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AD-A181 198 STRAINS AND STRESSES NEAR EXPLOSIONS AND EARTHOUAKES 
(U) MOODHARD-CLVDE CONSULTANTS PASfii>ENA CA 

L J BURDICK ET AL. 15 OCT 8S HCCP-R-88-82 

UNCLASSIFIED AF0L-TR-87-8889 F19628-85-C-8836 F/Q 19/9 

1/2 ^ 

NL 



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1 





















































































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national BUREAU Of STANDARDS-1963-* 






























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BDC FILE COPY 


AD-A181 198 


AFGL-TR-87-0089 


Strains and Stresses Near Explosions and Earthquakes 


by L. J. Burdick and J. S. Barker 


Woodward-Clyde Consultants 
566 El Dorado Street 
Pasadena, CA 91101 


15 October 1986 


Scientific Report No. 3 


Approved for public release; distribution unlimited 


Air Force Geophysics Laboratory 
Air Force Systems Command 
United States Air Force 

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s te 
i cat 


ES F. LEWKOWICZ 
ntract Manager 




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Branch Chief 


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DONALD H. ECKHARDT 
Division Director 


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ii title lingua# Saf M ,if» ciaa«/waiion;St rai ns and Stresses 
Near Explosions and Earthquakes 


12 PERSONAL AUThORISI 

L. J. Burdick and J. S. 


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COBATI cooes 


GROUP ! SUB GR 


IB SUBJECT TERMS 'CoahMuf on ffiwnt if meetmmry tify Py Mor* NMmfevri 

strain, stress,explosive source, earthquake 
source, nonlinear material response 


^CT CoNdNM on 1 1 N«r#iMO NNd ft fy ly Morft 


Laboratory evi 
low confining 
manifested by 
field strain a 
phenomenon is 
frequency theo 
theory has bee 
body wave stra 
Large data bas 
modeling them 
pulses into es 
■ neon't i ca 1 ve 


dence indicates that when strains exceed 
pressure, certain nonlinear processes beg 
a reduction in apparent Q Since direct 
re rare, it has been difficult to evaluat 
significant near to realistic seismic sou 
ry for computing stresses and strains usi 
n developed It can be shown using this 
in pulses are closely related to near fie 
es of near field velocity records and cru 
are available Transfer functions for tr 
timated strain pulses can be computed bv 
rsions of the former from the latter In 


10 6 in media under 
in to occur Thev are 
measurements of near 
e whether or not this 
rces A high 
ng generalized rav 
theory that near field 
Id velocity pulses 
stal structures for 
ansforming velocity 
deconvo1ving 
most cases t hev 11 > 


20 OiStR'EuTion avAilaOil'T, o» abstract 

UNClASS'1 EO uNv MiTEO SAME AS AFT St OTlC USERS 


22a NAME 3F RESPONSIBLE 'NOiviOuAl 

James Lewkowicz 


00 FORM 1473. S3 APR t o. non of i 


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SlCuRiTt Ct A*S»F ICATION Of TM»* RAGE 


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_ Unclassified _ 

MCUft'TV CLASSIFICATION OF THIS FAOt 


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A 


•r ^delta-like functions. These transfer operators have been computed for a 
1 ‘ suite of velocity records from 5 Pahute Mesa Nuclear explosions ranging in 

yield from 155 to 1300 kt and for an Imperial Valley earthquake of Mg“.6*10 24 
dyne-cm. For the explosion data base the strains were as high as l£r 3 ; 3 
orders of magnitude higher than the level at which the laboratory data 
suggests that nonlinear effects become important. The earthquake data base 
indicated strains levels between 10' 8 and 10" s . Because of the pressure 
dependence of the nonlinear phenomenon, it is probably only important in a 
thin layer near the surface of the earth. 

/ -I -.V 


Accession for 

iris ciuai 
DT 1C TAB 
Ifciannounoed 
Justification- 


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Distribution/ 


Availability Codss 
Avail and/or 
Special 













The exact solution for the dynamic stress and strain waves generated by a 
point explosive source in a whole space is a simple linear combination of the 
reduced displacement potential, the displacement pulse and the velocity 
pulse. The first decays as R' 3 , the second as R~ 2 , and the third as R* 1 
(Haskell 1964). The far-field strain wave pulse can be generated from the 
velocity pulse by simply multiplying the latter by the slowness of the medium. 
This suggests that a similar close relationship between the dynamic strain and 
stress fields and the dynamic velocity field might exist in more general 
media. Large data bases of near-field velocity recordings have been collected 
and analyzed in the past whereas high frequency dynamic strain measurements 
have seldom if ever been made. The purpose of this study has been to attempt 
to use the data base of velocity records to infer the levels of dynamic strain 
and stress that typically occur near to explosions and earthquakes. 

The reason that near-field dynamic strains are of current interest is 
that a variety of laboratory studies have shown that some typical geological 
materials begin to behave in a nonlinear fashion at shear strain levels 
between 10 s and 10'* (Havko, 1979). This nonlinearity manifests itself as a 
lowering of effective Q. The phenomenon is frequency, amplitude and 
overburden pressure dependent. Day and Minster (1986) have discussed the 
potential significance of nonlinear behavior on interpretation of ground 
motion data from a series of small explosions in salt, but the events were so 
small that It Is not straightforward to relate their results to nuclear 
explosions or earthquakes. Also, the recording geometry of their experiment 
was so simple that they could use whole space wave propagation results. 

Near-field wave propagation is usually much more complex near to general 
seismic sources (Burdick et. al., 1986, Heaton and Helmberger, 1978) It is 
important to establish the levels of dynamic strain that occur for these more 
typical sources in media where wave propagation is more complex 



We present here the results of an Investigation of the relationship 
between the velocity and strain fields near to seismic sources in realistic 
crustal structures. First we develop the theory necessary for computing 
stresses and strains (rather than seismic motions) using the generalized ray 
methodology. Then we demonstrate that in a layered half space the far field 
strain wave is indeed very similar to the far field velocity wave. We develop 
a transfer operator which, when convolved with an observed velocity record, 
produces an estimate of a strain record. As noted above, in a whole space, 
this operator would be a delta function with the amplitude of the slowness of 
the medium. Ue show that in a layered half space it is a delta-like function 
with approximately the amplitude of the slowness at the receiver. (For some 
strain components, it is the amplitude of the vertical slowness and for others 
the horizontal slowness.) Next we apply these transfer functions to a suite 
of velocity records from nuclear explosions and from a small earthquake to 
establish the levels of dynamic stress and strain which they generated. The 
strain levels for the earthquake were found to be comparable to those for a 
modest nuclear explosion once the difference in source depths is accounted 
for. Presuming that the laboratory measurements of nonlinearity are relevant 
to the earth, the results of this study indicate that there is a thin region 
at the surface of the earth where effective Q can be expected to be very low. 

STRESSES &££ STRAINS Hi A WHOLE SPACE 

The strain tensor in a whole space for a point explosive source has only 
one nonzero, far field component in spherical coordinates. This, the radial 
component, is given by 

F dV „/ dR~ -2p/R 3 -2v'/aR* - p" /a 2 R (1) 

The radial stress is given by 

P - - lpp 3 {p/ R 3 - p-/aR 2 ] - pv / R O) 









• is the reduced displacement potential, a, 0 and p are the compressional 
velocity, shear velocity and density of the medium and the primes denote 
differentiation. The last term on the right in Equation 1 is just the far 
field velocity pulse divided by the compressional velocity. Thus, the strain 
and stress fields are given exactly in terms of linear combinations of the RDP 
and its derivatives. Seismic motion parameters generally have a near-field 
term which decays as R' 2 and a far-field term decaying as R* 1 - Strains and 
stresses have additional near field terms that decay as R" 3 . 

Of course, these expressions become much more complicated for a general 
point source in a layered half space where, among other complications, 
cylindrical coordinates must be used. However, these half space expressions 
become much more tractable if near-field terms can be neglected. The simple 
whole space expressions can be used to estimate over what ranges the 
near-field terms are significant. Figure 1 shows the radial strains for two 
point explosions with yields of 100 and 1000 kt. The RDP’s were computed 
using the formalism of Helmberger and Hadley (1981) with the yield scaling 
relations published by Burger et al. (1987). The medium parameters are given 
in Table 1. The far-field term is shown in the top row, the near-field terms 
in the second row and the sum at the bottom. At a range of 1 km, the 
near-field terms are important. By 3 km however, they have become relatively 
insignificant. This result appears to have little dependence on yield. In 
the next section, we will present a theory for computing body wave stresses 
and strains using only the far-field terms. Based on this calculation, it 
should be valid for ranges larger than 3 km. 

The amplitudes of the strain pulses shown in Figure 1 should give a 
preliminary indication of how significant the nonlinear material behavior 
observed by Mavko (1979) is likely to be. Figure 2 has been redrafted from 
his paper and illustrates his basic result. The value of Q is observed to 


3 







Figure Lj. The analytic solution for the radial strain generated by a point 
explosion In a whole space. The left column Is for a range of 1 km. and the 
right for a range of 3 km. An RDP for a 100 kt. explosion is shown at the top 
and for a 1000 kt. shot at the bottom. In each Instance the near field terms 
are shown first by themselves, then the far field term and then the sum or 
complete solution. The near field terms become insignificant by 3 km. 












Iflkl£ ll CRUSTAL MODELS 


Whole Space and Half Space Calculations 


P-Velocity 

S-Velocity 

Density 

Thickness 

(km./sec.) 

(km./sec.) 

(gm./cc.) 

(km. ) 

5.00 

3.00 

2.00 



2.30 

Petwte Hesa Calculations 

1.35 1.90 

0.360 

2.80 

1.50 

2.00 

0.800 

3.30 

1.52 

2.25 

0.300 

4.00 

1.90 

2.30 

0.700 

4.60 

2.00 

2.40 

0.750 

5.30 

2.50 

2.50 

0.800 

5.50 

2.95 

2.70 

2.250 

6.10 

3.50 

3.00 

10.00 

7.00 

4.00 

3.01 

10.00 


1.69 

Imperial yalley Calculations 
0.35 1.52 

0.210 

1.72 

0.50 

1.56 

0.210 

1.93 

0.70 

1.74 

0.210 

2.10 

0.90 

1.89 

0.210 

2.25 

1.15 

2.03 

0.339 

2.50 

1.50 

2.26 

0.480 

2.67 

1.64 

2.36 

0.320 

2.85 

1.74 

2.39 

0.320 

3.45 

2.08 

2.48 

0.800 

3.69 

2.21 

2.51 

0.160 

4.20 

2.50 

2.60 

0.160 

4.55 

2.71 

2.63 

0.395 

4.75 

2.75 

2.65 

0.395 

4.92 

2.84 

2.65 

0.501 

5.09 

2.94 

2.65 

0.501 

5.37 

3.10 

2.65 

1.130 

5.65 

3.26 

2.65 

1.137 

5.68 

3.28 

2.66 

1.144 

5.72 

3.30 

2.68 

0.588 

5.75 

3.32 

2.70 

0.563 

5.79 

3.34 

2.72 

1.158 

5.83 

3.36 

2.74 

0.750 

5.85 

3.38 

2.76 

0.970 

7.20 

4.17 

3.07 

1.440 

7.27 

4.20 

3.10 

1.454 

7.34 

4.24 

3.12 

1.469 

7.42 

4.28 

3.14 

0.746 


5 







0.018 r- sandstone 


0.016 


anorthosite 


0.014 


I 0.012 


0.010 


ATTENUATION 

VS 

STRAIN 


pyroxenite 


x 

0.008 -j 
0.006 - 


0.004 


0.002 


_x—x—*" 


granite 


quartzite 


limestone 


0 10 20 30 40 50 60 70 80 

Microstrain 


different dr^MckJ 1 (redL^^Jo^MaJkras^U r< * in an P litude for six 


♦A'VS.':*. 












begin to increase at about 10* 6 strain. By 10* 5 strain the effect is very 
significant in most cases. The magnitude of the effect appears to also depend 
strongly on the geologic material involved. It is generally believed that the 
decrease in Q is caused by frictional sliding on cracks (Stewart et al., 

1983). The observed effect should therefore also depend on the density of 
cracks in the material. As overburden pressure closes these cracks, it 
becomes increasingly difficult for sliding to occur. Thus the nonlinear zone 
probably does not extend to any great depth in the earth. Extending the 1 km 
result in Figure 1 out in range by dividing by R, we find that for a 1000 kt 
explosion, far-field strain drops to 10' 5 at about 60 km and does not fall to 
10' 6 until almost 600 km The nonlinear zone would appear to occur over a very 
significant region. 

STRESSES AND STRAINS IN £ LAYERED HALF SPACE 

Once a far-field approximation has been made in generalized ray theory, 
the differences in the expressions for seismic motions and seismic strains are 
actually quite small. Stress tensors can be generated from strain tensors 
through the usual definitions. The necessary modifications can be most easily 
demonstrated by beginning with the expressions presented by Langston and 
Helmberger (1975). Figure 3 shows the coordinate system in which their 
formalism is based. The small rectangle at the origin represents a fault with 
given dip (6) and rake (A). Here we will consider the possibility of explosive 
sources as well. The vertical, radial and tangential motions are given by W, 

Q and V respectively. The displacements are given in terms of the Laplace 
transformed seismic potentials n and X by the Langston and Helmberger 
(1975) equation 5 
























where the near-field terms they give have been dropped. The Laplace 
transformed potentials for a generalized ray are given in their equation 6 by 




(4) 


A / 0 

4/rp 


M 0 is the seismic moment, p is the density at the source and p and r) are the 
horizontal and vertical slownesses respectively. The phase of the ray, P, is 


P 



pr 


X th, 


n, 


(5) 


where the thj's are the thicknesses of the layers encountered by a given ray. 
The AVs are horizontal radiation pattern terms and the Cj's, SVj's and SHj's 
are vertical radiation pattern terms. The J indices, 0 through 3, denote an 
explosion, a vertical strike slip, a vertical dip-slip and a 45 ° dipping 
normal fault viewed at an azimuth of 45* respectively. Any other point source 
can be built from these fundamental sources through linear combination. These 
radiation terms are not of importance to this discussion, so they will not be 
explicitly written out here. They are given in Langston and Helmberger 
(1975), though we have added the index 0 for an explosion source which they 
did not. For an explosion, A 0 is 1 and C 0 is 1/a 2 . The factor FI represents 










the product of transmission and reflection coefficients along the raypath. 

The inverse transform is evaluated using the usual Cagniard de-Hoop method 
(Wiggins and Helmberger, 1974, Helmberger, 1974). It is important to follow 
in some detail how the displacements in Equation 3 are related to the 
potentials given in Equation 4. The spatial derivatives in Equation 3 can be 
evaluated prior to the inverse transforms. If near field terms are neglected, 
they simply produce some additional multiplicative factors in Equation 4. 
Helmberger (1974) discussed these factors in some detail, and we shall follow 
his notation and utilize many of his results here. We need to derive these 
factors for both the case in which the receiver is embedded in the half space 
and when it is on the free surface. We shall show that the only difference 
between seismic motion generalized rays and strain generalized rays is that 
they have slightly different multiplicative factors, hereafter called receiver 
functions. 

To illustrate how these receiver functions are derived, let us consider 
the case shown in Figure 4. We have an incident P generalized ray and 
receiver points buried at depth h in the top layer of the stratified half 
space. The arriving P ray carries with it a 4> potential with initial 
amplitude A 0 If we wish to compute the vertical component of motion, we 
substitute the expression for the ^ from Equation 4 into the expressio: for W 
In Equation 3. For a single ray In the ray sum, the result is of the foi 

«• 

W-j sR„A 0 dp (6) 

o 

A' BZ m ~€' rj a 

The factor of s generates a time deriv. ’-.ive, and R pz is the receiver function. 
The first of the subscripts indicates tha the initial potential was for a P 
wave. The second indicates that the vertical component of motion was 
computed. The converted wave shown at the top c Figure 4 would have produced 
a similar result except that the receiver function -ould be R^. Also, the 

10 





sew? 













For the 



product n would include the free surface conversion coefficient R n 
reflected P, the receiver function would again be R pt but the value of the 
function would change sign due to the factor t' . It is defined to be -1 if 
the last leg of the ray is upgoing (Incident P) and +1 if the last leg of the 
ray is downgoing (reflected P). It arises because the phase of the ray is 
increasing with z in one case and decreasing in the other. It is prised to 
distinguish it froa the siailar tens, « defined by Langston and Helaberger 
(1975) which has siailar properties depending on whether or not the ray is up 
or downgoing at the source rather than the receiver. As indicated at the top 
of Figure 4, the free surface reflection coefficient, would again be 
included. The coaplete set of receiver functions for receivers buried in a 
layer are given at the top left of Table 2. It shows that converting 
potentials to dlsplaceaents involves no aore than aultiplylng by plus or minus 
the vertical or horizontal slowness of e ray 

Ue next consider the coaputatlon of strains within the aediun using 
generalized ray theory To transfora the three coaponent displaceaent, D, 
into a strain we need to take spatial derivatives according to the fora 

£„ - ^dD,/dx t * dD,/dx t ' ( / ) 

Ue can again take these derivatives of Equation 3 prior to the inverse Laplace 
transfora Again, they will result in additional aultiplylng factors of sp 
or -s«n Just as in the whole space case, transforaing from seismic motion 
to strain requires only aultiplication by slowness The additional facte: ct 
s causes a time derivative which transforms the displacement components to 
velocity The strain and velocity tiae histories appear to be closely related 
just as in the whole space case The additional slowness aultipliers will 
cause phase shifts in the Inverse Laplace transforas so the pulses are no 

longer exactly proportional Ue shall show, however, that in most cases the 
effect of the phase shifting is not large The strain 


12 




vly-V. 












TABLE 2 


Receiver Functions 


Stifle Motions 


In ths Him 

R>z - -c n. 

-p 

Rsz - P 

Rs „--f n, 
R s » m P 


At ths Frss Surface 
*,2-2r7.(r?J-p 2 )/0 2 /?(p) 
with Klp)« p 2 )’* 4 p , 9 .r?, 

*>•»- -*n a n</p 2 R(p) 

R sz - 4 pr/ a f 7 ,/ 0 2 fl(p) 

R s*“ p 2 )//? 2 P(p) 


--* n.R'z 


- - pR, 


-f'n.R, 


- -f 


- -f 5 * 

m - pR s * 

* - f 'J#*** 


Strains 


" c pR sz 

with c - (a 2 - 2/? 2 /a 2 

R >z* m - pRrz 
R>*z m pRfz 
R m* " ~ P R n 

R szz ~cpRs* 

R szn m ~P R sz 
R s *z “ P R sz 

Rs*K m -pRs* 


R st: “ 0 
























receiver functions for receiver points within the aediun ere given at the 
bottoa left of Table 2. A natural extension of the notation of Helmberger 
(1974) has been used. The contribution to the zz component of the strain 
tensor due to an incident P wave is computed using the coefficient R pzz For 
an incident S wave, it would be Rg U and so on. There are 10 strain receiver 
coefficients and only 5 motion coefficients, but as shown in Table 2 they are 
very closely related and they appear in Equation 6 in an identical fashion 

Most velocity records froa explosions and earthquakes come from 
instruments located on the surface of the earth. It would thus be best if we 
could establish something about the levels of stress and strain in the 
near-field utilizing this information. Furthermore, if we can develop models 
that successfuly predict levels of strain and strain decay rates at the 
surface of the earth, we can then use these models with some confidence to 
predict strain levels and decay rates within the earth. To derive the seismic 
motion receiver functions, we determine the composite response of the three 
phases illustrated at the top of Figure 4 in the limit that h becomes small 
compared to the shortest wavelength of interest. These are essentially factors 
which are the sums of the amplitudes of the direct and reflected waves near 
the free surface The geometry for the incident P wave case is illustrated in 
Figure 4 When the P, pP and pS arrive coincident in time the composite 
amplitude of the response is just A 0 (R PZ +R pp R pz +R ps R sz ) The reflected waves for 
incident SV would be SS+SP and for SH Just SS. This means there is some finite 
depth under a surface velocity receiver (defined by the shortest wavelength oi 
interest criterion) where the strains estimated from that receiver can be 
thought of as existing The highest frequency of interest here is about hr 
and the slowest wave speed about 1 km/sec Thus, the strains that we estimate 
probably exist in the earth down to depths of 200 m or more 

The final step needed is to derive the receiver coefficients for strain 
at the free surface It may appear that a reasonable wav to accomplish this 


U 









would be to differentlace Equation 6 while inserting the spproprlete 
displacement receiver coefficient end to make the usual far field 
approximation. However, this approach leads to nonzero vertical stresses on 
the free surface. To obtain the correct result, it is important to first take 
the required spatial derivatives of the displacements generated by the three 
phases shown at the bottom of Figure 4 and then to take the limit as h becomes 
small. The changes in sign caused by the factor c' and the factors of t) e 
generated by vertical derivatives of the S wave potential instead of q a 
generated by the P wave potential cause a very significant difference. The 
correct receiver functions for computation of free surface strains are shown 
at the bottom right of Table 2. They are factors of • slowness and • a 
dimensionless constant times different seismic motion receiver coefficients. 
Note, however, that for motions in the medium R rzz is generated from R pz 
whereas at the free surface it is generated from R^ Several other similar 
changes exist. The cancellation of the terms R rzx and R raz along with Rj^ and 
Rsr Z guarantees that E a will be zero. The OU/30) has no far field 
contribution, and ^ is identically zero, so E u will be zero. The diagonal 
term E zz is a linear combination of the terms R m , R m , R^ and R^ which 
always remains zero though the algebraic details are somewhat more 
complicated. The free surface condition is satisfied by the strain receiver 
coefficients at the bottom right of Table 2. 

The preceding has shown that the relationship between velocity and strain 
in a half space is very similar to their relationship in a whole space. 

Instead of multiplying velocity by the composite slowness of the medium to 
obtain strain, however.it is necessary to multiply by either the vertical or 
horizontal slowness. Figure 5 illustrates the degree to which this is true 
for a homogeneous half space. The source is the same 1000 kt explosion used 
in Figure 1, and tne medium parameters are again given in Table 1 On the 
left are the velocity traces Each generalized ray in the sum has been 
multiplied by a constant value of slowness equal to the value of p or »? at 










lAtOLt A coapari son of velocity trace* multiplied bv constant values of 
slowness (left) with actual strain traces (right) The traces compare well 
when the receiver is buried Differences occur when the receiver is on the 
free surface due to the free surface condition 


16 




V. /. •• V. / /. 




i J 


t r i. 


) r i 










which the Cagniard contour for that ray leaves the real axis. On the right 
are the exact strains. The case of a surface receiver is shown on the top and 
of a receiver buried at 15 km on the bottom. In each case, the range is 15 
km. At the surface, the shape of the velocity times slowness pulse shape is 
virtually the same as the E zz shape. The difference in amplitude is due to 
the fact that R pzz is not just fj a R pz but the more complicated form given in 
Table 2. If the velocity pulse is multiplied by the correct factor, again 
evaluated at the constant value of p, then the amplitudes of the pulses agree. 
The pulses agree in shape and amplitude. The true Ej^ strain is 
identically zero which is not predicted by the approximation. Within the 
medium, the approximation works very well. The reason it does not work 
exactly is because of the phase shifting that occurs as p evolves along the 
complex Cagniard contour. 

Though the effect of the phase shifting in Figure 5 is small, a 
homogeneous half space is a very simplified medium. In more realistic crustal 
structures where unusual raypaths may be important, the phase shifts can have 
a large effect. It is necessary to find a way to account for this phase 
shifting no matter whether it is strong or weak. The most straightforward 
approach to devising such a velocity to strain transfer method is to utilize 
theoretical frequency dependent transfer operators. These operators are 
generated by computing a theoretical velocity and a theoretical strain 
response for a site and deconvolving the former from the latter. Estimates of 
strain records are generated from velocity records by convolving the velocity 
records with the transfer operators. We shall illustrate in the following 
that in most cases these transfer operators are very delta-like functions with 
amplitudes controlled by the velocity at the receiver site. The latter is a 
relatively well known quantity and we believe that as long as the frequency 
shift between the velocity and the strain records is small the transformed 
records should be good estimates of actual strain time histories 









STRESSES AND STRAINS NEAR IQ NUCLEAR EXPLOSIONS 


The first data base to be processed using the transfer operators is a 
suite of near field velocity recordings from five NTS nuclear explosions. The 
events, which were detonated at Pahute Mesa, are SCOTCH (155 kt), INLET (324 
kt), MAST (406 kt), ALMENDRO (670 kt) and BOXCAR (1300 kt). (The yields are 
taken from Burger et. al. (1987).) The recording sites were at horizontal 
ranges between 3.3 and 22.5 km. The recording instruments were L7 velocity 
meters which have a response flat to velocity throughout the seismic band, so 
the signals recorded on them are essentially velocity versus time. The event 
locations, recording lines and receiver locations are shown on a map of Pahute 
Mesa in Figure 6. Not all of the available records were suitable for use here 
since some were too close and since some recording channels failed. 

Each recording site used needed to have produced a three component data 
set. In order to compute the transfer functions, it is also necessary to have 
theoretical estimates of the velocity and strain pulses for each 
source-station pair. The methodology for computing such synthetics is 
discussed in Helmberger and Hadley (1981) and in Burdick et al. (1984). 
Computation of body waves which are the phases of interest here is 
accomplished through summation of generalized rays. Several possible plane 
layered models for the crustal structure at Pahute Mesa are available in the 
literature, but not all of them produce synthetic near field seismograms which 
closely match the observations. The one used in this study was provided by S. 
H. Hartzell (personal communication) and was specifically developed to produce 
accurate near field synthetics. It is shown in Figure 7 along with the 
alternate models of Helmberger and Hadley (1981), Hamilton and Healy (1969) 
and Carroll (1966). The three models are in basic agreement, differing only 
in the fine detail of the gradients. The parameters of the model are given in 
Table 1. 

i 

I 







ftSuoJb. A “ P ° f the NTS * VentS 8tudied - lon 6 with the station line 


s and 



















^mis STUDY 

I 

i HAMILTON & 

I LEALYQ969) 


/ l .r 

I t£LTCERG0U! 

I HADLEY (1981J 


| CARR0LLL19G6) 

rf-i/ • 


Figure 7. p and S-wave velocity structure for Pahute Mesa obtained in this study (solid 
curve) compared with two other proposed structures for the area (dashed and dotted curves) 
















An example of the computation of a transfer function for the Pahute Mesa 
crustal structure is given in Figure 8. The calculation is for the same 
theoretical 1000 kt event considered in Figure 1 and Figure 5. It was placed 
at a depth of 1 km in the crust. The synthetic vertical and radial veloc ity 
pulses are shown on the left, the four nonzero partial derivatives of velocity 
with respect to spatial coordinates in the center and the transfer functions 
are on the right. The generalized ray sum used in computing the medium 

response contained the primary rays of the P and pP type and near receiver 

conversions of the PS type. The amplitude of the P wave velocity pulse is 

about 10 cm/s, the strain amplitudes are a few tens of ^strain and the 

transfer functions a few hundreds of pstrain/cm. The top strain is E zz and 
the bottom is The center two must be summed to form Note that they 

sum exactly to zero which guarantees the conservation of the free surface 
condition. The transfer functions are computed by transforming the velocity 
pulse and corresponding partial derivative pulse into the frequency domain 
using a fast fourier transform algorithm. The latter is divided by the former 
and the inverse transform taken. The resulting transfer operator strongly 
resembles a delta function with a signal to noise ratio of better than 5 to 1. 
To suppress the noise further a gaussian filter with a cutoff of 5 hz is 
applied before convolving the transfer function with actual data. 

A typical example of what happens when the transfer operators are applied 
to observations is shown in Figure 9. The records are from the BOXCAR event 
at a range of 7.3 km. The vertical and radial velocity traces are shown on 
the left. They display a relatively impulsive and simple P wave arrival. The 
amplitude of the first peak is about 30 cm./sec. on either component. 

Transfer operators like those shown in Figure 8 were computed and convolved 
through to produce the four derivative traces on the right. In this example 
partial derivatives of the vertical velocity trace are generated from the 
vertical trace and derivatives of the radial from the radial. In principle, 
this need not be the case as we discuss in the following. The first peak of 




VELOCITY TO STRAIN TRANSFER 



E-iguffi fij. An example of the computation of the velocity to 
strain transfer functions for the Pahute Mesa structure. The 
velocity traces on the left are deconvolved from the strain 
traces in the center to produce the transfer operators on the 
right. 


22 














LL&U£e 2.1. An example of the velocity to strain transfer for one of the 
stations from the event BOXCAR. The velocity pulses are shown on the lv^t and 
the estimated strain pulses on the right. The amplitude values refer to the 
first positive peak. 

















dV/dz is strongly reduced with respect to the later peaks. This is the 
component in which the phase shifting by the strain receiver function is 
generally the strongest. Its amplitude is also usually the lowest as it is in 
this example. The top trace is E zz the center two are combined to produce E ZR 
and the bottom is Err If the free surface condition is to be satisfied 
exactly, the center two traces should cancel. This clearly will not occur in 
the example shown. In order for this delicate cancellation to take place, the 
vertical and radial traces both need to be transfered into time series which 
are exactly proportional. The synthetics are never really exact, and 
generally the vertical component of motion is predicted better than the 
radial. The radial is presumably much more sensitive to lateral velocity 
variations directly under the instrument. In the following, we will force the 
free surface condition to be satisfied by using only the more reliable 
vertical records. In order for the stress P„ to remain zero 

E„--[l-2fi 2 /a 2 )E„ ( 8 ) 

Thus, we can generate one nonzero strain from the other in such a way that the 
free surface condition is satisfied. 

Figure 10 shows the strains along with the trace of the strain tensor 
next to the bottom and the maximum shear strain as a function of time at the 
bottom. The maximum shear strain is defined as the absolute value of the 
difference between the largest and smallest diagonal elements in the 
diagonalized strain tensor. The event BOXCAR appears to have generated a peak 
shear of 74 /istrain at 7.3 km and presumably higher at closer ranges. The 
laboratory data in Figure 2 extends up to only 70 ^strain. This figure shows 
that if the waves from BOXCAR propagated through a material like sandstone, 
they would be strongly attenuated indeed. Figure 11 shows the corresponding 
stresses. The pressure in the next to bottom row is the negative of 1/3 the 







trace of the stress tensor and the bottoa trace is .he maximum shear stress 
The sixteen processed records are presented in Appendix 1 in the saae format 
as Figures 10 and 11. 

The decay rate of the peak shear strain with range is shown in Figure 12. 
Theoretical curves are shown for event BOXCAR which is the largest in the data 
set and for SCOTCH which is the smallest. The curves are computed assuming 
elastic theory is appropriate and using the same velocity structure as in the 
calculation of transfer functions. Note in Figure 7 that this structure is 
consistant with models derived using a variety of different approaches. The 
observed values from the processed records are shown as data points. The 70 
pstrain level is only half way up the vertical scale. The theoretical curve 
for the smallest event does not drop below 1 ^strain by 25 km. Thus the 
entire data set is within the strain regime in which the nonlinear process 
observed in the laboratory is believed to be significant. It is interesting 
that the observations show the same rate of decay as the theoretical curve. 

The curve was computed using a theory which assumes linear elasticity holds. 
The nonlinear effects, if they are indeed significant, should have dropped the 
observed values below the elastic curves with range. However, it is important 
to remember that the nonlinearity associated with sliding on cracks (see 
Figure 2) probably only occurs very near to the surface. All of the 
generalized rays important to the P pulse dive downward into the crust and 
only enter the region where they might be attenuated as they emerge under the 
receiver. In other words, all of the signals in the data from a given event 
might be attenuated by more or less the same amount. The reduction in 
amplitude by the nonlinearity would then be reflected in an underestimate of 
the absolute size of the event. 









BOXCAR 7.3 KM. 



2 ^ 3 ! 00 


—1---—» 

4.00 S.00 S. 00 

TIME (SEC) 


7.00 


•. 00 


Figure 10, Strains from a typical BOXCAR station. The top two 
traces are the nonzero strains in a cylindrical coordinate system 
assuming that the free surface condition holds. The third trace 
is the trace of the strain tensor, and the bottom trace is the 
peak shear strain. 












4.553xl0- 1 MPa 


TIME (SEC) 


F iqrura 11 . Strassaa froa a typical BOXCAR station. The top two 
tracts art tha nonzero stresses in a cylindrical coordinate 
systea. Tha third trace is pressure and the fourth is peak shear 
stress. 









r 

» 

i 



1l gure 12 The decay of peak shear strain near to nuclear explosions The 
largest observed value of shear strain is 10 5 Theoretical curves are showi 
for the largest and smallest events studied The observations appeal to 
follow the theoretical predictions 


.AAA’s' - . 







STRAINS m STRESSES U£AE Ifl EARTHQUAKES 


The next records to which w« will apply our velocity to strein 
trensformetion procedure are froe a small aftershock of the IS October 1979 
Imperial Valley earthquake The aftershock was studied in some detail by Liu 
and Helmberger (1985) who providad a mechanism, moment and time function for 
it They reported the event depth as 9 5 km Figure 13 shows the strong 
motion recordings from it A map of the stations, the aftershock location and 
the mainshock location Is shown In an Inset The strong, clear pulse is the 
direct S wave The P wave was only recorded In its entirety at a few stations 
and was too complex to model Several polarity changes are apparent in the 
data Liu and Helmberger (1985) used this information to infer that the even: 
had a vertical strike slip mechanism They reported a moment of 1 0 x 10 a * 
dyne cm and a triangular time function with a rise of 0 1 sec and a fall of 
0 1 sec From our modeling studies, however, we conclude that a moment value 
of 0 6 x 10 J * dyne cm and a source with a rise of 0 3 sec and a fall of 0 1 
sec is more accurate 

Certain unusual characteristics of the strong motion records will guide 
how we will proceed to estimate strain from velocity in this Instance Figure 
14 shows the three components of motion observed at four of the stations at a 
representative set of ranges HOLT is the closest station and RRAV the 
farthest HOLT. ELCE and BNCR were three of the six stations that recorded 
the complete P as well as the S waves Note in these records that the P wave 
is smaller and much less coherent than the S wave The peak strains are 
carried by the S wave pulse, so we will transform the S waves alone and not 
attempt to process the P waves Also note that there is no clear SV arrival 
on the vertical records In some cases there is a burst of incoherent energy 
but there is no clear long period pulse as on the radial component The fact 
that the SV pulse is so small on the vertical component can be explained bv 
the fact that the shear velocity near the surface in Imperial valley is verv 


?9 









AR6 » 23.59 















tis u is. The redial ground velocities from the 23:19, 15 October 1979 

Imperial Valley aftershock 










E l fe VIS Four typical three component record sets from the Imperial Valley 

aftershock. The P wave Is more complex and much higher frequency than the S 
wave. The vertical S wave component is small. 










low. Thus the SV ray emerges almost vertically and the wave produces little 
vertical motion. We wish to avoid using the noisy vertical signals in our 
processing since they will probably only degrade the accuracy of our strain 
estimate. 

The nonzero strains generated by an incident SV wave are E lz E rr and E rr 
As before, we could use the vertical velocity record to generate the first of 
these and the radial to generate the other two. Instead, we again will use 
relation 8 to generate the information we need regarding E It from E rr and do 
it in such a way that the free surface condition is automatically satisfied. 

In essence, we generate an estimate of the vertical signal from the radial 
signal instead of using the noisy vertical channel itself. One other point 
worth noting about Figure 14 is the clear shift in frequency content between P 
and S waves. Liu and Helmberger (1985) attribute this shift to a low 
effective shear Q in the Imperial Valley. The value they used for shear Q in 
the top layer of their crustal model was only 6.2. This results in a 
relatively distance independent t* of .132 sec. In the calculations shown in 
the following, we use this value along with the crustal model they presented 
(see Table 1). A value for shear Q as low as 6.2 is surely atypical and could 
easily be interpreted as an indication that nonlinear processes like those 
suggested by the laboratory data shown in Figure 2 might be taking place. 

An example of the velocity to strain transfer operators for the 
earthquake case is given in Figure 15. As in Figure 8, the relevant 
theoretical velocity traces are shown on the left, the spatial derivatives of 
them in the center and the transfer operators on the right. In this instance, 
the velocity traces are Q (radial) and V (tangential). The transfer operators 
are shown with the gaussian filter (cutoff 5 hz) convolved through. Of the 
four partial derivatives shown, only two are actually used in the calculations 
that follow. The top one would be used to generate E ri but the other term in 
would always cancel it to satisfy the free surface condition. The third 


33 











VELOCITY TO STRAIN TRANSFER 

Imperial Valley Aftershock, Range = 10 km 



Fl yure 15. An example of the computation of the velocity to strain transfer 
functions for the Imperial Valley structure. The velocity traces on the left 
are deconvolved from the strain traces in the center to produce the transfer 
operators on the right. 











transfer function is always zero because the corresponding receiver 
coefficient is zero in Table 2. The second and fourth transfer functions 
generate nonzero strain components E rr and E rt . The range for the calculations 
shown in Figure 15 is 10 km just as in Figure 8. The strains for the 
earthquake are slightly larger than for the megaton explosion. This is not 
true at all ranges because, as we shall show in the following, the earthquake 
strains decay at a much slower rate. Also, because different components of 
the strain tensor are nonzero, the peak shear strains are somewhat larger in 
the explosion case. The transfer operators for the earthquake source are 
generally simpler than for the explosion case meaning that we are probably 
obtaining a more reliable estimate of dynamic strain for the earthquake. 

Figure 16 shows the transfer of the HOLT velocity record into strain. 

The strain traces on the right are not strongly altered from the velocity 
traces on the left. The changes in polarity that do or do not occur are just 
as predicted in Table 2. The smoothing out of the detail is primarily caused 
by the gaussian filter used in the deconvolution. The two nonzero strains are 
shown at the top of Figure 17 along with the trace of the strain tensor and 
the maximum shear. It is of interest to compare the peak strains for the HOLT 
record to those of the SCOTCH record from 6.1 km. The peak shear for SCOTCH 
is about twice as large and the peak compressive strain about three times as 
large. It is important to note, however, that the SCOTCH source is actually 
much closer to the station than the earthquake source. The depth of the 
earthquake is 9.5 km while that of SCOTCH is 0.97 km. A theoretical 
calculation of the strain for an earthquake source at the same depth and range 
as the SCOTCH record predicts that the strains from the earthquake would be 
slightly higher. Figure 18 shows the stresses associated with the HOLT 
strains. Stresses and strains from all 16 stations are given in Appendix 2. 
Figure 19 shows the decay of peak shear strain with range. The observations 
are shown as data points and the theoretical prediction of the model as a 
smooth curve. The theoretical curve was computed for the particular 








IMPERIAL VALLEY AFTERSHOCK 

Range = 7.5 km 

Velocity Strain 



.349 fi strain q 

6.79 cm /sec TT 



Fi&Vtg lsu An example of the velocity to strain transfer for station HOLT 
from the Imperial Valley aftershock. The velocity pulses are shown on the 
left and the estimated strain pulses on the right. 











VALLEY 10/15/79 23:19 


1.123*10“® 



1.699*10“® 



1.123*10“® 



3.404x10“® 


7.33 8.33 9.33 

TIME (SEC) 


10.33 11.33 


Uure LL. Si 
he top two ti 
he third tra< 
eak shear st 


station HOLT from the Imperial valley aftershock. 

; nonzero strains in a cylindrical coordinate system 
ice of the strain tensor. The bottom trace is the 


37 























strain 



Figure 19. The decay of peak shear strain near to the Imperial Valley 
aftershock. 


•50 














azimuth of 45' Here the SH and SV waves are equal amplitude and the peak 
shear strain is relatively high The data come from a variety of azimuths 


which is why many of the data points fall under the curve Also, the sout^e 
model of Liu and Helmberger (1985) fails to correctly predict the ratio o{ s. 
to SH. The SH data alone suggest a moment of 42 x 10 2 ‘ dyne cm and the S'. 

.73 x 10 2 * dyne-cm. The SH wave apparently has a more important effect in 
determining the peak shear strain in many cases The peak shear for the 
earthquake at the surface of the earth is lower than for the explosions but 
decays much less rapidly with range This is because of the vertical 
radiation pattern of the source and because the earthquake source is deeper 
The strains generated by the earthquake are large enough so that the nonlinear 
effects illustrated in Figure 2 are potentially significant 

DISCUSSION 

The bulk of all seismic observations have been very successfuly explained 
using linear elastic theory. It seems doubtful that nonlinear processes could 
be of great importance without having been noted previously On the other 
hand, the science is still evolving and new types of data are being studied 
Very high frequencies (5 to 20 hz) are being studied for potential use in 
discrimination between earthquakes and explosions. A thin, shallow layer with 
nonlinear response might have an effect on the generation of such energy but 
would be of no significance to 1 hz or lower frequency energy If the 
nonlinear zone has different characteristics for explosions and earthquakes, 
it might alter how regional phases are initiated in the two cases Such a 
layer would obviously also be important to the generation of free surface 
phases such as pP. At low frequency such phases would appear as elastic 
reflections, whereas at very high frequency they would appear to be strongly 
attenuated. Some observations of nuclear explosions suggest that this is the 







case Another piece of evidence that toae nonlinear losses are occurring is 
the strong motion data of Liu and Helaberger (1985) which does suggest that 
effective Q in the near field of che Imperial Valley earthquake was very low 


It is Important to note that even if the nonlinear process indicated by 
the laboratory data does occur in the earth and is significant, it is not 
clear exactly how it would manifest itself At one level of approximation 
effective Q could be considered to be a function of time with a value dictated 
by the strain wave field It is difficult to imagine exactly what effect this 
would have Stewart et al (1983) have suggested a model for how the 
nonlinearity would depend on the density of cracks in the medium and the 
overburden pressure presuming that it is indeed related to frictional sliding 
on cracks They proposed that 


Q-P*''/kkE ( 9 ) 

where P is the overburden pressure, k is a constant function of the 
material's elastic parameters, X is the crack density and E is the strain 
amplitude Day and Minster (1986) suggest an equivalent linear method for 
solving wave propagation problems in materials behaving in a weakly nonlinear 
fashion, but their method does not adapt easily to realistic media. Much 
additional progress will be needed before the role played by high strain 
nonlinearity in seismic wave propagation is understood. 

CONCLUSIONS 

The close relationship between velocity and strain wave pulses in a whole 
space appears to be maintained for the most part in a layered half space. The 
large data bases of near field velocity records which have been collected over 
the years can thus be transformed into a data base of near field dynamic 
stress and strain records. Near field strains for a large explosion appear to 
be as high as 10‘ 3 at the surface of the earth. Those near to a small 







tit] 


so that they «ay induce a nonlinear 





Burdick, L. J., T Wallace and T. Lay, Modeling the near field and teleseismic 
observations from the Amchltka test site, J. Ceophys Res., 89, 

4373-4388, 1984 

Burger, R. W , T. Lay, and L. J. Burdick, Average Q and yield estimates from 
the Pahute Mesa test site, Bull. Seism Soc. Am., (in press), 1987. 

Day, S M and J. B Minster, Decay of wave fields near to an explosive source 
due to high strain nonlinear attenuation, J. Ceophys Res , 91, 

2113-2122, 1986 

Carroll, R. D., Preliminary interpretation of geophysical logs, UE20F, Pahute 
Mesa, Nevada Test Site, technical letter: special studies -1 - 37, 
supplement 1, U. S Ceol Survey Open File Report, 1966. 

Haskell, N. A., Analytic approximation for the elastic radiation from a 

contained underground explosion, J. Ceophys. Res., 7, 2583-2587, 1967. 

Hamilton, R. M. and J. H Healy, Aftershocks of the BENHAM nuclear explosion, 
Bull. Seism. Soc. Am.. 59, 2271-2281, 1969. 

Heaton, T. H. and D. V. Helmberger, Predictability of strong ground motion in 
the Imperial Valley: modeling the M4.9, November 4, 19/6 Brawley 
Earthquake, Bull. Seism. Soc. Am., 68, 31-48, 1978. 

Helmberger, D. V., Generalized ray theory for shear dislocations, Bull. Seism. 
Soc. Am., 64, 45-64, 1974. 

Helmberger, D. V. and D. M. Hadley, Seismic source functions and teleseismic 
observations of the NTS events Jorum and Handley, Bull. Seism. Soc. Am., 
71, 51-67, 1981. 

Langston, C. A. and D. V. Helmberger, A procedure for modeling shallow 
dislocation sources, Geophys. J. R. astr. Soc., 42, 117-130, 1975. 

Liu, H. and D. V. Helmberger, The 23:19 aftershock of the 15 October 1979 

Imperial Valley earthquake: more evidence for an asperity, Bull. Seism. 
Soc. Am. , 75, 689-708, 1985. 

Mavko, G. M., Frictional attenuation:and inherent amplitude dependence, J. 
Ceophys. Res., 84, 4765-4775, 1979. 

Stewart, R. R. , M. N. Toksoz and A. Timur, Strain dependent attenuation: 
observations and a proposed mechanism, J. Ceophys. Res., 88, 546-554, 
1983. 

Wiggins, R. A., and D. V. Helmberger, Synthetic seismogram computation through 
expansion in generalized rays, Ceophys. J. R. astr Soc., 37, 73-90, 1974. 









APPENDIX 1. 
















ALMENDRO 5.1 KM. 



uso iTso aTso «!so "" 

TIME (SEC) 


5.50 


5. 50 


7.50 


< 


I 

I 


45 




a 











X7 


u y w v 


.176x10-* MPa 











ALMENDRO 6.1 KM 















ALMENDRO 6.1 KM 


L02 STRESSES 




0 KM 




1- 1 — ■« 1 — i 












ALMENDRO 10.0 KM 



2. SO 3. SO 4.50 S.SO 6.50 7.50 


TIME (SEC) 












ALMENDRO 12.6 KM 

LOl STRAINS 



2.481x10"® 


iViViVT 
























ALMENDRO 

17.0 KM. 


SOI STRAINS 

A 

2.066x10“® 






6.430xl0“ 7 


1.426x10“® 


WVr- 


2.711x10“® 


TIME (SEC) 

































BOXCAR 4.9 KM. 


S16 STRAINS 



4.778X10- 4 









BOXCAR 7.3 KM. 

S24 STRAINS 


A 


A 


5.648x10-® 


















BOXCAR 10.4 KM. 


S34 STRAINS 



1.975x10-® 


r* 


3.757x10"® 






















BOXCAR 22.5 KM. 




7.897x10-® 











BOXCAR 22.5 KM. 



.297x10-* MPa 




6.409x10-* MPa 












1.283x10"* 


3.991x10"® 














INLET 3.3 KM. 
















INLET 6.5 KM. 

S7 STRAINS 


6.289x10”® 


1.956x10”® 


4.333x10”® 


8.244x10-® 


4. 00 5.00 6. 00 7. 00 

TIME (SEC) 












INLET 6.5 KM. 



1.354x10-* |fpa 











g* tf r r* it * it « tf » t * \n y 1 * im iw v * » 


MAST 3.6KM 



Wv'V-x 


i.ei*xi<r« 












1.121x10° MPa 


2.660x10'* liPa 


4.624x10'* MPa 


8.462x10'* MPa 

























MAST 5.5 KM. 




2. SO 


9. SO 


4. SO 


5 ! SO 


B. SO 


7. 50 


.5 


TIME (SEC) 







MAST 7.3 KM. 


S7 STRAINS 

A 



2.623x10“® 

















MAST 7.3 KM. 




9.823x10“* MPa 











SCOTCH 4.1 KM. 

83A STRAINS 


4.641*10”* 



















SCOTCH 6.1 KM. 



MCfii 


3.076*10-® 










SCOTCH 6.1 KM. 














APPENDIX 2 











W ' b. * . - - * • 


IMPERIAL VALLEY 10/15/79 23:19 


HOLT STRAINS 


1.123x10-8 



1.699x10-8 



1.123x10-8 



3.404x10-8 


7. 33 8. S3 8. 33 

TIME (SEC) 


10.33 11.33 






m 








• — W <r v ' V -V : V" 


» UT v r *'. VrJ* LTryW ’J 


IMPERIAL VALLEY 10/15/79 23:19 


HOLT STRESSES 





sITa eTii i . 33 el 33 iiTsi to. 33 It. 33 

TIME ISEC1 


79 





















































IMPERIAL VALLEY 10/15/79 23:19 

ARY6 STRESSES 


2.036x10"* MPa 










IMPERIAL VALLEY 10/15/79 23:19 

ARY8 STRAINS 


1.931x10“® 



















IMPERIAL VALLEY 10/15/79 23:19 

ARY6 STRESSES 


1.376*10-* MPa 
















IMPERIAL VALLEY 10/15/79 23:19 

ELCI STRAINS 


2.048x10-* 




























IMPERIAL VALLEY 10/15/79 23:19 

ARY4 STRAINS 


2.408x10-* 







IMPERIAL VALLEY 10/15/79 23:19 

ARY4 STRESSES 


1.716x10-* MPa 














IMPERIAL VALLEY 10/15/79 23:19 

ARY9 STRAINS 

A 


1.963x10”® 
















IMPERIAL VALLEY 10/15/79 23:19 

ARY9 STRESSES 

A 


1.399x10-* MPa 

































A0-A181 196 
UNCLASSIFIED 


STRAINS AND STRESSES NEAR EXPLOSIONS AND EARTHQUAKES 
<U> HOODHARD-CLVDE CONSULTANTS PASADENA CA 
L J BURDICK ET AL. 15 OCT 66 MCCP-R-86-82 
AFGL-TR-87-B889 F19628-85-C-B8J6 F/O 19/9 


2/2 























































IMPERIAL VALLEY 10/15/79 23:19 

CALE STRAINS 


1.675x10”* 
















IMPERIAL VALLEY 10/15/79 23:19 

AR10 STRAINS 

A Q.lOOxlO”* 























IMPERIAL VALLEY 10/15/79 23:19 



.88 8.88 

TIME (SEC) 








IMPERIAL VALLEY 10/15/79 23:19 

BNCR STRESSES 


6.427x10“* MPa 























IMPERIAL VALLEY 10/15/79 23:19 

ARll STRESSES 


1.946XHT* HP* 































IMPERIAL VALLEY 10/15/79 23:19 


ARY3 STRESSES 



1.499x10-* MPa 


3.579x10-* MPa 


3.605x10-* MPa 


6.189x10“* MPa 


1.597x10-* MPa 


51 10.51 11.51 12. Si 13.51 

TIME (SEC) 
















IMPERIAL VALLEY 10/15/79 23:19 

ARY2 STRAINS 


1.001x10”® 

















IMPERIAL VALLEY 10/15/79 23:19 





0 . 


T-1 ~ 'I-1 


3 


12.36 13.36 

TIME (SEC) 


14. 36 


IS. 36 


























IMPERIAL VALLEY 10/15/79 23:19 

BRAW STRESSES 


3.013x10“* MPa 











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