The ANSS event ID is usp000jaep and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usp000jaep/executive.
2011/11/06 09:39:57 35.469 -96.865 5.0 3.7 Oklahoma
USGS/SLU Moment Tensor Solution ENS 2011/11/06 09:39:57:0 35.47 -96.86 5.0 3.7 Oklahoma Stations used: TA.Q35A TA.Q36A TA.R34A TA.R37A TA.R38A TA.S34A TA.S35A TA.S36A TA.S37A TA.S39A TA.T34A TA.T35A TA.T36A TA.T39A TA.TUL1 TA.U35A TA.U36A TA.U39A TA.U40A TA.V35A TA.V36A TA.V37A TA.V38A TA.V39A TA.V40A TA.W35A TA.W36A TA.W37B TA.W39A TA.X35A TA.X36A TA.X38A TA.Y36A TA.Y38A TA.Y39A US.KSU1 US.MIAR Filtering commands used: hp c 0.02 n 3 lp c 0.06 n 3 Best Fitting Double Couple Mo = 3.76e+21 dyne-cm Mw = 3.65 Z = 3 km Plane Strike Dip Rake NP1 320 90 -10 NP2 50 80 -180 Principal Axes: Axis Value Plunge Azimuth T 3.76e+21 7 5 N 0.00e+00 80 140 P -3.76e+21 7 275 Moment Tensor: (dyne-cm) Component Value Mxx 3.65e+21 Mxy 6.43e+20 Mxz 4.20e+20 Myy -3.65e+21 Myz 5.00e+20 Mzz 5.71e+13 ####### T #### ########### ######## -########################### ---########################### -------#########################-- ---------#######################---- ------------###################------- ---------------################--------- ----------------#############----------- ----------------#########-------------- P -----------------######---------------- -------------------##------------------ ----------------------#------------------- ------------------######---------------- ----------------#########--------------- ------------##############------------ --------###################--------- ----#######################------- ###########################--- ###########################- ###################### ############## Global CMT Convention Moment Tensor: R T P 5.71e+13 4.20e+20 -5.00e+20 4.20e+20 3.65e+21 -6.43e+20 -5.00e+20 -6.43e+20 -3.65e+21 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20111106093957/index.html |
STK = 320 DIP = 90 RAKE = -10 MW = 3.65 HS = 3.0
The NDK file is 20111106093957.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.
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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 0.06 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT WVFGRD96 0.5 315 80 -30 3.52 0.3899 WVFGRD96 1.0 320 90 -10 3.52 0.4134 WVFGRD96 2.0 135 70 -15 3.62 0.4824 WVFGRD96 3.0 320 90 -10 3.65 0.4945 WVFGRD96 4.0 140 90 15 3.68 0.4851 WVFGRD96 5.0 140 85 20 3.70 0.4716 WVFGRD96 6.0 140 85 25 3.72 0.4636 WVFGRD96 7.0 140 85 25 3.74 0.4590 WVFGRD96 8.0 140 55 0 3.78 0.4568 WVFGRD96 9.0 140 55 0 3.78 0.4511 WVFGRD96 10.0 140 55 0 3.79 0.4445 WVFGRD96 11.0 140 60 5 3.79 0.4373 WVFGRD96 12.0 140 60 5 3.80 0.4305 WVFGRD96 13.0 140 60 0 3.81 0.4275 WVFGRD96 14.0 140 60 -5 3.81 0.4242 WVFGRD96 15.0 140 60 -5 3.82 0.4201 WVFGRD96 16.0 140 65 -5 3.83 0.4156 WVFGRD96 17.0 140 65 -10 3.83 0.4111 WVFGRD96 18.0 140 65 -10 3.84 0.4069 WVFGRD96 19.0 135 65 -15 3.85 0.4024 WVFGRD96 20.0 135 65 -15 3.86 0.3982 WVFGRD96 21.0 135 65 -15 3.87 0.3938 WVFGRD96 22.0 135 65 -15 3.88 0.3888 WVFGRD96 23.0 135 65 -15 3.88 0.3837 WVFGRD96 24.0 135 70 -15 3.89 0.3789 WVFGRD96 25.0 135 70 -15 3.90 0.3745 WVFGRD96 26.0 135 70 -15 3.90 0.3701 WVFGRD96 27.0 135 70 -15 3.91 0.3658 WVFGRD96 28.0 135 70 -15 3.92 0.3616 WVFGRD96 29.0 135 70 -15 3.93 0.3570
The best solution is
WVFGRD96 3.0 320 90 -10 3.65 0.4945
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 0.06 n 3
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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