The ANSS event ID is usp000hyz9 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usp000hyz9/executive.
2011/03/31 05:41:30 35.439 -96.530 1.1 3.2 Oklahoma
USGS/SLU Moment Tensor Solution ENS 2011/03/31 05:41:30:0 35.44 -96.53 1.1 3.2 Oklahoma Stations used: TA.T34A TA.T35A TA.TUL1 TA.U34A TA.U37A TA.V35A TA.V36A TA.W35A TA.W36A TA.W38A TA.X36A TA.X37A TA.Y36A TA.Y37A Filtering commands used: hp c 0.02 n 3 lp c 0.10 n 3 br c 0.12 0.25 n 4 p 2 Best Fitting Double Couple Mo = 7.41e+20 dyne-cm Mw = 3.18 Z = 4 km Plane Strike Dip Rake NP1 130 90 20 NP2 40 70 180 Principal Axes: Axis Value Plunge Azimuth T 7.41e+20 14 357 N 0.00e+00 70 130 P -7.41e+20 14 263 Moment Tensor: (dyne-cm) Component Value Mxx 6.86e+20 Mxy -1.21e+20 Mxz 1.94e+20 Myy -6.86e+20 Myz 1.63e+20 Mzz -2.22e+13 #### ####### ######## T ########### ########### #############- ############################-- ---###########################---- ------########################------ ---------#####################-------- ------------##################---------- --------------###############----------- ------------------###########------------- --------------------########-------------- -- -----------------#####--------------- -- P -------------------#----------------- - -------------------###-------------- ---------------------#######------------ ------------------###########--------- ---------------###############------ ------------###################--- -------####################### -########################### ###################### ############## Global CMT Convention Moment Tensor: R T P -2.22e+13 1.94e+20 -1.63e+20 1.94e+20 6.86e+20 1.21e+20 -1.63e+20 1.21e+20 -6.86e+20 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20110331054130/index.html |
STK = 130 DIP = 90 RAKE = 20 MW = 3.18 HS = 4.0
The NDK file is 20110331054130.ndk The waveform inversion is preferred.
The following compares this source inversion to those provided by others. The purpose is to look for major differences and also to note slight differences that might be inherent to the processing procedure. For completeness the USGS/SLU solution is repeated from above.
USGS/SLU Moment Tensor Solution ENS 2011/03/31 05:41:30:0 35.44 -96.53 1.1 3.2 Oklahoma Stations used: TA.T34A TA.T35A TA.TUL1 TA.U34A TA.U37A TA.V35A TA.V36A TA.W35A TA.W36A TA.W38A TA.X36A TA.X37A TA.Y36A TA.Y37A Filtering commands used: hp c 0.02 n 3 lp c 0.10 n 3 br c 0.12 0.25 n 4 p 2 Best Fitting Double Couple Mo = 7.41e+20 dyne-cm Mw = 3.18 Z = 4 km Plane Strike Dip Rake NP1 130 90 20 NP2 40 70 180 Principal Axes: Axis Value Plunge Azimuth T 7.41e+20 14 357 N 0.00e+00 70 130 P -7.41e+20 14 263 Moment Tensor: (dyne-cm) Component Value Mxx 6.86e+20 Mxy -1.21e+20 Mxz 1.94e+20 Myy -6.86e+20 Myz 1.63e+20 Mzz -2.22e+13 #### ####### ######## T ########### ########### #############- ############################-- ---###########################---- ------########################------ ---------#####################-------- ------------##################---------- --------------###############----------- ------------------###########------------- --------------------########-------------- -- -----------------#####--------------- -- P -------------------#----------------- - -------------------###-------------- ---------------------#######------------ ------------------###########--------- ---------------###############------ ------------###################--- -------####################### -########################### ###################### ############## Global CMT Convention Moment Tensor: R T P -2.22e+13 1.94e+20 -1.63e+20 1.94e+20 6.86e+20 1.21e+20 -1.63e+20 1.21e+20 -6.86e+20 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20110331054130/index.html |
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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: mLg computed using the IASPEI formula. Center: mLg residuals versus epicentral distance ; the values used for the trimmed mean magnitude estimate are indicated.
Right: residuals as a function of distance and azimuth.
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 0.02 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 0.5 295 70 -25 2.92 0.3123 WVFGRD96 1.0 300 80 -10 2.94 0.3479 WVFGRD96 2.0 310 85 0 3.08 0.5103 WVFGRD96 3.0 130 90 10 3.14 0.5493 WVFGRD96 4.0 130 90 20 3.18 0.5558 WVFGRD96 5.0 135 70 25 3.22 0.5523 WVFGRD96 6.0 140 65 30 3.25 0.5504 WVFGRD96 7.0 140 65 25 3.26 0.5458 WVFGRD96 8.0 140 60 30 3.31 0.5408 WVFGRD96 9.0 140 60 25 3.31 0.5361 WVFGRD96 10.0 140 65 25 3.31 0.5313 WVFGRD96 11.0 135 70 20 3.32 0.5271 WVFGRD96 12.0 315 75 30 3.35 0.5223 WVFGRD96 13.0 315 75 30 3.36 0.5190 WVFGRD96 14.0 315 75 30 3.38 0.5143 WVFGRD96 15.0 315 75 25 3.38 0.5090 WVFGRD96 16.0 125 70 -25 3.39 0.5039 WVFGRD96 17.0 125 70 -25 3.40 0.4978 WVFGRD96 18.0 130 70 -20 3.39 0.4914 WVFGRD96 19.0 130 70 -20 3.40 0.4840 WVFGRD96 20.0 130 70 -20 3.40 0.4762 WVFGRD96 21.0 130 70 -20 3.41 0.4693 WVFGRD96 22.0 130 70 -20 3.42 0.4621 WVFGRD96 23.0 130 70 -20 3.42 0.4550 WVFGRD96 24.0 130 70 -20 3.43 0.4494 WVFGRD96 25.0 140 60 20 3.44 0.4441 WVFGRD96 26.0 140 60 25 3.46 0.4388 WVFGRD96 27.0 140 60 20 3.46 0.4342 WVFGRD96 28.0 140 60 20 3.46 0.4295 WVFGRD96 29.0 140 60 20 3.47 0.4244
The best solution is
WVFGRD96 4.0 130 90 20 3.18 0.5558
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 0.02 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 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