Waveform Inversion

The focal mechanism was determined using broadband seismic waveforms. The location of the event and the and stations used for the waveform inversion are shown in the next figure.
Location of broadband stations used for waveform inversion

The program wvfgrd96 was used with good traces observed at short distance to determine the focal mechanism, depth and seismic moment. This technique requires a high quality signal and well determined velocity model for the Green functions. To the extent that these are the quality data, this type of mechanism should be preferred over the radiation pattern technique which requires the separate step of defining the pressure and tension quadrants and the correct strike.

The observed and predicted traces are filtered using the following gsac commands:

hp c 0.02 n 3
lp c 0.10 n 3
The results of this grid search from 0.5 to 39 km depth are as follow:

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    0.5    90    40   -75   4.58 0.2576
WVFGRD96    1.0    85    45    90   4.38 0.1224
WVFGRD96    2.0    85    40    90   4.54 0.1643
WVFGRD96    3.0   335    45    30   4.63 0.1654
WVFGRD96    4.0   330    45    35   4.67 0.2074
WVFGRD96    5.0   330    45    40   4.71 0.2476
WVFGRD96    6.0   330    50    45   4.74 0.2837
WVFGRD96    7.0   325    50    35   4.74 0.3090
WVFGRD96    8.0   340    45    60   4.87 0.3544
WVFGRD96    9.0   350    45    75   4.91 0.3750
WVFGRD96   10.0   310    60   -20   4.87 0.3983
WVFGRD96   11.0   310    60   -20   4.90 0.4347
WVFGRD96   12.0   310    65   -20   4.93 0.4571
WVFGRD96   13.0   310    65   -20   4.95 0.4815
WVFGRD96   14.0   310    65   -20   4.96 0.4915
WVFGRD96   15.0   310    65   -15   4.98 0.4961
WVFGRD96   16.0   310    70   -15   5.00 0.5026
WVFGRD96   17.0   310    70   -15   5.01 0.4978
WVFGRD96   18.0   135    70    -5   5.05 0.4945
WVFGRD96   19.0   130    65   -10   5.05 0.4898
WVFGRD96   20.0   135    70     0   5.07 0.4790
WVFGRD96   21.0   130    65   -10   5.07 0.4709
WVFGRD96   22.0   130    65   -10   5.07 0.4544
WVFGRD96   23.0   130    65    -5   5.08 0.4365
WVFGRD96   24.0   130    65   -10   5.08 0.4239
WVFGRD96   25.0   130    65   -10   5.08 0.4030
WVFGRD96   26.0   130    65    -5   5.09 0.3835
WVFGRD96   27.0   130    65    -5   5.09 0.3692
WVFGRD96   28.0   135    65     5   5.10 0.3546
WVFGRD96   29.0   130    60     0   5.11 0.3498
WVFGRD96   30.0   130    60    -5   5.11 0.3415
WVFGRD96   31.0   130    60    -5   5.11 0.3345
WVFGRD96   32.0   130    60    -5   5.12 0.3297
WVFGRD96   33.0   130    60    -5   5.12 0.3209
WVFGRD96   34.0   130    60    -5   5.12 0.3120
WVFGRD96   35.0   135    65     0   5.13 0.3050
WVFGRD96   36.0   135    65     0   5.14 0.2960
WVFGRD96   37.0   135    70     5   5.15 0.2890
WVFGRD96   38.0   135    70     0   5.16 0.2831
WVFGRD96   39.0   135    75     5   5.17 0.2774

The best solution is

WVFGRD96   16.0   310    70   -15   5.00 0.5026

The mechanism corresponding to the best fit is
Figure 1. Waveform inversion focal mechanism

The best fit as a function of depth is given in the following figure:

Figure 2. Depth sensitivity for waveform mechanism

The comparison of the observed and predicted waveforms is given in the next figure. The red traces are the observed and the blue are the predicted. Each observed-predicted component is plotted to the same scale and peak amplitudes are indicated by the numbers to the left of each trace. A pair of numbers is given in black at the right of each predicted traces. The upper number it the time shift required for maximum correlation between the observed and predicted traces. This time shift is required because the synthetics are not computed at exactly the same distance as the observed and because the velocity model used in the predictions may not be perfect. A positive time shift indicates that the prediction is too fast and should be delayed to match the observed trace (shift to the right in this figure). A negative value indicates that the prediction is too slow. The lower number gives the percentage of variance reduction to characterize the individual goodness of fit (100% indicates a perfect fit).

The bandpass filter used in the processing and for the display was

hp c 0.02 n 3
lp c 0.10 n 3
Figure 3. Waveform comparison for selected depth
Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to thewavefroms. Each solution is plotted as a vector at a given value of strike and dip with the angle of the vector representing the rake angle, measured, with respect to the upward vertical (N) in the figure.

A check on the assumed source location is possible by looking at the time shifts between the observed and predicted traces. The time shifts for waveform matching arise for several reasons:

Assuming only a mislocation, the time shifts are fit to a functional form:

 Time_shift = A + B cos Azimuth + C Sin Azimuth

The time shifts for this inversion lead to the next figure:

The derived shift in origin time and epicentral coordinates are given at the bottom of the figure.