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 ok2021cnhw and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/ok2021cnhw/executive.
2021/02/05 17:48:43 36.289 -97.516 6.7 4.2 Oklahoma
USGS/SLU Moment Tensor Solution
ENS 2021/02/05 17:48:43:0 36.29 -97.52 6.7 4.2 Oklahoma
Stations used:
GS.KS28 GS.OK029 GS.OK038 GS.OK048 GS.OK052 N4.R32B N4.T35B
N4.TUL3 N4.U38B O2.ALVA O2.ARC2 O2.CALT O2.CHAN O2.CRES
O2.DOVR O2.DRIP O2.DRUM O2.DUST O2.ERNS O2.FREE O2.FW03
O2.FW06 O2.GORE O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09
O2.PW18 O2.SC07 O2.SC11 O2.SC13 O2.SC15 O2.SC16 O2.SC19
O2.SC20 O2.SMNL O2.STIG OK.AMES OK.CHOK OK.CROK OK.CSTR
OK.DEOK OK.FNO OK.HTCH OK.MOOR OK.NOKA OK.W35A TX.DRZT
US.CBKS US.KSU1
Filtering commands used:
cut o DIST/3.3 -40 o DIST/3.3 +50
rtr
taper w 0.1
hp c 0.03 n 3
lp c 0.10 n 3
Best Fitting Double Couple
Mo = 1.78e+22 dyne-cm
Mw = 4.10
Z = 5 km
Plane Strike Dip Rake
NP1 45 85 -175
NP2 315 85 -5
Principal Axes:
Axis Value Plunge Azimuth
T 1.78e+22 0 180
N 0.00e+00 83 90
P -1.78e+22 7 270
Moment Tensor: (dyne-cm)
Component Value
Mxx 1.78e+22
Mxy 1.35e+20
Mxz -1.25e+19
Myy -1.75e+22
Myz 2.17e+21
Mzz -2.69e+20
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-----------------#########--------------
-----------------######----------------
P -------------------##------------------
-------------------##------------------
--------------------######----------------
-----------------#########--------------
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######### ##########
##### T ######
Global CMT Convention Moment Tensor:
R T P
-2.69e+20 -1.25e+19 -2.17e+21
-1.25e+19 1.78e+22 -1.35e+20
-2.17e+21 -1.35e+20 -1.75e+22
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210205174843/index.html
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STK = 315
DIP = 85
RAKE = -5
MW = 4.10
HS = 5.0
The NDK file is 20210205174843.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 o DIST/3.3 -40 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.10 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 1.0 315 75 -10 3.83 0.4423
WVFGRD96 2.0 140 85 20 3.97 0.5500
WVFGRD96 3.0 140 90 10 4.02 0.6007
WVFGRD96 4.0 315 80 -10 4.07 0.6247
WVFGRD96 5.0 315 85 -5 4.10 0.6282
WVFGRD96 6.0 315 85 -5 4.13 0.6219
WVFGRD96 7.0 315 85 -5 4.16 0.6108
WVFGRD96 8.0 315 80 -5 4.20 0.5967
WVFGRD96 9.0 315 80 -5 4.21 0.5714
WVFGRD96 10.0 315 80 -5 4.23 0.5455
WVFGRD96 11.0 315 85 -5 4.24 0.5207
WVFGRD96 12.0 315 85 -5 4.25 0.4972
WVFGRD96 13.0 315 85 -5 4.26 0.4748
WVFGRD96 14.0 135 85 -10 4.27 0.4562
WVFGRD96 15.0 135 85 -10 4.28 0.4389
WVFGRD96 16.0 135 85 -10 4.29 0.4222
WVFGRD96 17.0 135 85 -10 4.29 0.4061
WVFGRD96 18.0 315 90 10 4.30 0.3891
WVFGRD96 19.0 135 85 -10 4.31 0.3771
WVFGRD96 20.0 135 85 -10 4.31 0.3644
WVFGRD96 21.0 315 90 10 4.32 0.3522
WVFGRD96 22.0 135 85 -10 4.32 0.3449
WVFGRD96 23.0 135 85 -10 4.33 0.3375
WVFGRD96 24.0 135 80 -10 4.33 0.3309
WVFGRD96 25.0 135 85 -10 4.34 0.3259
WVFGRD96 26.0 135 85 -10 4.34 0.3214
WVFGRD96 27.0 225 80 5 4.34 0.3192
WVFGRD96 28.0 225 80 0 4.35 0.3258
WVFGRD96 29.0 225 85 5 4.36 0.3328
The best solution is
WVFGRD96 5.0 315 85 -5 4.10 0.6282
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 o DIST/3.3 -40 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.10 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