going into the formation of seismic waves that
are transmitted to large distances. It is seen in Figure 7c that when
the energy in the possible observed long period field is extrapolated
24
to the elastic-inelastic boundary a source efficiency of about 15 percent is obtained.
The former value is more consistent with the find-
ings of other investigators for the amount of source energy contained
in seismic waves from an explosion (Berg et al. 4, p. 1124).
Hardhat
The decrease of the Fourier transform amplitudes with distance
is shown for the Hardhat theoretical data in Figure 8a.
Between the
ranges of 0. 3 and 1. 5 kilometers the theoretical transform amplitude
at 0. 5 cps decreases with approximately the inverse square power of
the distance. This amplitude would diminish with the inverse first
power at distances greater than about 10 kilometers. The transform
amplitudes at 1. 0 and 3. 0 cps diminish as the inverse 1. 6 and 1. 2
power respectively between 0. 3 and 1. 5 kilometers. The transform
amplitudes at 1. 0 and 3. 0 cps diminish with the inverse first power
beyond 1. 5 kilometers.
The decrease of the Fourier transform amplitudes with distance for the Hardhat observed displacement pulses is shown in
Figure 8b at 0. 5, 1. 0 and 3. 0 cps. The straight solid lines through
the observed data were obtained by the method of least mean squares
using all of the data shown on the graph. The transform amplitudes
diminish with the 1. 5 power of distance at 0. 5 and 1. 0 cps and with
a.
C.
22VR
1-)
0.Scps
S 1.9
10-I
'0-I
1019
W
C,
"I
Id
"- RADIATION
FIELD
211.3
-iQ
(I,
I.Ocps_,
io-
-
.
S=I.6
-
0,0-2
'9
z
3.Ocps,
cp$
3
1.04
..!.
S - I.?
I.Ocps -,
POSSIBLE
FIELD
$ (06
RADIATION
B
'
I-
0.5 cps_'
$ 1.2
I
I
10
IO
10
10
DISTANCE
FROM
SOURCE
IN
0
2
4
6
8
II
10
12
KILOMETERS
Figure 8. Hardhat: a) Fourier transform of theoretical displacement versus distance
b) Fourier transform of observed displacement versus distance
c) Total energy of theoretical and observed displacement versus distance.
26
the 1. 7 power of distance at 3. 0 cps. If the long period field is pre-
sent on this graph, it is masked by the scatter of the data or other
reasons that are unknown.
The total energy was computed for the Hardhat theoretical and
observed primary displacement pulses. Figure 8c is a plot of total
energy values versus distance from the source. The energy of the
theoretical displacement pulse is shown by curve A.
The radiation
field energy is representative of the total energy beyond about 2
kilometers. Line B was fitted by the method of least mean squares
using the data beyond 0. 5 kilometers. The observed data indicate
the presence of the energy of the long period field at ranges closer
than 1. 0 kilometers. The radiation field is predominant beyond 1. 0
kilometers from the source.
When the energy values of the possible observed radiation field
are extrapolated to the elastic-inelastic boundary, the seismic efficiency is found to be about 2 percent.
When the energy in the pos-
sible long period field is extrapolated to the elastic-inelastic boundary, the seismic efficiency is found to be about 13 percent.
Shoal
A pronounced azimuthal asymmetry in the seismic waves gen-
erated by the Shoal explosion was measured. Due to this asymmetry,
27
comparisons between the theoretical and measured waveforms (see
Figure 6) were made for the three azimuths. A theoretical source
was matched to the subsurface recording for each azimuth. The data
are presented dealing with each of the three azimuths separately.
The subsurface station located in the northeastern quadrant
from the Shoal explosion was station number PM-2 (see Figures 4 and
6b).
Figure 9a shows the decrease of the Fourier transform ampli-
tudes for the theoretical displacement pulses applicable in the northeastern quadrant. Amplitudes at 0. 5, 1. 0 and 3. 0 cps are shown
diminishing with distance from 0. 6 to 13 kilometers,
Between 0. 6
and 2. 0 kilometers the theoretical transform amplitudes at all frequencies show the existence of the long period field. Between these
ranges the transform amplitudes at 0. 5 cps decrease with approxi_
mately the inverse square power of distance, At 1. 0 and 3. 0 cps the
transform amplitudes diminish as the 1. 4 power of distance. Beyond
2 kilometers, the transform amplitudes at 0. 5 cps diminish as the
1. 3 power of distance and those for 1. 0 and 3. 0 cps diminish with
approximately the first power of distance. Figure 9b shows the
Fourier transform amplitudes of the observed displacement pulses
for the northeastern quadrant at 0. 5, 1. 0 and 3. 0 cps. Straight lines
were fitted to the data by the method of least mean squares. The
amplitudes diminish with the 1. 7 power of distance at 0. 5 and 1. 0 cps
a.
101
\
b.
C.
19
0.5cps
\
\4
-
S -1.9
$ -
\
I.Ocps
PM-2'
(G-SS..4
i.ocps
I.7
$sJ4
'
\
C.,
102
RADIAT1ON FIELD
\
10-
3.Ocps
3.0cps
S=l.4
C
\
I.Ocps
$ 1.0
3.0 cps
-
s.-.
\.
O.5cps
ZIir
S.I.3
ZI
I
I
ID
10
I0
I
l0
I
DISTANCE
FROM
SOURCE
IN
I9,
_______________________________
2
4
6
8
10
K(LOMETERS
Figure 9. Shoal northeastern quadrant:
a) Fourier transform of theoretical displacement versus distance
b) Fourier transform of observed displacement versus distance
c) Total energy of theoretical and observed displacement versus distance.
12
and with the 1. 8 power of distance at 3. 0 cps. The distinction between
the long period field and the radiation field is not evident in the observed data. The two most distant stations on this azimuth were not
on the same type of medium as the other stations.
They were located
on a thick layer of alluvium which was bounded by steeply dipping nor-
mal faults (see Figure l?c, Appendix 3). Geological corrections ap-
plied to the data for these stations may be in error due to uncertainties in the geological model.
Figure 9c is a plot of the energy of the observed and theoretical
displacement pulses versus distance from the source. The energy of
the theoretical displacement pulse is shown by curve A. The radia-
tion field energy is seen to be representative of the total energy beyond about 4 kilometers.
The straight line B, through the observed
data was fitted by the method of least mean squares using all of the
data shown on the graph except the last one, number 21. A seismic
efficiency of 1. 9 percent is obtained when line B is extrapolated to the
elastic-inelastic boundary. Due to the uncertainty of the energy value
at the most distant station, the decrease of energy beyond 8. 0 kilometers is not known. The dashed curve, C, has been placed on the
figure as a possible variation in rate of energy decrease.
Figure 10a shows the decrease of the Fourier transform amplitudes of the theoretical pulse for the southeastern azimuth. Between
a.
C.
0.Scps
-17
I.J
lOcps
0-I
S-I.3
RADIATION FIELD
\
U)
lii
0
lii
ILl
3.Ocps
(I,
2
0
z
\\
C.)
\
O.5cps
S-I.7
S-I2
02
\
IO
0
C)
I.Ocps
U
S.-I.O
B
3.Ocps)\
I.-
$ -121
I-
o
17
I 0
0
K1
DISTANCE
:4
f
POSSIBLE
RADIATION FIELD
0171
10°
S.
0
3
3
FROM
SOURCE
IN
I
2
4
I
A
6
KILOMETERS
Figure 10. Shoal southeastern quadrant:
a) Fourier transform of theoretical displacement versus distance
b) Fourier transform of observed displacement versus distance
c) Total energy of theoretical and observed displacement versus distance.
8
I
10
31
0. 6 and about 2. 0 kilometers the long period field is present at all
frequencies. Between these ranges, the amplitudes for 0. 5 and 3. 0
cps decrease as the 1. 7 power of distance. Beyond 2. 0 kilometers,
the amplitudes for 0. 5 and 3. 0 cps diminish as the 1. 2 power of distance. For 1. 0 cps, the amplitudes between 0. 6 and 2. 0 kilometers
decrease as the 1. 3 power of distance and as the 1. 0 power of distance beyond 2. 0 kilometers.
Figure lOb shows the Fourier transform amplitudes of the ob-
served displacement pulses for the southeastern quadrant. A much
larger displacement was measured on this azimuth than on the other
two azimuths (see Appendix 2). The primary displacement pulse, at
the surface stations SS-1 and SS-2 (see Figure 6) were truncated to
omit the second pulse. The Fourier analysis of the primary dis-
placement pulses at these stations were effected by this truncation by
an unknown amount. Straight lines were fitted to the Fourier ampli-
tudes of the truncated pulses (Figure lOb), by the method of least
mean squares using all of the data on the graph. The amplitudes for
0. 5 and 1. 0 cps diminish as the 2. 3 and 2. 2 power of distance, respectively. For 3. 0 cps, the amplitudes decrease as the square of
the distance.
Figure lOc shows the total energy of the observed primary displacement pulse versus distance.
The break in the slope of the solid
32
line is interpreted to mean that the radiation field becomes representative of the total energy beyond 3. 0 kilometers from the source. The
plot of the theoretical energy versus distance, shown by curve A sup-
ports this interpretation. The straight lines are asymptotes to the
second degree curve shown by curve C in Figure lOc.
The seismic efficiency obtained by extrapolating the possible
observed radiation field to the elastic-inelastic boundary is about 0, 7
percent. The seismic efficiency obtained by extrapolating the possible
long period field to the elastic-inelastic boundary is about 5 percent.
Figure lla shows the variation of the Fourier transform amplitude with distance for the theoretical data in the southwestern quadrant. Amplitudes at 0. 5, 1. 0 and 3. 0 cps are shown varying between
ranges of 0. 6 to 6. 0 kilometers from the source. Between 0. 6 and
0. 9 kilometers, the amplitude increases with distance at all frequencies.
Beyond 1. 0 kilometer the amplitude decreases with approxi-.
mately the first power at all frequencies. The increase of the amplitude between the ranges of 0. 6 and 0. 9 kilometers is due to the cocIt was
efficient of the exponential term in equation 1 (i. e., rc
found that in order to obtain the best theoretical approximation to the
observed displacement pulse measured at the subsurface station in
this quadrant, a value for the pressure pulse attenuation constant, o,
had to be used which was larger than the compressional wave
a.
C.
I
to_I
\\\
1020
(I,
-7
C,
POSSIBLE LONG
PERIOD FIELD
I
U
C,
Id
0,
,1PM1
a,
o
U
IO-2
Z
U
\
z
POSSIBLE
RADIATION
FIELD
IO
\sS-3
C,
O.5cps
S-l.6
I.Ocps
S-L7
IO
'
3.Ocps
S-I.7
100
10'
10°
DISTANCE
FROM
\
\
'
to18
to'
SOURCE
IN
.7
\
0
2
4
6
KILOMETERS
Figure 11. Shoal southwestern quadrant:
a) Fourier transform of theoretical displacement versus distance
b) Fourier transform of observed displacement versus distance
c) Total energy of theoretical and observed displacement versus distance.
8
34
velocity, c, making the term, c -ro 1
, negative.
This resulted in
rc
the amplitude increase at ranges between 0. 6 and 0. 9 kilometers.
Figure lib shows the Fourier transfOrm amplitudes for the data
observed in the southwestern quadrant. The solid line through the
observed data was obtained by the method of least mean squares using
all of the data shown on the graph. The amplitudes at 0. 5, 1. 0 and
3. 0 cps decrease as the 1. 5, 1. 7 and 1. 7 power of distance, respectively.
There is no increase of amplitude with distance from the ob-
served source. When only the data from the surface stations are
considered, the presence of a possible long period and a radiation
field is shown by the dashed lines on Figure llb.
Figure llc shows the energy of the theoretical displacement
pulses plotted versus distance. The energy is seen to increase between 0. 6 and 4. 0 kilometers from the theoretical source. Beyond
4. 0 kilometers the energy is seen to be quite high in comparison to
the total source energy (12 kilotons = 5. 04 x
1020
ergs).
Figure llc shows the energy values computed for the observed
primary displacement pulses, also. The line B was fitted to the data
from stations 7, 8, 12, and 16 only. This would represent the energy
in the radiation field. The seismic efficiency obtained by extrapo-
lating line B to the elastic-inelastic boundary is 0. 7 percent. The
straight lines in Figure llc are only approximations and the energy
35
probably decreases as shown by the dashed curve, C, with the straight
lines asymptotes.
Haymake r
Figure lZa shows the variation of the Fourier transform ampli-.
tudes for the Haymaker theoretical displacement pulses at 0. 5,
1. 0
and 3. 0 cps. Between 0. 6 and 2. 0 kilometers, the amplitudes in-
crease with distance at all frequencies. Beyond 2. 0 kilometers the
amplitudes diminish with the inverse first power of distance. As in
the case of the southwestern quadrant for Shoal, the increase of the
transform amplitude between 0. 6 and 2. 0 kilometers is due to the coefficient of the exponential term in equation 1 as experienced on page
32.
Figure l2b shows the variation of the Fourier transform amplitudes with distance for the observed data from the Haymaker source.
The computations were made assuming that the medium was an infin-
ite half-space. The solid line through the observed data was obtamed by the method of least mean squares using all of the data shown
on the graph.
The amplitudes at 0. 5, 1. 0 and 3. 0 cps diminish with
the 1. 6, 1. 8 and 1. 5 power of distance respectively.
Figure lZc shows the variation of total energy with distance
from the Haymaker source. The theoretical data are shown by curve
h
a.
C.
,00_
I O
/
0
)I
'0-I
°
iOcps
-10
\,-'s --1.6
\
0.5cps
-!
O.Scps
IO
x
A2
o iv
2\\
\ \
0
Id
Iii
0,
0
\
\
\
\
\
\
\ Z
0
\
I
3
\
I0_
-
Id
ie
(0.05%
0
\
z
I '
A 4uR
0)
0
z
IOcps
0
'r--I.8
-
2
Id
z
Id
IT
6
4'.
3.0cps)\..
SI.7
'1
\
-
10
I
10
10
DISTANCE
FROM
0
10
SOURCE
IN
I
4
8
12
16
20
KILOMETERS
Figure 12.- Haymaker: a) Fourier transform of theoretical displacement versus distance
b) Fourier transform of observed displacement versus distance
c) Total energy of. theoretical and observed displacement versus distance.
°
37
A and the empirical data are plotted for each recording station. Line
B was fitted to the observed data for the ranges of 2. 0 and 8. 0 kilo-
meters from the source to determine how the energy of the direct
wave is attenuated in the alluvium.
The line is dashed because of un-
certainties in the geological model. A seismic efficiency of 0. 05 percent is obtained when B is extrapolated to the assumed elastic-inelastic boundary.
The Haymaker observed data was next interpreted by taking into
account the geological model (see Appendix 3).
The model consists of
a flat-lying layer of alluvium which is 1. 1 kilometers thick overlying
an infinite half-space having a higher velocity. If this model correct-
ly represents the geology, the first arrival at all of the recording
stations beyond 2. 9 kilometers from the source would be a head
wave." The measurements from the Haymaker recording stations in
this range were corrected using the head wave coefficient given by
Zvolinskii (25, p. 6), see Appendix 3.
The measurements of parti-
cle displacement at the surface recording stations were used to calculate the reduced displacement potential of the seismic wave at the
elastic-inelastic boundary. The reduced displacement potential was
divided by R2 to obtain particle displacement at the elastic-inelastic
boundary. This assumes that the shape of the reduced displacement
potential is independent of the range from the source when in the
elastic region.
The results of these calculations are given in Table 2.
If the model and interpretation were correct all of the observed displacement pulses would show about the same amplitudes at the elasticinelastic boundary when corrected, There are major disagreements
in the data when this is done and the geological correction is open to
question.
The travel times for first arrivals at stations 3 and 4 in-
dicate that the first arrivals are head waves. However, from the data
presented in Figure 12a, b and c and Table 2 and from a geological
map of the area (McKay, 17), it is felt that the first arrivals at stations 3 and 4 were not head waves. The fact that the travel times at
these two stations happen to coincide with the arrival of a head wave
is felt to be coincidental.
Travel time data and the geological map
Table 2. Maximum Displacement and Fourier Amplitudes at ElasticInelastic Boundary Calculated Using, Data Obtained at
Ranges Between 3.8 and 19.2 Kilometers From Haymaker
Explosion.
Maximum Displacement Fourier T ransform Amplitude
Station Range Amplitude at Elastic- @ 1 cps at Elastic-Inelastic
Number (Km) Inelastic Boundary (Cm)
Boundary (Cm-sec)
1
2
3
4
5
6
7
8
9
------3.8
5. 3
7. 9
12.6
14. 3
14. 6
19. 2
l.8?xl04
0.01
0.167
6. 00 x lO
0. 232
9. 10 x l0
1.15
1.07
0. 85
1. 78
3.60xl02
3.00 x l0
3. 30 x i02
6. 70 x
39
above indicate that the first arrival at station 5 could be a head wave.
The amplitudes given in Table 2 at station 5 indicate that it is not a
head wave.
It is not known which interpretation is correct. The
amplitude at station 9 is high in comparison to other stations. A geological model of the area indicates that station 9 may be separated
from the source by a major fault. The effect of the fault has not been
taken into account in Table 2. Not enough is known about the complex
local geology of stations 3, 4, 5 and 9 to interpret the measurements
correctly. The seismic arrivals at stations 6, 7, and 8 would appear
to be head waves from the data given in Table 2.
Attrr,i,t r,r,
The energy of the seismic waves is attenuated by at least three
processes. These include geometrical spreading, losses at boundaries and frictional absorption. In this thesis absorption is described
in the form lO
where K is the absorptive attenuation constant and
R is the range from the source.
Geometrical spreading and losses at boundaries were taken into
account in calculating the total energy in the seismic waves, Therefore, an approximation of the absorptive attenuation constant K for
each medium considered in this research can be obtained from the
decrease of energy in the observed radiation field. The values of K
40
obtained are shown in Table 3. The calculations of K were made
assuming that the seismic waves diverge spherically; thus, the energy
decreases as the square of the distance due to geometrical spreading.
In all cases except Haymaker, this is felt to be a valid assumption
after the corrections for geology have been made. Not enough is
known about the complex geology of Haymaker to be confident of the
geological corrections.
The values given for K are approximate due to the scatter in the
observed data. No reliable value of K could be calculated for the
Shoal northeastern quadrant because of the large amount of scatter
and the amount of uncertainty in some data points. No value of K
could be calculated for the Haymaker explosion because of the uncertainties in the geological model.
It is possible that the differences in amplitude variation with
distance between the long period and radiation fields may be obscured
by attenuation due to absorption.
Table 3.
Energy Attenuation Constants for Near Source
Radiation Fields of Explosions
Explosion
Gnome
Hardhat
Shoal: Northeastern Quadrant
Southeastern Quadrant
Southwestern Quadrant
Haymaker
Radiation Field
Ener
r
Abs orption Constant, K (km
0.16
0.12
--0. 15
0. 12
--
-1
41
SUMMARY AND CONCLUSIONS
Seismograms from the four undergound nuclear explosions
Gnome, Hardhat, Shoal and Haymaker were analyzed. The ground
motion in the first half cycle of the displacement trace on the seismo-
grams was assumed to represent the primary displacement generated
by the sources. Insofar as the recording instruments follow the
ground motion and the theoretical source describes it, this interpretation is reasonable. All frequencies are not present in the first half
cycle because the instruments are insensitive to very low frequencies
(less than 0. 3 cps), and the waveforms were arbitrarily truncated.
The variation with distance of Fourier transform amplitudes and
total energy of the theoretical displacement pulses have been compared to the observed data. The theoretical pulses for Gnome,
Hardhat and the northeast and southeast quadrant of Shoal indicate the
presence of a long period field and a radiation field in the close-in
region.
The variation with distance of the total energy of the observed
pulses from these explosions indicate the presence of the long period
and radiation fields. The variation of observed transform amplitudes
with distance for these explosions do not clearly show the presence of
these fields, but the scatter of the data and uncertainties mentioned
below make the data difficult to interpret (see Figures 7, 8, 9 and 10,
and pages 21, 25, 28, and 30.
In the development of the expression for particle displacement
from Blake' s theoretical source it was assumed that the medium was
perfectly elastic, infinite and homogeneous. It was found that when
the geological conditions are approximated, for which the theoretical
source was developed, then the comparison of measurements between
the observed and theoretical data indicate Blake' s model approximates
the source. However, the theoretical model did not yield waveforms
that approximated those observed from all of the explosive sources
used in this research (see Figures 11 and 12, pages 33and36). This
could be due to any combination of the following reasons: (a) the
elastic-inelastic boundaries were not correctly defined for these observed sources, (b) the media were not elastic and elastic theory did
not apply, and (c) the solution for the theoretical displacement pulses
given by equation 1 does not completely apply to all cases.
Removing the effects of local geology from the observed meas-
urements is very difficult and many uncertainties are involved. For
all of the explosions, the best geological model was chosen with re-
gard to travel-times, measured angles of incidence and amplitude and
frequency considerations. Due to the uncertainties in these factors
accurate interpretation of seismograms near an explosion is very
difficult.
43
Not enough is known about the absorption of seismic waves in
the close-in region to a seismic source. Scatter in the observed data
makes it difficult to compare the observed measurements with the
theoretical measurements and to obtain reliable attenuation factors.
It was found that a pronounced asymmetry in the seismic wave
pattern was measured near the Shoal explosion. The measurements
indicate that this asymmetry is due to differences of local geology on
the different azimuths. The amount of energy measured in the total
primary displacement field close to the source in the southeastern
quadrant was larger than in the other two quadrants (see Figures 9,
10 and 11, pages 28, 30, and 33). However, the energy that is the
transmitted to large distances, the radiationfield energy, is approximately the same as on the southwestern quadrant.
This is inter-
preted to mean that the asymmetry may not be recognized in the pri-
mary displacement pulse at the outer limits of the close-in region.
Measurements of ground motion at subsurface stations close to
underground explosions may be distorted due to waves reflected from
the surface of the ground. Evidence for the presence of these arri-
vals has been presented, and they should be considered when making
quantitative calculations from recordings.
Measurements of the primary displacement of ground motion at
surface stations in the close-in region to underground explosions
44
have been found to be distorted by other arrivals after about the first
half cycle of motion. Work needs to be done to identify these arrivals
and to determine the process by which they are generated.
45
BIBLIOGRAPHY
1.
Adams, William, et al. Summary report of strong-motion
measurements, underground nuclear detonations. Journal of
Geophysical Research 66(3):903-942.
1961.
2.
Berg, J. W.
3.
Berg, J. W. , Jr. and G. E. Papageorge. Elastic displacement
of primary waves from explosive sources. Bulletin of the
, Jr.
Seismic waves from large explosions.
tin of the University of Utah 5l(lO):4-l9. 1959.
Bulle-
Seismological Society of America 54(3):947-960. 1964.
4.
Berg, J. W., Jr., L. D. Trembly and P. R. Laun. Primary
ground displacements and seismic energy near the Gnome explosion. Bulletin of the Seismological Society of America 54(4):
1115-1126.
1964.
5.
Bhattacharyya, Topan K. Seismic model investigation of energy
partitioning in multilayered media. Ph. D. thesis. College
Station, Agricultural and Mechanical College of Texas, 1961. 115
numb. leaves.
6.
Blake, F. G. , Jr. Spherical wave propagation in solid media.
Journal of the Acoustical Society of America 24(2):Zll-215.
1952.
7.
Brehoviskih, Leonid M. Waves in layered media. (English
translation) New York, Academic Press, 1960. 561 pp.
8.
Bullen, K. E. An introduction to the theory of seismology. 3d
ed. Cambridge, Cambridge University Press, 1963. 381 pp.
9.
Carder, Dean S. Ground effects from the Gnome and Logan explosions. Bulletin of the Seismological Society of America 52(5):
1047-1056.
10.
Clay, C. S. and H. McNeil. An amplitude study on a seismic
model.
11.
1962.
Geophysics 20(4):766-773. 1955.
Duval, W. I. and T. C. Atchinson. Vibrations associated with a
spherical cavity in an elastic medium. 1950. (U. S. Bureau of
Mines. Reports of Investigations no. 4692)
46
1 2.
Gutenburg, Beno. Energy ratio of reflected and refracted seis mic waves. Bulletin of the Seismological Society of America
34(2):85-l02. 1944.
1 3.
Howell, Ben F. , Jr. and D. Budenstein. Energy distributions
in explosion-generated seismic pulses. Geophysics 20(l):33-52.
1955.
14.
Johnson, G. W., G. H. Higgins and C. E. Violet. Underground
nuclear detonations. Journal of Geophysical Research 64(10):
1457-1470.
15.
1959.
Kisslinger, Carl. The generation of the primary seismic signal
by a contained explosion, Vesiac. State-of-the-art-report. Ann
Arbor, Institute of Science and Technology, University of
Michigan, 1963.
85 pp.
1 6. McCamey, Keith, R. Meyer and T. J. Smith. Generally applicable solutions of Zoepritz amplitude equations. Bulletin of the
Seismological Society of America 52(4):923-956. 1962.
1 7. McKay, E. J. Geology of Yucca Flat quadrangle.
Geological Survey Technical Letter NTS-38). 1962.
1 8.
5
pp.
(U. S.
Murphy, Byron F. Particle motions near explosions in halite.
Journal of Geophysical Research 66(3):947-958. 1961.
19. Nevada Bureau of Mines. Nevada Mining Analytical Laboratory.
Desert Research Institute. Geological, geophysical and hydrological investigations of the Sa.ndSprings Range, Fairview Valley
and Fourmile Flat, Churchill County, Nevada for Shoal event,
Project Shade, Vela Uniform program, Atomic Energy
Commission. Reno, University of Nevada, 1962. 127 pp.
20.
Richter, Charles F. Elementary seismology. San Francisco,
Freeman, 1958.
768 pp.
21.
Sharpe, J. A. The production of elastic waves by explosion
pressures. Part 1. Geophysics 7(2):l44-l54. 1942.
22.
Weart, W. D. Particle motion near a nuclear detonation in
halite. Bulletin of the Seismological Society of America 52(5):
981-1005.
1962.
47
23.
Werth, Glenn C., R. F. Herbst and D. L. Springer. Amplitudes
of seismic arrivals from the M discontinuity. Journal of
Geophysical Research 67(4):1587-l6lO.
24.
1962.
Werth, Glenn C. and R. F. Herbst. Comparisons of amplitudes
of seismic waves from nuclear explosions in four mediums.
Journal of Geophysical Research 68(5):1463-l476. 1963.
25.
Zvolinskii, N. V. Reflected waves and head waves arising at a
plan interface between two elastic media, 2, Izvestia, Akademii
NAUK. SSSR, Series, Geofizicheskia, 1:3-16. 1958.
APPENDICES
APPENDIX 1
Each of the four explosions in Table 1 were near to the surface of
the ground (see Table 1 for depths of the shots). The measurements
that were used as representing the ground motion of the source in the
elastic region were obtained at shot depth. Due to the presence of the
free boundary, the recordings from the subsurface stations recorded
not only the wave from the source, but waves which were reflected
from the free surface of the ground also. The subsurface recording
stations for the four nuclear explosions were corrected for the arrival
of the surface reflected waves. Plane wave reflection coefficients
with corrections applied for geometrical spreading were used to cal-.
culate the amplitude of the surface reflected waves. This technique
is considered to be a good approximation to the reflection of spherical
waves by Clay and McNeil (10, p. 768) and T. K. Bhattacharyya (5,
p. 78).
The correction applied to the amplitudes of the reflected
waves for geometrical spreading over the additional path length was
determined empirically from the subsurface recordings for the
Hardhat explosion. No data were available from the other explosions
for the calculation of the spreading factor, so the geometrical
spreading correction was assumed to be
r2
o
The plane wave reflection coefficients for the reflected corn-
pressional waves (PP) and the reflected, vertically polarized shear
49
waves (PSV) were taken from Brehoviskih (7, p. 36) and Bullen (8,
p. 105).
From theoretical considerations it was found that for all
cases considered the reflected compressional wave was 180 degrees
out of phase with the direct cornpressional wave. The phase of the
PSV wave at the surface of the ground was determined by applying the
boundary conditions of continuity of stress and particle displacement
across a free boundary. By combining the known phase and amplitude
of the PP wave with the direction and amplitude of the movement at the
surface of the ground (Gutenburg 12, p. 99), the horizontal component
of the PSV wave was found to be in phase with the direct compressional wave.
The recorded wave, the PP and PSV waves andthe resulting
corrected particle displacement wave for each explosion are shown in
Figures 13 and 14.
The phase of the waves are presented in the Fig-
ures as they would appear at the subsurface recording stations. With
the exception of the Gnome, all of the displacement waves at the sub-
surface station for eachsource were corrected for the PP and PSV
waves.
The corrections were found to be negligible for Gnome. In all
cases except Hardhat the magnitudes of the correction for these reflections were not large enough to take into consideration. However,
the data in this thesis have been corrected.
8
a.
storted compressional wave
6
ecorded
C.)
z
'
Surface reflected shear wave
w
0
composite wove
4
2
I-J
a-
4
0
F-
z
Surface reflected
ILl
Id
o
-2
-J
0.
4
4
0
0.2
compression wave
0.6
0.4
Cl)
0
-J
4
4
62
0.2
0.4
0.6
0.8
TIME MINUS TRAVEL TIME
1.0
IN
1.2
1.4
SECONDS
Figure 13. a) Waves recorded at Hardhat explosion sub-
surface station 22VRat shot depth;
b) Waves recorded at Haymaker explosion subu.rface station 4-UR at shot depth.
51
4
a.
2
0
C.,
0.2
0
w
0.4
I-
4
I-
z
v
...-----
144
0.4
0.2
144
C.)
4
C.
U)
Recorded
0
\ed
6
-J
4
0
4
21-
compressn wave
/
b/I.
'V
0
composite wave
0
0.2
... -.-. .4- - -4- .4Surfoce reflected shear wave
I
I
-4-
I
0.6
0.4
TIME MINUS TRAVEL TIME
-4-
IN
SECONDS
Figure 14. Waves recorded at subsurface stations at shot
depth, Shoal explosion; a) southwestern quadrant,
b) northeastern quadrant, and c) southeastern
quadrant.
52
APPENDIX 2
Some of the surface instruments located in the close-in region to
the Shoal explosion were the same type instruments as those at shot
depth.
The instruments measured both the vertical and radial corn-.
ponents of ground motion. Hodo graphs of the ground motion were
constructed and studiedto identify the waves which distort the direct
compressional wave. An example of the displacement records and
hodographs is shown in Figure 15. The range of this recording station
was 0. 92 kilometers.
The hodographs indicate that motion similar to
that of a direct compressional wave was recorded to about 0.3 seconds
after the explosion. Only about the first one-half cycle of motion of
the radial displacement trace is due to the undistorted direct cornpressional wave.
The displacement pulse amplitudes measured in the southeastern
quadrant from the Shoal explosion were greater than amplitudes mea-
sured in the other quadrants (see Figures 4 and 5). The displacement
wave recorded in the southeastern quadrant was observed to separate
into two distinct pulses as distance from the source increased. The
phase velocities of the peaks and troughs on the vertical and radial
displacement meters are shown in Figure 16. Geologic maps of the
region indicate that a shear zone is crossed in this quadrant.
The
interfering wave may have been generatedin crossing this shear zone.
It has the characteristic ground motion of a Rayleigh wave
53
4
a.
SS-3
Radial
Displacement
2
z
0
I
0
-
a
I'1"
I
0.2
0.4
.
.
0.2
0.4
2
0.6
0,8
SS-3 Vertical
0
0.6
cm
I
1.2
1.4
Displacement
0.8
TIME MINUS TRAVEL TIME
01
1.0
1.0
IN
1.2
SECONDS
I
Figure 15. a) Shoal surface station SS.-3 vertical and radial
displacement traces
b) Hodograph of ground displacement recorded at
Shoal surface station SS-3.
54
04
0.2
SS-5
0
0
0.2
I
I
0.4
0.6
DISTANCE
SS-2
I
0.8
FROM
SS-I
I
I
1.2
1.0
SOURCE
IN
I
1.4
I
1.6
KM
Figure 16. Travel time curves showing the phase velocities
of the peaks and troughs of the first motion on
Shoal surface stations SS-5, SS-Z, and SS-l.
55
APPENDIX 3
In order to compare the observed measurements of ground displacement with the theoretical ground motion, the surface strong-
motion measurements had to be corrected for the effects of local geol
ogy. A geological model was assumed for the close-in region to each
explosion.
Gnome: The geological model that was assumed for the Gnome
explosion was described by Berg et al. (4, p. 1117), see Figure 17a.
Hardhat: Figure l7b shows the instrument stations relative to the
assumed geological model for the Hardhat explosion. A U. S.
Geological Survey geological map was used as a guide in developing
this model. The geological model for stations 1 anft 3 was a half-
space witha constant compressional wave propagational velocity of
5. 1 km/sec. No travel times were available for the strong-motion
stations 1 and 3 due to cable breakage, so the velocity of the granite
was taken from the travel times recorded at the subsurface stations.
The geological model for stations 5,
6,
7 and 8 was a half-space over-
lain by a layer of alluvium with thickness increasing away from the
granitic intrusive. The measurements at these stations were corrected
for free surface effects using Gutenburg' s curves (12, p.
99).
The
resulting measurements were considered to be the confined displacement in the alluvium layer. The Zoepritz equations were used to
56
VELOCITY (KM /SEC)
24
LITNOLOGY
a,
4
âTUN*
PM
PIE NC
CAt2ON
SEDE
IOU N
MEMIE
MIDDLE
ME N 02 P
NO
01211
I
10020
MEMIEN
NOON
NIl N
2*1420
NLITE
-ASSUMED VELOCItY VS. DEPTH CUIVE
3
67
5
8
b.
Shot
1.0
2.2 km/sec
2.0 gm/cc
0.30
Vp
0.5
Limestone
-
p
8 Granite
v:5.0km/s.c, p22.7gm
CC
': 0.25
C.
w
0
U4
Alluvium
Shot
Vp2 2.2 km/sec
?
Granite
\
Vp: 5.0 km/sec
p : 2.7 gm/cc
': 0.30
'S
'S
: 025
d.
p:27gm/cc
0
Alluvium
Shot
0.5
v: 2.0 km/sec
2.0 gm/cc
g.: 0.30
p
1.0 -
Poleozoic
1.5
v: 5.0 km/sec1
p
Rock
2.7 gm/cc, 0= 0.25
Figure 17. Geological models of the close-in region of the following
explosions: a) Gnome (Weart (22, p. 982)), b) Hardhat,
c) Shoal northeastern quadrant, and d) Haymaker.
57
obtain the confined displacement in the half-space, (McCamey et al.
16, p. 963).
The resulting corrected ground displacement was con-
sidered to be of spherically diverging waves propagating elastically
from the source.
Shoal: The Shoal explosion was located in the Sand Springs.
Range, a mountain range in central Nevada. For details of the region see Nevada Bureau of Mines et al. (19, p. 1-127). Apparent
angles of incidence were measured using the peak amplitudes of the
first half-cycle of the motion on the vertical and radial displacement
meters. Because the peaks normally do not occur at the same time
on the two instruments angles of incidence are considered to be approximate only. It is felt that the calculations based upon these
measurements of apparent angle of incidence are accurate to within
10 percent.
Apparent angles of incidence were corrected to actual
angles of incidence (Bullen 8, p. 129). From travel time data and the
data on angles of incidence, it was assumed that the compressional
wave propagational velocity increased with depth in the granite re-
sulting in curvature of the ray paths.
The geological model for all of the recording stations in the
southeastern and southwestern quadrants was a half-space with cornpressional wave propagational velocity increasing with depth from
4. 5 km/sec at the surface to 5. 4 km/sec at shot depth. All except
the two most distant recording stations in the northeastern quadrant
were located on granite. Stations 19 and 21 were located on a very
thick layer of alluvium. Figure 17c shows the geological model as-
sumed for this northeastern quadrant. The exact shape of the contact
between the granite and alluvium is not known.
The corrections ap-
plied to the measurements at 19 and 21 are approximate.
Haymaker: Figure 17d shows the geological model assumed for
the Haymaker source area. The model was constructed on the basis
of travel time data and by the model given by Werth and Herbst (24,
p. 1467) for this area. The model consists of a layer of alluvium 1. 1
kilometers thick overlying an infinite half-space of higher velocity
material. If this model is correct, the first arrival at stations 1 and
2 will be the direct compressional wave and the first arrival at more
distant stations will be the 'head
wavet
arrival. The measurements
at stations 1 and 2 were corrected for free surface effects using the
curves given by Gutenburg (12, p. 99).
The measurements from the
remaining recording stations were corrected using the head wave
coefficient given by Zvolinskii (25, p. 6).