Seismic Remote Sensing for
the Earthquake Source Process and Near-Source Strong Shaking: A Case Study of
the October 16, 1999 Hector Mine Earthquake

Submitted to GRL and
presently under revision

By Douglas Dreger and Anastasia Kaverina

UC Berkeley Seismological Laboratory

A new
methodology to automatically determine the source process and near-source
strong ground motions using regional and local distance data was used to study
the October 16, 1999 Hector Mine earthquake (M_{W}7.1). Broadband displacement
data were used to determine the seismic moment tensor and resolve the fault
plane ambiguity independent of aftershock location and surface faulting
information. The identified NNW
striking fault plane was used to invert for the distribution of fault slip over
a planar surface. The slip model was
used to predict near-fault peak ground velocity, which was found to agree well
with the TriNet ShakeMap, and also with near-fault observations that were not
available at the time of our initial analysis. Our method if automated is
capable of providing near-source strong ground motion information within 30
minutes of the earthquake origin time even in cases where there are few
near-fault recording instruments.

It is possible
to rapidly determine the time, location and magnitude of an earthquake, and
while this information is of value in characterizing the extent of an
earthquake emergency a regional assessment of the extent of strong shaking is
more relevant to emergency response. In southern California the TriNet ShakeMap
(Wald et al., 1999) provides near-realtime characterization of strong ground
motions. Where there is very dense coverage, this approach provides a ‘ground
truth’ assessment of shaking level. We have developed a regional distance
finite fault methodology that makes use of near-realtime broadband data to
determine the gross properties of the earthquake source process. The derived
source parameters are then used to simulate near-fault strong ground motions. In areas where there is very sparse local
coverage (if any at all) the model provides strong ground motion estimates that
include the influences of earthquake-specific source finiteness and rupture
directivity. In areas where there are adequate numbers of local instruments the
method may be integrated with direct observations of strong ground motions
using the approach developed by Wald et al. (1999), and can provide needed
redundancy in the event of seismic telemetry or other network failure that
interrupts the retrieval of near-source strong-motion information. A seamless,
regional scale, shakemap method is needed by the emergency response community
since much of the supporting transportation, water and power infrastructure, as
well as at-risk rural communities, extend beyond areas where dense
instrumentation is likely to be deployed. Our approach is being developed for
the monitoring situation that exists in sparsely instrumented areas of northern
California and for the monitoring situation anticipated for the Advanced National
Seismic System (ANSS, e.g. USGS, 1999). We demonstrate the technique using data
recorded for the recent October 16, 1999 M_{W} 7.1 Hector Mine,
California, earthquake (02:46:44UTC; 34.594 N 116.271 W; depth=6 km) using
broadband data from TriNet (Figure 1).

Figure 1. Map showing regional faults, the surface trace of the fault (bold line), and TriNet stations (triangles). Stations used in the quasi-automatic slip inversion are denoted by open solid triangles. The HEC and BC3 were used to determine a revised slip model. Fault plane solution obtained by inversion of low-frequency waves at the BDSN station KCC (A) is compared to that for an inversion, which included TriNet stations (filled triangles).

We use three component broadband data that may be obtained from either on-scale velocity sensors or co-located strong-motion instruments, such as is available from the Berkeley Digital Seismic Network (BDSN), TERRAscope, and TriNet, to invert the representation theorem (equation 1) for finite source parameters (e.g. Hartzell and Heaton, 1983). The observed seismogram is related to the spatio-temporal integration of slip distributed over the discretized plane where,

_{}, (1)

and *U _{n}* is the n

The finite fault inverse method is initiated from seismic moment tensor input, where the moment tensor is used to define the orientation of the two possible double-couple nodal planes and the moment magnitude is used to scale the source model dimension using the relations of Wells and Coppersmith (1994),

A=10^{
-3.49+0.91*Mw}; L=10^{
-2.44+0.59*Mw}; W=A/L; (2)

where A is the
fault area, L is the fault length, and W is the fault width. Because we do not know the rupture plane *a priori* nor whether the earthquake is
unilateral or bilateral, we double the source dimension and add a 20% safety
factor when constructing the fault model space. This is done to ensure that the
fault model for each of the two possible nodal planes is large enough to
accommodate unilateral rupture in either direction. The fault model is discretized
and the slip for each discrete sub-fault is solved for.

The integration
over dΣ may be transformed to an integration in time by considering a
model of the rupture evolution. In our quasi-realtime application we simplify
the problem in which a sub-fault is allowed to slip only once at the arrival
time of the rupture front. The slip rise time is also assumed to be constant
and is estimated from the total rupture duration T=L/V_{r}, where V_{r}
is the rupture velocity initially assumed to be 80% of the shear wave velocity.
The dislocation rise time is taken to be 0.10*T after the observation of Heaton
(1990). Alternatively, the empirical relationship, T_{R}=4.37*10^{-7}*M_{0}^{1/3}
(rewritten for SI units), of Somerville et al. (1999) may be used. To stabilize
the inversion slip positivity and smoothing constraints are applied (e.g.
Hartzell and Heaton, 1983). Although
the source parameterization is simpler than what is commonly applied to
strong-motion data sets (e.g. Wald and Heaton, 1994), it is appropriate given
the regional distances of the stations used and our objective to use the method
to obtain fault dimension and the gross slip distribution in a timeframe useful
for emergency response.

Any waveform inverse method for source parameters is only as good as the Green’s functions that are assumed to represent regional wave propagation characteristics. We use the SoCal model to calculate complete Green’s functions because it has been shown that the model is effective in describing regional wave propagation in southern California (Dreger and Helmberger, 1993). The application of this method requires that calibrated Green’s functions are available.

Our method
begins with an estimate of the seismic moment tensor. Figure 1 shows the seismic moment tensor solution obtained by
inverting three-component long-period data
(0.02 to 0.05 Hz) from the Berkeley Digital Seismic Network station KCC,
located 407 km NW of the event. We use
this preliminary solution (strike=343^{o}, rake=175^{o}, dip=70^{o},
Mo=4.01*10^{19} Nm, M_{W}=7.0) because it was the one
disseminated via email 33 minutes after the event and it is the moment tensor
solution that we used in our quasi-realtime implementation of the finite source
inversion the morning of the earthquake. This solution agrees well with first
motions and other regional and teleseismic moment tensor solutions. It is very
similar to the moment tensor solution (strike=330^{o}, rake=180^{o},
dip=82^{o}, Mo=2.07*10^{19} Nm) we obtained using the five
stations in Figure 1 including KCC. Based on the initial moment magnitude of
7.0 the source dimension (L) was determined to be 48 km and the total dimension
of our source model, 115 km. Given L and a rupture velocity of 2.91 km./s (80%
of the shear wave velocity at hypocentral depth) the total duration was
estimated to be T=16.8s, and a rise time of 1.7s was obtained. If Somerville et
al. (1999) is used a rise time of 1.5s is obtained. The factor of two lower scalar seismic moment of the 6 station
moment tensor inversion results in a 90 km fault model, which is large enough
to accommodate the slip (below), and rise time of 1.2s. The down-stream
processing depends upon a moment tensor solution for input and an incorrect
moment tensor will produce unreliable results. If the event cannot be
approximated by a point-source for f≤0.05 Hz (~M_{W}7.5) then
alternative input such as aftershocks, and teleseismic moment tensor solutions
may be used.

The first stage of the finite source processing is the identification of the causative fault plane. To accomplish this we perform a series of line source calculations using broadband (0.02 to 5.0 Hz) displacement data for the two double-couple nodal planes of the moment tensor inversion. In the line source calculations the spatial integration over dS in equation 1 is collapsed to an integration over fault length, dL. Figure 2 compares the variance reduction versus rupture velocity for both the NNW-striking and ENE-striking planes. The NNW-striking plane provides a superior fit to the data, and there is a peak in the variance reduction curve for a rupture velocity of 2.6 km/s. Additionally, the line source results indicate that most of the slip in the event was located SSE of the assumed hypocenter. The calculation of 20 line source models (10 rupture velocities for each plane) required 4.2 minutes of processing time on a 200MHz Sun Ultra 1 Workstation.

Figure 2. Percent variance reduction as a function of rupture velocity.

Figure 3. Fault slip. The entire inverse model space is shown and the hypocenter plotted at the center of the model (white circle).

The second stage
inverts the broadband displacement data for planar slip assuming the fault
orientation and rupture velocity determined in stage one. For the Hector Mine earthquake
the finite fault inversion consisted of 440 sub-faults on the 110x25 km^{2}
fault model and required 5.0 minutes of processing time. Figure 3 shows the
distribution of slip that was determined using the 5 three-component stations
that were available in realtime, and by applying a 3s delay in rupture to
account for the emergent onset of the
waveforms. The fit to the displacement data is found to be quite good (Figure
4). Most of the slip in the Hector Mine earthquake was located 5-33km SSE of
the hypocenter (Figure 3), although the asperity 11-18 km to the northwest
indicates a bilateral rupture. There is a deeper patch of slip located
approximately 3 km SSE of the hypocenter that fits large lapse time signal in
the data, but whose depth is likely an artifact of the simplifying assumptions.
The average and peak slip were found to be 138 and 826 cm respectively. The
total seismic moment was determined to be 6.85*10^{19} Nm equaling a
moment magnitude of 7.2. Aftershocks confirm the bilateral nature of the source,
and the dimension of the slip model compares well with the observed 40 km of
surface faulting (Scientists from the USGS, SCEC and CDMG, 2000).

Figure 4. Synthetic displacement seismograms (dashed) for the model shown in Figure 3 are compared to observations (solid). Both the data and synthetics have been bandpass filtered between 0.02 to 5.0 Hz.

The final stage of processing solves the forward representation problem (equation 1) using the derived fault slip distribution to determine near-fault strong ground motions. The SoCal model (Dreger and Helmberger, 1993) was used in the forward simulations. A map of simulated PGV (Figure 5A) is obtained from the geometric mean of bandpass filtered (0.02 to 3.0 Hz) synthetic seismograms. Recall that 0.02 to 5.0 Hz data was used to determine the slip distribution. The predicted PGV are found to agree well with observed values, even though the observations are not band limited and the predictions are. In particular, station HEC has a peak value of 37 cm/s and the station lies between the 20 and 40 cm/s contours of predicted PGV even though it was not used to derive the slip model. The area of greatest predicted shaking, has a peak value of 97.6 cm/s and is in an area SE of the epicenter.

Figure 5. (a) Simulated PGV obtained from the slip map in Figure 3 (contours begin at 20 cm/s and are plotted at intervals of 20 cm/s) is compared to observations (values shown in cm/s). The peak velocity is 97.6 cm/s. The boxes identify the four closest stations whose data was available in realtime, and the surface fault trace is shown in bold. (b) Simulated PGV (circles) is combined with direct observations following the interpolation and site correction method of Wald et al. (1999). Contour intervals are the same as in (a). Small scale variation along contours is an artifact of the site corrections. The peak velocity is 99.5 cm/s.

It is possible to combine the model predictions with direct observations (Figure 5B) to produce a more comprehensive shakemap using the procedure outlined in Wald et al. (1999). The circles (Figure 5B) show the locations where model predictions were used to interpolate the map between observed values. It is satisfying that the 20 and 40 cm/s contours only required slight modification from the model predicted shakemap (Figure 5A).

The allowed source process in the applied method has been simplified considerably. In the quasi-realtime results presented here we applied a 3s delay to account for the emergent onset of the waveforms, and we found that the PGV map is qualitatively similar to that in Figure 5A however the peak in PGV is further to the SE. It has since been found that the Hector Mine earthquake occurred on a curved fault surface (Scientists of the USGS, SCEC and CDMG, 2000). We have examined the spatio-temporal complexity of the event using a 3-segment model to approximate fault curvature, variable slip rake angle, and multiple time windows to allow for variable dislocation rise time. A detailed discussion of the results is beyond the scope of this letter and will be the focus future work (but can be viewed by following this link). We have found, however, that when these complexities are considered the slip tends to focus near the hypocenter and is bilateral in nature. The dislocation rise time varies and can be as large as 6s. Forward predictions of PGV based on the revised model are qualitatively very similar to that given in Figure 5A, except that the peak values are approximately 30% lower. Thus the estimated PGV shakemaps for three-levels of approximation describe an elongate, near-fault region of elevated ground motions and the patterns agree well with the observed near-fault observations.

We
have used near-regional distance displacement seismograms to constrain the
seismic moment tensor, the causative fault plane, and the slip distribution for
the October 16, 1999 Hector Mine earthquake, and have shown that it is possible
to predict near-fault strong shaking from the derived source parameters. Although the software was not operating in
an automated fashion at the time of the earthquake, it was possible to simulate
a realtime application. The
determination of the best fault plane and slip distribution were obtained the
morning of the earthquake, and were subsequently verified by the observed fault
offsets and aftershock locations. This method may be applied in both densely
and sparsely instrumented regions. In densely instrumented regions it may provide
needed redundancy in the event of telemetry or other failure of the primary
realtime strong-motion network. In sparsely instrumented areas it may be the
only viable approach to estimate the level of near-fault strong-ground motions.
Finally, the computer processing times of the individual components of the
method as applied to the Hector Mine earthquake indicate that the method may be
applied in near-realtime and provide strong shaking information within the
30-minute post-earthquake time frame.

**Acknowledgements**

** **

We are grateful to the TriNet organizations for making the data used in this study available in a timely fashion. David Oppenheimer and an anonymous reviewer provided constructive comments that greatly improved the manuscript. The methodology used in this paper was conceived using funding from the USGS NEHRP program (USDI 1434-HQ-GR-02742) and was developed as part of a PGE/PEER Phase II contract (PGE-009566). This is contribution number 00-x of the UC Berkeley Seismological Laboratory.

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