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.
The ANSS event ID is usc000p7n7 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usc000p7n7/executive.
2014/04/06 14:58:54 35.890 -97.269 5.0 3.8 Oklahoma
USGS/SLU Moment Tensor Solution
ENS 2014/04/06 14:58:54:0 35.89 -97.27 5.0 3.8 Oklahoma
Stations used:
AG.HHAR AG.WLAR GS.OK025 GS.OK026 GS.OK027 GS.OK028
GS.OK029 N4.237B N4.P38B N4.R32B N4.R40B N4.S39B N4.T35B
N4.T42B N4.U38B N4.Z35B OK.CROK OK.FNO OK.U32A TA.U40A
US.CBKS US.KSU1 US.MIAR US.WMOK
Filtering commands used:
cut a -30 a 180
rtr
taper w 0.1
hp c 0.03 n 3
lp c 0.06 n 3
Best Fitting Double Couple
Mo = 4.47e+21 dyne-cm
Mw = 3.70
Z = 4 km
Plane Strike Dip Rake
NP1 320 90 10
NP2 230 80 180
Principal Axes:
Axis Value Plunge Azimuth
T 4.47e+21 7 185
N 0.00e+00 80 320
P -4.47e+21 7 95
Moment Tensor: (dyne-cm)
Component Value
Mxx 4.33e+21
Mxy 7.64e+20
Mxz -4.99e+20
Myy -4.33e+21
Myz -5.94e+20
Mzz -6.78e+13
##############
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---------------#########----------------
----------------######------------------
-------------------#----------------------
------------------##-------------------
----------------######----------------- P
--------------#########----------------
-----------#############----------------
---------################---------------
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--#########################-------
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#### T #######
Global CMT Convention Moment Tensor:
R T P
-6.78e+13 -4.99e+20 5.94e+20
-4.99e+20 4.33e+21 -7.64e+20
5.94e+20 -7.64e+20 -4.33e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20140406145854/index.html
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STK = 320
DIP = 90
RAKE = 10
MW = 3.70
HS = 4.0
The NDK file is 20140406145854.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.
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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:
cut a -30 a 180 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.06 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 1.0 140 90 -10 3.52 0.4243
WVFGRD96 2.0 140 90 -15 3.63 0.5018
WVFGRD96 3.0 320 90 15 3.67 0.5258
WVFGRD96 4.0 320 90 10 3.70 0.5282
WVFGRD96 5.0 145 90 -15 3.73 0.5206
WVFGRD96 6.0 145 90 -15 3.75 0.5105
WVFGRD96 7.0 145 90 -15 3.77 0.4985
WVFGRD96 8.0 325 80 15 3.80 0.4906
WVFGRD96 9.0 325 75 15 3.82 0.4775
WVFGRD96 10.0 325 70 10 3.83 0.4658
WVFGRD96 11.0 325 70 10 3.84 0.4549
WVFGRD96 12.0 325 70 10 3.86 0.4458
WVFGRD96 13.0 325 70 10 3.87 0.4358
WVFGRD96 14.0 325 70 10 3.87 0.4268
WVFGRD96 15.0 325 70 10 3.88 0.4178
WVFGRD96 16.0 325 70 10 3.89 0.4090
WVFGRD96 17.0 330 70 15 3.90 0.4013
WVFGRD96 18.0 330 70 15 3.91 0.3938
WVFGRD96 19.0 330 70 15 3.92 0.3866
WVFGRD96 20.0 330 70 15 3.93 0.3797
WVFGRD96 21.0 230 80 -10 3.92 0.3752
WVFGRD96 22.0 230 80 -10 3.93 0.3791
WVFGRD96 23.0 230 80 -10 3.94 0.3820
WVFGRD96 24.0 230 80 -10 3.95 0.3839
WVFGRD96 25.0 230 80 -10 3.96 0.3849
WVFGRD96 26.0 230 80 -5 3.96 0.3849
WVFGRD96 27.0 230 80 -5 3.97 0.3845
WVFGRD96 28.0 230 80 -5 3.98 0.3842
WVFGRD96 29.0 230 80 -5 3.98 0.3829
The best solution is
WVFGRD96 4.0 320 90 10 3.70 0.5282
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
cut a -30 a 180 rtr taper w 0.1 hp c 0.03 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