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PL-TR-96-2300 


SOURCE FUNCTIONS OF NUCLEAR EXPLOSIONS 
FROM SPECTRAL SYNTHESIS AND INVERSION 


Peter Puster 
Thomas H. Jordan 


Massachusetts Institute of Technology 

Department of Earth, Atmospheric, and Planetary Sciences 
Cambridge, MA 02139 


20 November 1996 


Scientific Report No. 1 


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"Source Functions of Nuclear Explosions 

from Spectral Synthesis and Inversion"__ 


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Peter Puster, Thomas H. Jordan __ 

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Massachusetts Institute of Technology 

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13. ABSTRACT (Maximum 200 words) 

We apply methods for the recovery of the frequency-dependent moment-rate tensor, M(to), to the study of Lop Nor nuclear ex¬ 
plosions. This approach encompasses many source parameter diagnostics that have been traditionally used to discriminate nu¬ 
clear explosions from chemical explosions and earthquakes and has the potential to provide new discrimination tools. We pa¬ 
rameterize the source as M(co) = M,(co) + M 0 (©), where M/fm) and M D (o) are isotropic and deviatoric components, 
respectively. Our goal is to quantify both isotropic and deviatoric components, and investigate the different contributions to 
Mn(©) in particular the tectonic release. Since tectonic release can bias estimates of M/(<u) and may limit discrimination 
capabilities of sparse networks, it is important to be able to characterize the amount of tectonic release - in particular as a func¬ 
tion of frequency. Our approach uses synthetic seismograms to improve the localization of signal measurements in both time 
and frequency domains. We adapt our earthquake-source inversion algorithms to account for isotropic sources at very shallow 
depths We test our algorithms using a synthetic case with a known moment-tensor source composed in equal parts of isotropic 
and deviatoric sources; we successfully recover both M D and M using body waves and surface waves on horizontal and vertical 
components. We apply our methods to a data set containing both Sh and Love waves as well as the body-wave portion between 
p and Rl and the minor-arc Rayleigh waves from the 92/5/21 Chinese nuclear test. We recover a significant tectonic release 
component for this event; the deviatoric moment tensor is a dip-slip reverse fault with a scalar moment M D = 1.9 ± 0.2 xiu 
Nm. The strike of the best-fitting double-couple is 320°. The source-time function derived from ^//-polarized waves shows 
some complexity, with a sharp pulse in moment release followed by a long, smooth tail. The former is hypothesized to be 
explosion energy s catte red in Sfj waves by near-source heterogeneities, and the latter appears to be an earthquake-like component 
of tectonic release. At low frequencies, the scalar moment ratio is M d /Mi = 0.61 ± 0.01. 

. .. T ^„; ~- - - 115. NUMBER OF PAGES 

14. SUBJECT TERMS 

Lop Nor nuclear test, frequency-dependent moment-tensor, tectonic release, -32- 

spectral inversion, source-time function 16 price code 


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CONTENTS 


Objectives and Approach 


Research Accomplishments 

Modifications to the Analysis Procedures 
Synthetic Test Case 

Lop Nor Nuclear Test From May 21, 1992 
Summary and Conclusions 


References 






Objectives and Approach 

The seismological problem most relevant to nuclear monitoring under a Comprehensive Test 
Ban Treaty (CTBT) is to discriminate small nuclear explosions from chemical explosions and 
small earthquakes in a variety of geological settings. The dual challenges posed by the desire for 
a small detection threshold and a global reach, which includes areas of low seismicity, call for an 
approach to discriminate nuclear explosions from chemical explosions and earthquakes that 
simultaneously uses multiple diagnostics, such as M s -mb ratio, radiation pattern, and amplitude 
spectrum. A general method for studying seismic sources that encompasses many traditional 
source parameter discriminants is based on the recovery of the broad-band moment-rate tensor, 
M(m). This moment tensor can be modeled as the product of a complex function, /(G)), whose 
inverse Fourier transform is the source-time function, f(t), and a time-independent mechanism 
tensor, M, usually taken to be the (zeroth-order) spatial moment of the stress glut-rate tensor 
[Backus, 1977; Silver and Jordan, 1982]. In explosion seismology, the source-time function is 
often equated to the reduced displacement potential (RDP), y{t), via f(t) = Aitpa 2 y/(t) [e.g., 
Denny and Johnson, 1991]. More generally, however, several processes contribute to M(g>), 
these include the release of tectonic prestress, spall and slapdown, as well as the RDP of the 
explosion itself. 

The comprehensive nature of an approach based on recovering M(g>) is appealing. For 
example, writing /(G)) = A{(0)e m<0) in polar form illustrates that the amplitude spectrum, 
A{(o), is just the modulus of /(G)). Furthermore, to the extent that good synthetic seismograms 
can be computed from M(o), relative excitations of different waves (e.g., M s -m b ratio) can also 
be obtained. In addition, several new types of discriminants are potentially derivable from 
/(G)) . The moment-tensor approach is amenable for setting up inverse problems to separate the 
isotropic explosion component, M/(g)) = M/(g>)I, from deviatoric sources of wave excitation, 
M d (g)). The shallow depth of explosion sources makes an inversion for all six moment-tensor 
components (M/(G)) and the five independent elements of M£>(&))) difficult. Long-period 
surface waves, for example, are able to constrain only three components [Given and Mellman, 
1986; Ekstrom and Richards, 1994]. In addition to m r6 and m r<t> , poorly constrained since their 
Green's functions vanish for surface sources, an independent estimation of m rr and m ee + 
is difficult using only surface waves [Patton, 1988]. To overcome these limitations Patton 
[1988; 1991] performed moment-tensor inversions of regional observations from NTS 
explosions using both fundamental-mode and higher-mode surface waves. The higher-mode data 
provide additional constraints on the source, since Green's functions of m rr and m eQ + 
differ substantially even for shallow sources for these waves. 


1 



An important goal of this study is to utilize our broad-band source recovery algorithms 
employing both surface-wave and body-wave data to determine M/(o)) and M£,(&)) and to 
quantify the different contributions to M D {(0), especially the tectonic release component, 
M r (£0), whose contribution dominates the deviatoric component at low frequencies. Tectonic 
release contributes to source parameter estimates, such as the surface-wave magnitude M s [e.g., 
Patton , 1991], and has the potential to bias both discriminants and minimum-yield detection 
maps, in particular when the amount of tectonic release is significant. A quantitative measure for 
the tectonic component is the "F factor", defined by Toksoz et al. [1964] as the ratio of the 
Rayleigh-wave amplitude generated by the explosion to that generated by the tectonic release. 
For a Poisson solid M t /Mj =2/3 F [Wallace, 1991]. 

The presence of a tectonic release component in seismic recordings from nuclear explosions, 
manifested in the presence of S/Hype seismic waves, has been recognized since the 1960s [Press 
and Archambeau, 1962; Brune and Pomeroy, 1963]. Models proposed for explaining the 
generation of Sh- type energy include explosion-triggered slip at preexisting, nearby faults [Aki 
and Tsai, 1972], release of tectonic prestress around the explosion source [Archambeau, 1972], 
and a combination of the two [Wallace, 1991]. Important unresolved questions associated with 
the tectonic release component are: (1) What is the scaling of the tectonic component with 
frequency? (2) Is there a change in the character of tectonic release with explosion yield/depth? 
(3) How does tectonic release vary in different geologic settings? 

Most previous studies of tectonic release have focused on the Nevada Test Site [Aki and Tsai, 
1972; Wallace et al., 1983; Wallace et al., 1985; Given and Mellman, 1986; Patton, 1988] and 
the Shagan River, Kazakhstan nuclear test site [Helle and Rygg, 1984; Given and Mellman, 
1986; Walter and Patton, 1990; Ekstrom and Richards, 1994], while little attention has been 
devoted to investigating the tectonic component from nuclear tests near Lop Nor, China [Zhang, 
1996]. 

Furthermore, most studies have utilized either surface waves [e.g.. Given and Mellman, 1986; 
Ekstrom and Richards, 1994; Zhang, 1996] or body waves [Wallace et al., 1983; Wallace et al., 
1985] alone, making a broad-band estimate of M(n>) difficult. Therefore, the variation of F with 
frequency has received little attention, although scarcity of high-frequency Sh waves indicates 
that it decreases with frequency. Our approach based on a broad-band source recovery will allow 
us to constrain this quantity and improve our physical understanding of explosion source 
processes. 

Another important question concerns the scaling of tectonic release for different explosions. 
Some authors have suggested, for example, that F decreases with time for explosions detonated 
in close proximity to each other [Aki and Tsai, 1972; Wallace, 1991], and that it is affected by 
other factors such as explosion yield and depth of burial [Aki and Tsai, 1972]. From a moment- 


2 


tensor inversion of 16 explosions on Pahute Mesa, Patton [1991] concluded that the character of 
the tectonic component changes with explosion yield, going from vertical strike-slip mechanisms 
to dip-slip reverse faulting at yields of about 200-300 kT. Since M s is biased high (low) for 
strike-slip (thrust) mechanisms [Patton, 1980], it is important to test this hypothesis at other 
nuclear test sites. 

In this study, we consider explosions from the Chinese nuclear test site at Lop Nor. We have 
collected a large number of broad-band and long-period three-component seismograms at 
regional and teleseismic distances for several nuclear tests from 1990-1996 spanning a range of 
sizes. Applying our broad-band source recovery algorithms to this data set, we will be able to 
improve our physical understanding of the processes affecting seismic wave excitation from 
explosion sources. Gaining new insights into how tectonic release scales with frequency and 
explosion yield/depth should also lead to a better understanding on how high-frequency 
discriminants such as P/Lg are affected by tectonic release. 

Recovering broad-band estimates of the source-time function from seismic data at regional 
and teleseismic distances is a difficult inverse problem, requiring precise corrections for 
deterministic propagation effects and careful averaging procedures to reduce stochastic 
fluctuations due to non-deterministic scattering. Our approach is based on techniques developed 
by Jordan and coworkers for determining earthquake source-time functions. In particular, we 
adapt waveform isolation and analysis tools developed by Gee and Jordan [1992] and Ihmle and 
Jordan [1995], which use synthetic seismograms to improve the localization of signal 
measurements in both time and frequency domains. We proceed as follows: 

(1) For each observed seismogram Sj(t) (j = station index), we generate six Green s function 
seismograms gj(t) (k = component index; k e [rr, 66, 0</>, r6 , r<p, 6<j>]) from the 
best available structural model. At teleseismic distances, we use a global tomographic 
model, such as the Preliminary Reference Earth Model (PREM) of Dziewonski and 
Anderson [1981] in conjunction with the degree-12 structure S12_WM13 of Su et al. 
[1994], Using Green's functions calculated for an aspherical earth model reduces 
contamination due to propagation effects and enables us to obtain a clearer image of the 
source. For the work at regional distances, we adopt appropriate path-averaged models 
[e.g., Gaherty and Jordan, 1995], where available. We use an iterative inversion 
algorithm to determine a source mechanism, m(ft)), from a series of narrow-band filtered 
cross-correlations between Sj (t) and g){t). (m(G>) is the isomorphic equivalent of the 
symmetric tensor M(a>) [Silver and Jordan, 1982].) 


3 



(2) Using an average source mechanism, m = m(ot>o)> we generate synthetic seismograms 
Sj ( t) = g j (r) • m assuming that the source is a step-function at r 0 • 

(3) Using the isolation-filtering procedures detailed by Gee and Jordan [1992], we extract 
two functions of frequency, an amplitude ratio Aj (<u) / Aj(co) and a differential phase 
delay Atj(co) = tj(co)-tj(co), from individual waveforms on Sj(t). At teleseismic 
distances, the waveforms we analyze typically include the P and S body phases and the 
R { and G! surface waves. Corrections are applied to account for the amplitude and phase 
distortions due to the time- and frequency-localization operations intrinsic to the analysis 
[Gee and Jordan, 1992]. 

(4) We average Atj(O)) and the logarithm of Aj(co)/ Aj(co) over the network from which 
we obtain estimates of At(co) and A(a>). Note that averaging is not done over the 
complex spectrum, f(co ); if it were, the small phase delays associated with unmodeled 
propagation effects would cause destructive interference among the signals, and therefore 
lead to amplitude bias. 

(5) We invert the estimates of A(co) and At(co) for fit), subject to an appropriate set of 
smoothing constraints and functional bounds. 

Research Accomplishments 

Modifications to the Analysis Procedures . We have adapted our algorithms to synthesize broad¬ 
band amplitude and phase-delay estimates from regional and teleseismic data, developed in the 
context of our research on earthquake source mechanisms [Ihmle et al., 1993; Ihmle and Jordan, 
1994], to inversions of explosion sources. In our previous earthquake studies, we have assumed 
that the source-time function is non-negative. Physically, this is a statement that there is no 
backslip in the fault. The mathematical advantage of this assumption is that a lower bound is 
imposed on the inversion for fit), which constrains the solution by reducing the size of the 
model space [Ihmle and Jordan, 1994]. This assumption is not generally valid for nuclear 
explosions, because many of them are observed to have overshoot, which means that fit) 
becomes negative over some time interval of the source. However, when inverting for the 
deviatoric (tectonic) component of the source-time function, foit), non-negativity should be a 
good first-order approximation. Another constraint commonly applied to earthquake moment 
tensor inversions is to require the moment tensor to be deviatoric. Such a constraint is clearly 
inappropriate when inverting for a moment tensor that is composed of both explosion and 
deviatoric components. A further difficulty encountered when inverting for explosion source 
mechanisms is due to the fact that the depth of moment release is very close to the earth's 


4 



surface. At shallow depths the Green's functions g r0 (t) and g r ^(t) almost vanish, since the 
normal component of the stress tensor is zero at the free surface. This means that m rQ and m r< p 
cannot be well constrained. A common practice in source inversions of nuclear explosions and 
shallow earthquakes is to simply set these two components equal to zero [Kanamori and Given, 
1981; Given and Mellman, 1986]. However, this procedure is adequate only for narrow-band 
moment-tensor inversions, since the sensitivity to shallow structure becomes larger with 
increasing frequencies, which leads to high-frequency moment-tensor solutions that are biased 
with respect to the low-frequency inversions when m r6 = m r( p = 0 is assumed. We overcome 
this problem by recasting the inverse problem using a projection operator, P* = I - g s gj. This 
operator annihilates any possible information on m rQ and m r( p contained in the Green's functions 
g or in the data s. This modifies the inverse problem from: 

g-m = g d ■ [m rr ,m 96 , ,m d<p ] + g s -[m r6 , m r4> ] = s (1) 

to 

P s g m = P s s, 

and allows a recovery of the moment tensor over a broad frequency range. Another advantage of 
the projection operator approach is that it allows a self-consistent error analysis, since the 
posterior model covariance matrix will reflect the constraints used in obtaining the solution. 

Our formalism for obtaining the source mechanism is based on determining the elements of 
the moment tensor directly. This contrasts with methodologies that formulate the Green's 
functions using three fundamental faults [Kanamori and Given, 1981] plus an explosion source 
[Given and Mellman, 1986]. We also do not impose any a priori constraint on the fault geometry 
or even require the deviatoric component to be a double couple. 

Synthetic Test Case . To examine the performance of our algorithms we construct the following 
test case. Using a fictitious source located at the Lop Nor test site with a moment tensor 
composed of an isotropic part plus a deviatoric mechanism with identical scalar moment, we 
calculate 3-D synthetic seismograms for a PREM plus S12_WM13 earth structure for 20 IRIS 
and Geoscope stations at regional and teleseismic distances to simulate the data. The aspherical 
synthetics are calculated employing the asymptotic formalism of Woodhou.se and Dziewonski 
[1984]. The deviatoric moment tensor is the Harvard-CMT solution of the 94/9/7 event in 
Southern Xinjiang, China (a predominantly strike-slip earthquake with a small CLVD 
component and a scalar moment of 7.7 x 10 16 Nm) mimicking the tectonic release component. 
Green’s functions are calculated for the 1-D PREM model. Our imprecise knowledge of 3-D 
earth structure is a primary source of signal-generated noise which makes an inversion for the 
source-time function difficult. Using 3-D synthetics as data and 1-D Green's functions provides 


5 


a proxy for difficulties encountered with real data. Since the explosion source is located at 
shallow depth (1 km), the m r6 and m r<p components of the moment tensor are ill-constrained; we 
therefore project out these components using the algorithm outlined above. Utilizing the fact that 
transverse-component (LHT) seismograms do not contain any energy from a purely isotropic 
source our moment-tensor inversion proceeds in two steps. First, we invert the LHT 
seismograms and obtain an estimate for the tectonic release. Second, we invert the vertical- 
component data, which yields a moment tensor that is a combination of the isotropic component 
plus the tectonic release. 

Figure 1 shows the results of the initial moment-tensor inversion using long-period, minor- 
arc Love waves recorded on the transverse component. We apply a series of narrow-band filters 
to the broad-band cross-correlation function and obtain independent moment-tensor solutions 
for each frequency band. The source mechanism plots are constructed using the 
methodology described by Riedesel and Jordan [1989]. Column A displays the three principal 
axes of the source mechanism (T, N, P) together with the unit mechanism vector (X) and the 
canonical unit vectors d, 1 , and i, representing a pure double couple, a compensated linear 
vector dipole, and a pure dilatation, respectively. The contours of the P-wave first motion are 
shown in column B. This approach provides a comprehensive visualization of the source 
mechanism. In particular, it is possible to directly assess the uncertainties in the source 
mechanism and quantify the contribution of an isotropic component, a very useful feature when 
investigating non-deviatoric sources (see below). While all solutions are strike-slip mechanisms, 
the source mechanisms vary rapidly between adjacent frequency bands and differ from the 
projected ground-truth mechanism (bottom right). This instability in the inversion is primarily a 
result of mapping phase-shifts due to unmodeled lateral heterogeneities along the propagation 
path into the source mechanism. To account for these propagation effects we iterate our 
inversion by (1) calculating the phase-shifts between data and synthetics (computed from a 
moment tensor obtained in the initial inversion), (2) phase-shifting the Green s functions, and (3) 
reinverting for M D (co). The results depicted in Figure 2 document the success of this 
methodology. The agreement between different frequency bands and with the projected ground- 
truth moment tensor is excellent. 

Horizontally polarized shear waves provide additional constraints on (&>) and are less 
contaminated by shallow heterogeneity than surface waves. Figure 3 shows the results of the 
moment-tensor inversion using Sh waves, adjusted for the phase-shifts due to aspherical 
heterogeneities. The agreement with the Love-wave solutions is good, and indicates that the two 
data sets can be used to cross-check the inversion results and provide a broad frequency band. 


6 



A B 



A B 



A B 



Figure 1. Source mechanism plots (A) and initial P -wave radiation patterns (B) for M D (e>) in 2 
mHz frequency bands ranging from 9 to 31 mHz plotted using equal area projection. On each 
plot (A), the three principal axes e lf e 2 , e 3 (eigenvectors of M D (co)) corresponding to 
eigenvalues A, > A 2 ^ A 3 , are plotted as T, N, and P on the lower focal hemisphere. The 
mechanism is characterized by the unit vector A = XA t ej, which can be compared with the 
canonical unit vectors d, 1 , and i, representing a pure double couple, a pure compensated linear 
vector dipole, and a pure dilatation, respectively. The dashed line shows the locus of all 
deviatoric mechanisms. Vectors are plotted as downward pointing filled triangles if they are on 
the lower focal hemisphere and as upward pointing if they are projected from the upper 
hemisphere. For a pure double couple the axes T, N, and P are the tension, neutral, and 
compression axes, respectively. The contours of the P -wave first motion are shown in (B). Solid 
(dashed) contours denote compressional (dilatational) first motion, thick contours are nodal lines. 
Initial moment-tensor inversion results using first-orbit, transverse-component Love wave-forms 
from a synthetic test case. "Data" seismograms are calculated using PREM plus the 3D model 
S12_WM13. Green’s functions are calculated for the ID PREM model. The m rB and m r( p 
components are projected out from both solution and data space. The moment tensor is 
constrained to be deviatoric. For comparison, the projected input moment tensor ("Ground 
Truth") is shown on the lower right. 


7 






B 


A B 

9—11 mHz 



A B A 




Figure 2. Mechanism plots (A) and P-wave radiation patterns (B) from the Love-wave inversion 
(phase-aligned) for the test case described in Figure 1. Prior to performing the moment-tensor 
inversions, a phase-shift, A tj(co), is calculated for each seismogram in each frequency band 
using a preliminary M c from the initial moment-tensor inversion (Figure 1). The Green's 
functions are phase-shifted by A tj(co) and a new inversion for M£>(&)) is performed. The 
agreement between the frequency bands and with the projected ground-truth moment tensor is 
remarkable. 


A B 


10 - 15 mHz 



A B 


30 - 35 mHz 



Ground Truth 



8 


Figure 3. Mechanism plots 
(A) and P-wave radiation 
patterns (B) from the mo¬ 
ment-tensor inversion (after 
phase alignment) using S# 
waveforms for the same test 
case described in Figure 1. 
The m rQ and m r(p compo¬ 
nents are projected out and 
the moment tensor is con¬ 
strained to be deviatoric. 
Results from the body-wave 
inversions agree very well 
with the surface-wave results 
displayed in Figure 2. 























Network-averaged amplitudes, A{(o)l A(co), and time-shifts, Ar(cw), for the Sh waves 
obtained from cross-correlations of data and synthetics (using an average moment tensor from 
Figure 3) are displayed in Figure 4. The small residuals ( A(co) / A(co) - 1 and At(co) ~ 0) are 
further proof of the success of the moment-tensor inversion. The residual time shifts in Figure 4, 
are due to 3D propagation effects not removed by the network average. Using these amplitude 
and time shift spectra we can invert for the source-time function. 



Figure 4. Network-averaged amplitude ratios, A(co)/A(co), and time-shifts, A t(co), measured 
from narrow-band cross-correlations of Sh waveforms using an average moment tensor M c 
from Figure 3. Agreement between data and synthetics indicates the success of the moment- 
tensor inversion. Residual time shifts are due to 3D propagation effects not removed by the 
network average. 

Transverse-component data do not constrain m rr (since the corresponding Green’s function, 
g rr (t), is zero for a spherically symmetric earth). Furthermore, g 66 (t) = -£^(0> which results 
in m ee = -m^. The LHT inversion, therefore, always recovers a double-couple, vertical strike- 
slip source. However, since m rr is unconstrained it is possible to fit the LHT data equally well 
with an alternative source mechanism, the one corresponding to a 45° dip-slip fault with a strike 
rotated by 45° and a scalar moment twice that of the strike-slip source [e.g., Aki and Richards, 
1980]. To resolve this ambiguity in M D (m) and to recover M ; ((U) we apply our inversion 
procedure to the body-wave portion between P and the minor-arc Rayleigh waves (R{) on 
vertical-component recordings. We calculate synthetic test data using the S12_WM13 3D earth 
model and a moment tensor M = Mj I + Mq M/>, with Mq/Mj = 1 and from above. The 
inversion allows for a non-zero isotropic component; however, m r6 and m r( p are projected out. 
Figure 5 shows M(co) between 10 and 45 mHz. Displaying the source mechanism unit vector, 
i, together with the canonical double couple, CLVD, and isotropic vectors makes it particularly 
easy to assess the contribution of the purely dilatational component. The angular distance 


9 





between X and i measures the deviation from an isotropic source. This is the first time that the 
Riedesel and Jordan [1989] formalism has been applied to assess and display significantly non- 
deviatoric mechanisms. The agreement between different frequency bands and with the known 
solution (lower right), although not as good as for the transverse-component data, is still rather 
remarkable. These synthetic tests indicate that we can recover both deviatoric and isotropic 
source mechanisms from vertical-component and transverse-component data. 



A 



30 - 35 mHz 







Figure 5. Mechanism plots 
(A) and P -wave radiation 
patterns (B) from the (phase- 
aligned) moment-tensor in¬ 
version using the body-wave 
portion of vertical-component 
records arriving prior to R\. 
Uncertainties in the mecha¬ 
nism vectors are depicted by 
95% confidence ellipses 
(heavy lines). The projected 
input moment tensor (ground 
truth) consists of both 
isotropic, MfL, and devia¬ 
toric, M d M d , components 
( M d /Mj = 1) and is dis¬ 
played on the bottom right. 
Data and synthetics are calcu¬ 
lated for the same models as 
in Figure 1. The inversion is 
performed with m rQ and m r(p 
components projected out; 
the moment tensor is no 
longer constrained to be 
deviatoric. 


Lop Nor Nuclear Test from 92/5/21 . Having established the performance of our moment-tensor 
recovery methodology on a synthetic example, we next apply our algorithms to data from the 
Chinese nuclear test conducted on 92/5/21. While this is the largest Chinese nuclear test to date, 
the station coverage provided by the IRIS and Geoscope networks, is sparse by today's standards. 
Love waves are clearly identifiable on the LHT recordings from this event and are of equal or 
larger amplitude than the Rayleigh waves (Figure 6), demonstrating that a significant component 
of tectonic release is present. 


10 




Figure 6. Vertical-component Rayleigh-wave and transverse component Love-wave 
seismograms for six stations at varying epicentral distance. A, and source-receiver azimuth, <j>, 
from the 92/5/21 Chinese nuclear test near Lop Nor. Seismograms are band-pass filtered with a 
six-pole Butterworth filter (comers at 8.5 and 31.5 mHz). Traces are aligned on the theoretical 
Love wave arrival time; maximum trace amplitude is displayed below the individual traces. 


11 





Using the same analysis procedure as above, we invert these data traces for the deviatoric 
moment tensor. However, we utilize our knowledge of long-wavelength aspherical earth 
structure to calculate 3-D Green's functions using PREM together with the 3-D model 
S12_WM13. Figure 7 displays the inversion results using transverse-component, first-orbit Love 
waves (Gj). The resulting moment tensor, Mplto), is a strike-slip mechanism which shows 
little variation between frequency bands, with the strike of the faults plane varying only by a few 
degrees. 



Figure 7. Mechanism plots (A) and P -wave radiation patterns (B) from the (phase-aligned) 
Love-wave inversion for the 92/5/21 nuclear test near Lop Nor, China. The analysis procedure is 
the same as for the synthetic test case described earlier, except that we calculate Green's function 
seismograms for the aspherical model S12_WM13. The resulting moment tensor, M 0 (a)) 
remains unchanged across the entire frequency band. 


This event also generated Sh waves clearly observable at several stations at regional and 
teleseismic distances. Inverting these shear waves for M o ( 0 )) yields results consistent with the 


12 








Love-wave inversion (Figure 8). Since the S waves are less influenced by strong, near-surface 



Figure 8. Mechanism plots (A) and P-wave radiation patterns (B) from the inversion of phase- 
aligned Sh waveforms for the 92/5/21 nuclear explosion near Lop Nor, China. The resulting 
moment tensor, M 0 (<u), is nearly identical to that obtained from the Love-wave inversion. 


Figure 9 depicts the source mechanism averaged over all frequency bands from the Gj and 
Also shown is the dip-slip mechanism that satisfies the data equally well. The 
moments of these two mechanisms are, = 0.85±0.05x 10 17 Nm and 
2M S q = 1.7±0.1xl0 17 Nm, respectively. 


B 


scalar 
AA DS _ 

M d = 

A 



Figure 9. Mechanism plots (A) and P-wave 
radiation patterns (B) averaged over all 
frequency bands from the Love-wave and Sh 
inversions. Due to the ambiguity intrinsic in 
inverting transverse-component data, both 
vertical strike-slip and dip-slip mechanisms 
satisfy the data equally well. 













The network-averaged amplitude and time-shift spectra for the Sh waves using the average 
moment tensor are shown in Figure 10. While the absolute amplitude is uncertain within a factor 
two, owing to the ambiguity between strike-slip and dip-slip mechanisms, the amplitude spectral 
roll-off suggests a decrease in the size of the tectonic component, as long as the source 
mechanism does not change from dip-slip to strike-slip between 0.01 and 0.08 Hz. The time 
shifts at low frequencies (At(co) = 4-7 s) indicate a centroid time more appropriate for an 
earthquake than an explosion. 



Figure 10. Network-averaged amplitude ratios, A(cq)/a(cq), and time-shifts, A t(co), (triangles 
with 1-c standard errors) measured from narrow-band cross-correlations of Sh waveforms using 
an average moment tensor from Figure 9. The solid lines indicate the data fit obtained from 
the source-time function displayed in Figure 11. 


Figure 11 depicts the source-time function associated with the deviatoric mechanism, fo(t), 
obtained from a constrained inversion of the network-averaged amplitude and time-shift spectra. 
The inversion is performed using a quadratic programming approach that allows for smoothness 
constraints and one-sided constraints [Ihmle et al., 1993]. To limit the size of the solution space, 
we constrain //>(?) to be non-negative. The source-time function shows some complexity, with 
a sharp pulse in moment release followed by a long, smooth tail (Figure 2f). Although we must 
still examine potential sources of bias, we hypothesize that the pulse-like component is caused by 
scattering of energy from the explosion into S//-polarized waves, perhaps by near-source lateral 
structure, and the smoothly varying component is earthquake-like radiation due to tectonic 
release. If correct, this interpretation would favor a tectonic release model where the explosion 


14 






triggers slip at nearby faults [Aki and Tsai, 1972] over the shatter-zone model advocated by 
Archambeau [1972]. 

Figure 11. Source-time function, f D {t), 
obtained from a constrained inversion of the 
network-averaged amplitudes and time- 
shifts depicted in Figure 10. Although not 
unique, the source-time function provides a 
good spectral fit. The pulse-like component 
is hypothesized to be due to scattering of 
explosion energy, while the smoothly 
varying component, comprising about 60% 
of the total moment can be explained by 
tectonic release. The moment-rate is scaled 
assuming a dip-slip mechanism. 


0 5 10 15 20 25 

Time (s) 


To recover the complete moment tensor M(t») = M j (co) + M p((o) and to discriminate 
between the two candidate mechanisms obtained from inverting the S H -type data, we use the 
vertical-component data. We perform separate inversion using (1) first-orbit Rayleigh waves and 
(2) the body-wave portion between P and R v The Rayleigh-wave inversions reveal the presence 
of a strong isotropic component to the source mechanism, X, evident by the small angular 
distance between X and i (Figure 12). With a few exceptions the inversions are stable across 
the entire frequency range. The mechanism uncertainties, quantified by the 95% confidence 
ellipses, illustrate a trade-off between isotropic and CLVD mechanisms. Rayleigh waves are 

A 

unable to differentiate between an isotropic component and a vertical CLVD, 1', corresponding 
to horizontal extension and vertical compression. 

The body-wave data includes various phases (P, S, pP, pS, sS, sP, etc.), leaving the source at 
different take-off angles, thus providing good constraints on the source mechanism. We exclude 
higher-mode surface waves that show a strong contamination due to near-surface heterogeneities. 
Body-wave phases turning in the mantle are less affected by shallow structure than surface 
waves, and should therefore allow us to improve on the Rayleigh-wave moment-tensor estimates. 
Indeed, the body-wave inversions show consistency between M(ct)) determined in different 
frequency bands and compare well with the Rayleigh-wave results (Figure 13). 



15 



B 


A B A B 

7 - 9 mHz 15 _ 17 m u 7 




A 


23 - 25 mHz 



Figure 12. Mechanism plots (A) and P-wave radiation patterns (B) from the (phase-aligned) 
vertical-component Rayleigh-wave (/?j) inversion for the 92/5/21 nuclear explosion near Lop 
Nor, China. The inversion attempts to recover M(<y) = M/(<y) + MpCfo); however, m rQ and 
m r(p are projected out. The resulting moment tensor, M(<a), is relatively stable across the 
frequency range and exhibits a significant isotropic component, evident by the deviation of the 
mechanism vector, X from the great-circle of deviatoric sources. The angular distance between 
X and i measures the size of the isotropic component. 


Figure 14 displays a frequency-averaged moment tensor using both surface-wave and body- 
wave data. Removing the isotropic component (Mj = 3.1±0.3xl0 17 Nm) leads to the 
deviatoric moment tensor (Mq = 1.9 ± 0.2 x 10 17 Nm) shown. The mechanism plot reveals an 
insignificant contribution of a CLVD component; it is virtually indistinguishable from a double¬ 
couple. The best-fitting double-couple mechanism is displayed separately to facilitate a 
comparison with the thrust-fault mechanism obtained from the inversion of the transverse- 
component data. These two independently derived mechanisms (and the scalar moments) are 
quite similar (Table 1), reassuring us that the inversion of the vertical-component data 
successfully separated isotropic and deviatoric components. The tectonic release component 
determined from our inversions is also consistent with the limited amount of geologic 
information available for this area [Matzko, 1994]. Gao and Richards [1994], investigating 
earthquakes near the Lop Nor nuclear test site, find a predominance of reverse-faulting events 
striking NW to SE, in good agreement with our results. 


16 















B 


A B 


10 - 15 mHz 



A 


25 - 30 mHz 



N 





Figure 13. Mechanism plots (A) and 
P -wave radiation patterns (B) from the 
(phase-aligned) moment-tensor in¬ 
version using the body-wave portion of 
vertical-component records that arrive 
prior to R\ for the 92/5/21 nuclear test 
near Lop Nor, China. The resulting 
moment tensor, M(<y) (m r Q and m r(p 
are projected out) agrees well with the 
predominant mechanism found from 
the Rayleigh-wave inversion. 


Figure 14. Mechanism plots (A) and 
P -wave radiation patterns (B) averaged 
over frequency bands from the surface- 
wave and body-wave inversions. The 
proximity of the mechanism vector X 
to i on the focal sphere illustrates the 
strong isotropic component. The 
deviatoric component of the moment 
tensor is nearly a double-couple, and 
differs only slightly from the best 
fitting pure double-couple mechanism. 
For comparison, the dip-slip double¬ 
couple mechanism obtained from 
inverting the transverse-component 
data is also depicted. Double-couple 
source parameters are listed in Table 1. 


Table 1. Source parameters of 92/5/21 Lop Nor nuclear test 


Data 

/—\ 

o 

t—‘ 

I 

I 

r- 

»-H 

o 

2? 

M d /Mj 

<5t 

At 

05 + 

i?j and body waves 

3.1 ±0.3 

1.9 ±0.2 

0.61 ±0.01 

48° 

98° 

320° 

Gi and Sh waves 

0 

1.7 ±0.1 


45° 

90° 

329° 


+Dip, 8, slip, A, and strike, <j) s , of best-fitting double-couple mechanism. 


A 


B 


B 




17 










Summary and Conclusions 

We have developed a methodology for studying explosion sources that is based on the 
recovery of the broad-band moment-rate tensor, M(o>), utilizing both body waves and surface 
waves. We parameterize the source as being composed of an isotropic and a deviatoric 
component, i.e., M(co) = M/(<y) + This comprehensive approach encompasses many 

source parameter diagnostics that have been traditionally used to discriminate nuclear explosions 
from chemical explosions and earthquakes and has the potential to provide new discrimination 
tools. Our formalism uses synthetic seismograms to improve the localization of signal 
measurements in both time and frequency domains. We employ body waves and surface waves 
from vertical component recordings to invert for M(<y). Transverse-component Sh and Love 
waves provide independent estimates for M D (<o), albeit with an intrinsic ambiguity between 
strike-slip and dip-slip mechanisms. 

In our initial year of funding we have accomplished the following tasks: 

(1) We have developed procedures for inverting 3-component seismic data for moment-tensor 

representations of nuclear explosions. These algorithms have the following features: 

(a) they allow for the facts that explosion sources are located at very shallow depths by 
projecting out the m rd and m r( p components, 

(b) they allow for a source mechanism composed of both isotropic and deviatoric 
components, and 

(c) they incorporate 3-D propagation models. 

(2) We have validated our moment-tensor inversion algorithms using a synthetic test case with 

a known moment-tensor source, containing both isotropic and deviatoric components. 
The source inversions yield stable and self-consistent results across a broad frequency 
range using both body waves and surface waves (Figures 1-5). 

(3) We have successfully applied graphical display tools, developed for assessing deviatoric 

earthquakes, to sources with a significant dilatational component. These plots provide an 
immediate assessment of various features of the mechanism; for example, the relative 
importance of isotropic and deviatoric (tectonic) contributions to the moment release 
(Figures 5,12-14). 

(4) We have successfully applied algorithms to invert source spectra for source time functions. 

These inversions employ a quadratic programming algorithm that allows various types of 
time-dependent constraints to be imposed, including smoothness constraints and one¬ 
sided constraints. 


18 



(5) To improve our understanding of tectonic release in a variety of geologic settings, we have 
focused on the Chinese nuclear test site near Lop Nor, which has received less attention 
than the U.S. and Soviet test sites. Using recordings from the 92/5/21 Chinese nuclear 
test we have obtained moment-tensor solutions for both isotropic and deviatoric 
mechanisms. The deviatoric component of moment release for this nuclear test is 
significant ( M t /Mj = 0.61 ± 0.01).and has a negligible non-double-couple component 
(Figure 14). The best-fitting double-couple shows a reverse-faulting mechanism (Table 

I) , consistent with focal mechanisms from earthquakes near the Lop Nor nuclear test site. 
Transverse-component data (Sh and Love waves), although ambiguous by themselves, 
provide an independent confirmation for M D derived from vertical-component 
recordings (Figure 14). The network-averaged amplitude spectrum rolls off above 0.04 
Hz, indicating a decrease in the size of the tectonic component (Figure 9) with frequency. 
The source-time function associated with the deviatoric mechanism, f D (t), shows some 
complexity, with a sharp pulse in moment release followed by a long, smooth tail (Figure 

II) . Although we must still examine potential sources of bias, we hypothesize that the 
pulse-like component is caused by scattering of energy from the explosion into Sh- 
polarized waves, perhaps by near-source lateral structure, and the smoothly varying 
component is earthquake-like radiation due to tectonic release 

Tectonic release can lead to biased estimates of M/(a>). Furthermore, the detection 
threshold for a given explosion yield also depends on the amount of tectonic energy released by 
the explosion. It is therefore important to better understand how geology and explosion 
size/depth, influence the amount of tectonic release - in particular as a function of frequency. 
Gaining new insights into how tectonic release scales with frequency and explosion yield/depth 
should also lead to a better understanding on how high-frequency discriminants such as P/L g are 
affected by tectonic release. At present, we are addressing these questions by applying our 
source recovery algorithms to data from a number of nuclear tests of varying sizes. To better 
quantify the importance of tectonic release as a function of frequency, we are adapting our source 
inversion tools to higher frequencies. We are also investigating formulations for directly 
inverting for the relative contributions of tectonic and isotropic components as a function of 
frequency. At higher frequencies, apparent attenuation due to scattering as well as the effects of 
frequency-dependent intrinsic attenuation are expected to dominate the source amplitude 
spectrum, making an inversion algorithm based on the relative magnitude of tectonic and 
explosion components desirable. 


19 



References 


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21 




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INSTITUTE FOR THE STUDY OF THE CONTINENTS 
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PACIFIC NORTHWEST NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

PO BOX 999, MS K6-48 
RICHLAND, WA 99352 


PACIFIC NORTHWEST NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

PO BOX 999. MS K7-34 
RICHLAND. WA 99352 


3 



PACIFIC NORTHWEST NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

PO BOX 999, MS K6-40 
RICHLAND, WA 99352 


PACIFIC NORTHWEST NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

PO BOX 999, MS K5-72 
RICHLAND, WA 99352 


PACIFIC NORTHWEST NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

POBOX 999, MS K5-12 
RICHLAND, WA 99352 


KEITH PRIESTLEY 
DEPARTMENT OF EARTH SCIENCES 
UNIVERSITY OF CAMBRIDGE 
MADINGLEY RISE, MADINGLEY ROAD 
CAMBRIDGE, CB3 OEZ UK 

PAUL RICHARDS 
COLUMBIA UNIVERSITY 
LAMONT-DOHERTY EARTH OBSERVATORY 
PALISADES, NY 10964 


PACIFIC NORTHWEST NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

PO BOX 999, MS K7-22 
RICHLAND, WA 99352 


PACIFIC NORTHWEST NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

PO BOX 999, MS K6-84 
RICHLAND, WA 99352 


FRANK PILOTTE 
HQ/AFTAC/TT 
1030 S. HIGHWAY A1A 
PATRICK AFB, FL 32925-3002 


JAY PULLI 

RADIX SYSTEMS, INC. 
6 TAFT COURT 
ROCKVILLE, MD 20850 


DAVID RUSSELL 
HQ AFTAC/TTR 
1030 SOUTH HIGHWAY A1A 
PATRICK AFB, FL 32925-3002 


CHANDAN SAIKIA 

WOOODWARD-CLYDE FEDERAL SERVICES 
566 EL DORADO ST, SUITE 100 
PASADENA, CA 91101-2560 


SANDIA NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

DEPT. 5791 

MS 0567, PO BOX 5800 
ALBUQUERQUE, NM 87185-0567 

SANDIA NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

DEPT. 5704 • 

MS 0655, PO BOX 5800 
ALBUQUERQUE, NM 87185-0655 

THOMAS SERENO JR. 

SCIENCE APPLICATIONS INTERNATIONAL 

CORPORATION 

10260 CAMPUS POINT DRIVE 

SAN DIEGO, CA 92121 

ROBERT SHUMWAY 
410 MRAK HALL 
DIVISION OF STATISTICS 

UNIVERSITY OF CALIFORNIA .4 

DAVIS, CA 95616-8671 


SANDIA NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

DEPT. 5704 

MS 0979, PO BOX 5800 
ALBUQUERQUE, NM 87185-0979 

SANDIA NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

DEPT. 9311 

MS 1159, PO BOX 5800 
ALBUQUERQUE, NM 87185-1159 

SANDIA NATIONAL LABORATORY 
ATTN: TECHNICAL STAFF (PLS ROUTE) 

DEPT. 5736 

MS 0655, PO BOX 5800 
ALBUQUERQUE, NM 87185-0655 

AVI SHAPIRA 
SEISMOLOGY DIVISION 

THE INSTITUTE FOR PETROLEUM RESEARCH AND 
GEOPHYSICS 

P.O.B. 2286, NOLON 58122 ISRAEL 

MATTHEW SIBOL 
ENSCO, INC. 

445 PINEDA COURT 
:i MELBOURNE; FL3294C 




DAVID SIMPSON 
IRIS 

1616 N. FORT MEYER DRIVE 
SUITE 1050 

ARLINGTON, VA 22209 

BRIAN SULLIVAN 
BOSTON COLLEGE 
INSITUTE FOR SPACE RESEARCH 
140 COMMONWEALTH AVENUE 
CHESTNUT HILL, MA 02167 

NAFITOKSOZ 

EARTH RESOURCES LABORATORY, M.I.T. 
42 CARLTON STREET, E34-440 
CAMBRIDGE, MA 02142 


GREG VAN DER VINK 
IRIS 

1616 N. FORT MEYER DRIVE 
SUITE 1050 

ARLINGTON, VA 22209 

TERRY WALLACE 
UNIVERSITY OF ARIZONA 
DEPARTMENT OF GEOSCIENCES 
BUILDING #77 
TUCSON, AZ 85721 

JAMES WHITCOMB 
NSF 

NSF/ISC OPERATIONS/EAR-785 
4201 WILSON BLVD., ROOM785 
ARLINGTON, VA 22230 

JIAKANG XIE 
COLUMBIA UNIVERSITY 
LAMONT DOHERTY EARTH OBSERVATORY 
ROUTE 9W 

PALISADES, NY 10964 

OFFICE OF THE SECRETARY OF DEFENSE 
DDR&E 

WASHINGTON, DC 20330 


TACTEC 

BATTELLE MEMORIAL INSTITUTE 
505 KING AVENUE 

COLUMBUS, OH 43201 (FINAL REPORT) 


PHILLIPS LABORATORY 
ATTN: GPE 

29 RANDOLPH ROAD 5 

HANSCOM AFB, MA 01731-3010 


JEFFRY STEVENS 
MAXWELL TECHNOLOGIES 
P.O. BOX 23558 
SAN DIEGO, CA 92123 


DAVID THOMAS 
ISEE 

29100 AURORA ROAD 
CLEVELAND, OH 44139 


LAWRENCE TURNBULL 

ACIS 

DCI/ACIS 

WASHINGTON, DC 20505 


FRANK VERNON 

UNIVERSITY OF CALIFORNIA, SAN DIEGO 
SCRIPPS INSTITUTION OF OCEANOGRAPHY IGPP, 0225 
9500 GILMAN DRIVE 
LA JOLLA, CA 92093-0225 

DANIEL WEILL 

NSF 

EAR-785 

4201 WILSON BLVD., ROOM 785 
ARLINGTON, VA 22230 

RUSHAN WU 

UNIVERSITY OF CALIFORNIA SANTA CRUZ 
EARTH SCIENCES DEPT. 

1156 HIGH STREET 
SANTA CRUZ, CA 95064 

JAMES E. ZOLLWEG 
BOISE STATE UNIVERSITY 
GEOSCIENCES DEPT. 

1910 UNIVERSITY DRIVE 
BOISE, ID 83725 

DEFENSE TECHNICAL INFORMATION CENTER 
8725 JOHN J. KINGMAN ROAD 
FT BELVOIR, VA 22060-6218 (2 COPIES) 


PHILLIPS LABORATORY 
ATTN: XPG 
29 RANDOLPH ROAD 
HANSCOM AFB, MA 01731-3010 


PHILLIPS LABORATORY 
ATTN: TSML 
5 WRIGHT STREET 
HANSCOM AFB, MA 01731-3004 




PHILLIPS LABORATORY 
ATTN: PL/SUL 
3550 ABERDEEN AVE SE 
KIRTLAND, NM 87117-5776 (2 COPIES)