The ANSS event ID is NONE and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/NONE/executive.
2010/12/19 05:05:28 35.824 -96.822 5.0 3.60 Oklahoma
USGS/SLU Moment Tensor Solution
ENS 2010/12/19 05:05:28:0 35.82 -96.82 5.0 3.6 Oklahoma
Stations used:
TA.234A TA.M31A TA.M33A TA.M35A TA.N38A TA.O33A TA.O35A
TA.P31A TA.P32A TA.P34A TA.P35A TA.P37A TA.Q30A TA.Q31A
TA.Q32A TA.Q35A TA.Q37A TA.R29A TA.R32A TA.R33A TA.R34A
TA.R35A TA.R36A TA.R37A TA.S33A TA.S34A TA.S35A TA.S36A
TA.S37A TA.T32A TA.T33A TA.T34A TA.T35A TA.T36A TA.T37A
TA.U34A TA.U35A TA.U36A TA.V36A TA.W33A TA.W35A TA.W36A
TA.WHTX US.WMOK
Filtering commands used:
hp c 0.03 n 4
lp c 0.06 n 4
Best Fitting Double Couple
Mo = 1.12e+21 dyne-cm
Mw = 3.30
Z = 2 km
Plane Strike Dip Rake
NP1 93 45 -95
NP2 280 45 -85
Principal Axes:
Axis Value Plunge Azimuth
T 1.12e+21 0 186
N 0.00e+00 4 96
P -1.12e+21 86 278
Moment Tensor: (dyne-cm)
Component Value
Mxx 1.11e+21
Mxy 1.26e+20
Mxz -1.20e+19
Myy 1.01e+19
Myz 6.81e+19
Mzz -1.12e+21
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#######-----------------############
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##-------------------------------#######
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---------------- -------------------####
---------------- P --------------------###
#--------------- ---------------------##
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###########---------------##########
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####### ############
### T ########
Global CMT Convention Moment Tensor:
R T P
-1.12e+21 -1.20e+19 -6.81e+19
-1.20e+19 1.11e+21 -1.26e+20
-6.81e+19 -1.26e+20 1.01e+19
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20101219050528/index.html
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STK = 280
DIP = 45
RAKE = -85
MW = 3.30
HS = 2.0
The NDK file is 20101219050528.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.
Left: ML computed using the IASPEI formula for Horizontal components. Center: ML residuals computed using a modified IASPEI formula that accounts for path specific attenuation; the values used for the trimmed mean are indicated. The ML relation used for each figure is given at the bottom of each plot.
Right: Residuals from new relation as a function of distance and azimuth.
Left: ML computed using the IASPEI formula for Vertical components (research). Center: ML residuals computed using a modified IASPEI formula that accounts for path specific attenuation; the values used for the trimmed mean are indicated. The ML relation used for each figure is given at the bottom of each plot.
Right: Residuals from new relation as a function of distance and azimuth.
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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 0.03 n 4 lp c 0.06 n 4The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 0.5 115 55 -65 3.22 0.4532
WVFGRD96 1.0 285 40 -75 3.26 0.4680
WVFGRD96 2.0 280 45 -85 3.30 0.4815
WVFGRD96 3.0 100 45 -85 3.36 0.4778
WVFGRD96 4.0 100 40 -85 3.40 0.4323
WVFGRD96 5.0 295 25 -65 3.44 0.3938
WVFGRD96 6.0 85 70 -105 3.42 0.3809
WVFGRD96 7.0 305 25 -55 3.40 0.3739
WVFGRD96 8.0 310 25 -50 3.45 0.3849
WVFGRD96 9.0 310 25 -50 3.44 0.3821
WVFGRD96 10.0 315 25 -40 3.41 0.3810
WVFGRD96 11.0 325 30 -30 3.41 0.3806
WVFGRD96 12.0 335 35 -15 3.40 0.3820
WVFGRD96 13.0 345 45 10 3.42 0.3851
WVFGRD96 14.0 345 45 15 3.43 0.3894
WVFGRD96 15.0 345 45 20 3.43 0.3920
WVFGRD96 16.0 345 45 20 3.43 0.3943
WVFGRD96 17.0 345 50 25 3.45 0.3960
WVFGRD96 18.0 345 50 25 3.45 0.3970
WVFGRD96 19.0 345 50 25 3.46 0.3971
WVFGRD96 20.0 345 50 25 3.46 0.3965
WVFGRD96 21.0 345 50 25 3.48 0.3931
WVFGRD96 22.0 345 50 30 3.48 0.3910
WVFGRD96 23.0 345 50 30 3.49 0.3885
WVFGRD96 24.0 345 50 30 3.49 0.3853
WVFGRD96 25.0 345 50 30 3.50 0.3817
WVFGRD96 26.0 345 50 30 3.50 0.3776
WVFGRD96 27.0 350 50 35 3.51 0.3732
WVFGRD96 28.0 345 55 35 3.52 0.3686
WVFGRD96 29.0 345 55 35 3.53 0.3637
The best solution is
WVFGRD96 2.0 280 45 -85 3.30 0.4815
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 0.03 n 4 lp c 0.06 n 4
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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 WUS.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
Model after 8 iterations
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
1.9000 3.4065 2.0089 2.2150 0.302E-02 0.679E-02 0.00 0.00 1.00 1.00
6.1000 5.5445 3.2953 2.6089 0.349E-02 0.784E-02 0.00 0.00 1.00 1.00
13.0000 6.2708 3.7396 2.7812 0.212E-02 0.476E-02 0.00 0.00 1.00 1.00
19.0000 6.4075 3.7680 2.8223 0.111E-02 0.249E-02 0.00 0.00 1.00 1.00
0.0000 7.9000 4.6200 3.2760 0.164E-10 0.370E-10 0.00 0.00 1.00 1.00