The ANSS event ID is us10003pl4 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/us10003pl4/executive.
2015/10/19 04:55:29 36.735 -97.840 5.6 3.1 Oklahoma
USGS/SLU Moment Tensor Solution ENS 2015/10/19 04:55:29:0 36.74 -97.84 5.6 3.1 Oklahoma Stations used: GS.KAN01 GS.KAN06 GS.KAN08 GS.KAN12 GS.KAN14 GS.KAN16 GS.KAN17 GS.KS21 GS.OK025 GS.OK029 GS.OK032 N4.T35B OK.BCOK OK.CROK OK.FNO OK.X37A Filtering commands used: cut o DIST/3.3 -20 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.04 n 3 lp c 0.10 n 3 Best Fitting Double Couple Mo = 6.03e+20 dyne-cm Mw = 3.12 Z = 3 km Plane Strike Dip Rake NP1 50 90 -175 NP2 320 85 0 Principal Axes: Axis Value Plunge Azimuth T 6.03e+20 4 185 N 0.00e+00 85 50 P -6.03e+20 4 275 Moment Tensor: (dyne-cm) Component Value Mxx 5.91e+20 Mxy 1.04e+20 Mxz -4.02e+19 Myy -5.91e+20 Myz 3.38e+19 Mzz 0.00e+00 ############## ###################### -########################### ----########################## --------#######################--- -----------###################------ -------------################--------- ----------------############------------ ------------------########-------------- ------------------####------------------ P ---------------------------------------- ------------------###------------------- ------------------#######----------------- --------------###########--------------- ------------###############------------- ---------##################----------- ------######################-------- ---#########################------ ###########################--- ###########################- ######## ########### #### T ####### Global CMT Convention Moment Tensor: R T P 0.00e+00 -4.02e+19 -3.38e+19 -4.02e+19 5.91e+20 -1.04e+20 -3.38e+19 -1.04e+20 -5.91e+20 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20151019045529/index.html |
STK = 320 DIP = 85 RAKE = 0 MW = 3.12 HS = 3.0
The NDK file is 20151019045529.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: 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.
![]() |
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.
![]() |
|
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:
cut o DIST/3.3 -20 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.04 n 3 lp c 0.10 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT WVFGRD96 1.0 320 80 -5 2.92 0.4381 WVFGRD96 2.0 320 75 -15 3.06 0.5179 WVFGRD96 3.0 320 85 0 3.12 0.5421 WVFGRD96 4.0 320 85 5 3.17 0.5113 WVFGRD96 5.0 320 80 5 3.19 0.4732 WVFGRD96 6.0 325 75 10 3.20 0.4536 WVFGRD96 7.0 145 75 15 3.23 0.4384 WVFGRD96 8.0 145 75 25 3.28 0.4304 WVFGRD96 9.0 325 75 15 3.28 0.4187 WVFGRD96 10.0 145 70 20 3.31 0.4064 WVFGRD96 11.0 145 70 20 3.32 0.3994 WVFGRD96 12.0 145 70 20 3.34 0.3954 WVFGRD96 13.0 150 65 20 3.34 0.3908 WVFGRD96 14.0 150 65 15 3.35 0.3851 WVFGRD96 15.0 150 65 15 3.36 0.3773 WVFGRD96 16.0 145 65 15 3.37 0.3683 WVFGRD96 17.0 150 60 10 3.37 0.3590 WVFGRD96 18.0 145 60 10 3.38 0.3493 WVFGRD96 19.0 325 75 25 3.40 0.3430 WVFGRD96 20.0 225 60 -25 3.41 0.3382 WVFGRD96 21.0 225 60 -25 3.42 0.3375 WVFGRD96 22.0 225 60 -25 3.43 0.3335 WVFGRD96 23.0 225 60 -25 3.44 0.3295 WVFGRD96 24.0 225 55 -25 3.45 0.3231 WVFGRD96 25.0 225 55 -25 3.46 0.3170 WVFGRD96 26.0 50 70 -35 3.44 0.3106 WVFGRD96 27.0 55 75 -35 3.44 0.3126 WVFGRD96 28.0 55 75 -35 3.45 0.3157 WVFGRD96 29.0 55 75 -35 3.45 0.3168
The best solution is
WVFGRD96 3.0 320 85 0 3.12 0.5421
The mechanism corresponding to the best fit is
![]() |
|
The best fit as a function of depth is given in the following figure:
![]() |
|
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
cut o DIST/3.3 -20 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.04 n 3 lp c 0.10 n 3
![]() |
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. |
![]() |
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