The ANSS event ID is usp000hsa5 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usp000hsa5/executive.
2010/12/30 12:55:21 40.430 -85.914 5.0 3.8 Indiana
USGS/SLU Moment Tensor Solution
ENS 2010/12/30 12:55:21:0 40.43 -85.91 5.0 3.8 Indiana
Stations used:
IU.WCI IU.WVT NM.BLO NM.SIUC NM.SLM TA.SFIN US.AAM US.BLA
US.HDIL US.JFWS
Filtering commands used:
hp c 0.04 n 3
lp c 0.10 n 3
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 6.76e+21 dyne-cm
Mw = 3.82
Z = 14 km
Plane Strike Dip Rake
NP1 211 81 155
NP2 305 65 10
Principal Axes:
Axis Value Plunge Azimuth
T 6.76e+21 24 165
N 0.00e+00 63 12
P -6.76e+21 11 260
Moment Tensor: (dyne-cm)
Component Value
Mxx 5.07e+21
Mxy -2.49e+21
Mxz -2.23e+21
Myy -5.97e+21
Myz 1.87e+21
Mzz 8.99e+20
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- --------------##############----------
- P -------------################---------
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----############ T #########
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Global CMT Convention Moment Tensor:
R T P
8.99e+20 -2.23e+21 -1.87e+21
-2.23e+21 5.07e+21 2.49e+21
-1.87e+21 2.49e+21 -5.97e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20101230125521/index.html
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STK = 305
DIP = 65
RAKE = 10
MW = 3.82
HS = 14.0
The NDK file is 20101230125521.ndk The waveform inversion is preferred.
Given the availability of digital waveforms for determination of the moment tensor, this section documents the added processing leading to mLg, if appropriate to the region, and ML by application of the respective IASPEI formulae. As a research study, the linear distance term of the IASPEI formula for ML is adjusted to remove a linear distance trend in residuals to give a regionally defined ML. The defined ML uses horizontal component recordings, but the same procedure is applied to the vertical components since there may be some interest in vertical component ground motions. Residual plots versus distance may indicate interesting features of ground motion scaling in some distance ranges. A residual plot of the regionalized magnitude is given as a function of distance and azimuth, since data sets may transcend different wave propagation provinces.
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The focal mechanism was determined using broadband seismic waveforms. The location of the event (star) and the stations used for (red) the waveform inversion are shown in the next figure.
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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's 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 0.04 n 3 lp c 0.10 n 3 br c 0.12 0.25 n 4 p 2The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 0.5 115 70 -20 3.66 0.4985
WVFGRD96 1.0 120 80 -15 3.66 0.5134
WVFGRD96 2.0 120 75 -15 3.70 0.5287
WVFGRD96 3.0 300 70 -15 3.72 0.5332
WVFGRD96 4.0 300 75 -20 3.73 0.5368
WVFGRD96 5.0 300 75 -20 3.74 0.5397
WVFGRD96 6.0 300 75 -20 3.75 0.5408
WVFGRD96 7.0 300 75 -20 3.75 0.5423
WVFGRD96 8.0 300 80 -20 3.76 0.5448
WVFGRD96 9.0 300 80 -20 3.77 0.5471
WVFGRD96 10.0 305 60 15 3.79 0.5619
WVFGRD96 11.0 305 65 15 3.80 0.5651
WVFGRD96 12.0 305 65 10 3.81 0.5657
WVFGRD96 13.0 305 65 10 3.82 0.5673
WVFGRD96 14.0 305 65 10 3.82 0.5675
WVFGRD96 15.0 305 65 10 3.83 0.5674
WVFGRD96 16.0 305 65 10 3.84 0.5666
WVFGRD96 17.0 305 65 10 3.85 0.5642
WVFGRD96 18.0 305 65 10 3.86 0.5638
WVFGRD96 19.0 305 65 10 3.87 0.5616
WVFGRD96 20.0 305 65 10 3.89 0.5569
WVFGRD96 21.0 305 65 10 3.89 0.5524
WVFGRD96 22.0 305 65 10 3.90 0.5467
WVFGRD96 23.0 305 65 15 3.91 0.5416
WVFGRD96 24.0 305 60 15 3.92 0.5340
WVFGRD96 25.0 305 65 15 3.92 0.5278
WVFGRD96 26.0 305 65 20 3.93 0.5208
WVFGRD96 27.0 305 65 20 3.94 0.5133
WVFGRD96 28.0 305 65 20 3.94 0.5070
WVFGRD96 29.0 310 60 25 3.97 0.5014
The best solution is
WVFGRD96 14.0 305 65 10 3.82 0.5675
The mechanism corresponding to the best fit is
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The best fit as a function of depth is given in the following figure:
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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, the velocity model used in the predictions may not be perfect and the epicentral parameters may be be off. 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 0.04 n 3 lp c 0.10 n 3 br c 0.12 0.25 n 4 p 2
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| Figure 3. Waveform comparison for selected depth. Red: observed; Blue - predicted. The time shift with respect to the model prediction is indicated. The percent of fit is also indicated. The time scale is relative to the first trace sample. |
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| Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to the waveforms. 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:
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.
The CUS.model used for the waveform synthetic seismograms and for the surface wave eigenfunctions and dispersion is as follows (The format is in the model96 format of Computer Programs in Seismology).
MODEL.01 CUS Model with Q from simple gamma values ISOTROPIC KGS FLAT EARTH 1-D CONSTANT VELOCITY LINE08 LINE09 LINE10 LINE11 H(KM) VP(KM/S) VS(KM/S) RHO(GM/CC) QP QS ETAP ETAS FREFP FREFS 1.0000 5.0000 2.8900 2.5000 0.172E-02 0.387E-02 0.00 0.00 1.00 1.00 9.0000 6.1000 3.5200 2.7300 0.160E-02 0.363E-02 0.00 0.00 1.00 1.00 10.0000 6.4000 3.7000 2.8200 0.149E-02 0.336E-02 0.00 0.00 1.00 1.00 20.0000 6.7000 3.8700 2.9020 0.000E-04 0.000E-04 0.00 0.00 1.00 1.00 0.0000 8.1500 4.7000 3.3640 0.194E-02 0.431E-02 0.00 0.00 1.00 1.00