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 us2000d36z and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/us2000d36z/executive.
2018/02/16 13:21:08 36.534 -98.969 6.9 3.7 Oklahoma
USGS/SLU Moment Tensor Solution
ENS 2018/02/16 13:21:08:0 36.53 -98.97 6.9 3.7 Oklahoma
Stations used:
GM.IWM01 GS.KAN14 GS.OK029 GS.OK032 N4.T35B N4.U38B O2.SHWN
OK.CROK OK.CSTR OK.FNO OK.GORE OK.U32A TA.TUL3 TX.DKNS
TX.RTBA US.CBKS US.KSU1
Filtering commands used:
cut o DIST/3.3 -30 o DIST/3.3 +40
rtr
taper w 0.1
hp c 0.03 n 3
lp c 0.08 n 3
Best Fitting Double Couple
Mo = 3.76e+21 dyne-cm
Mw = 3.65
Z = 9 km
Plane Strike Dip Rake
NP1 47 86 150
NP2 140 60 5
Principal Axes:
Axis Value Plunge Azimuth
T 3.76e+21 24 360
N 0.00e+00 60 220
P -3.76e+21 17 98
Moment Tensor: (dyne-cm)
Component Value
Mxx 3.08e+21
Mxy 4.23e+20
Mxz 1.54e+21
Myy -3.36e+21
Myz -1.08e+21
Mzz 2.84e+20
##############
######### ##########
-########### T #############
-############ ##############
----###########################---
-----#########################------
------#######################---------
--------####################------------
--------###################-------------
----------################----------------
-----------#############------------------
------------##########--------------- --
--------------######----------------- P --
--------------###------------------- -
--------------##------------------------
-----------#####----------------------
--------##########------------------
----###############---------------
####################----------
#########################---
######################
##############
Global CMT Convention Moment Tensor:
R T P
2.84e+20 1.54e+21 1.08e+21
1.54e+21 3.08e+21 -4.23e+20
1.08e+21 -4.23e+20 -3.36e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20180216132108/index.html
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STK = 140
DIP = 60
RAKE = 5
MW = 3.65
HS = 9.0
The NDK file is 20180216132108.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 -30 o DIST/3.3 +40 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.08 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 1.0 315 80 -35 3.35 0.4647
WVFGRD96 2.0 295 60 -65 3.54 0.6174
WVFGRD96 3.0 125 35 -35 3.58 0.6979
WVFGRD96 4.0 130 40 -30 3.58 0.7298
WVFGRD96 5.0 135 45 -20 3.58 0.7441
WVFGRD96 6.0 140 55 -5 3.58 0.7608
WVFGRD96 7.0 140 60 0 3.60 0.7688
WVFGRD96 8.0 140 55 0 3.64 0.7732
WVFGRD96 9.0 140 60 5 3.65 0.7741
WVFGRD96 10.0 140 65 10 3.66 0.7675
WVFGRD96 11.0 140 65 10 3.68 0.7552
WVFGRD96 12.0 140 65 10 3.69 0.7427
WVFGRD96 13.0 140 65 10 3.70 0.7246
WVFGRD96 14.0 145 60 10 3.70 0.7060
WVFGRD96 15.0 145 60 10 3.71 0.6870
WVFGRD96 16.0 145 60 15 3.72 0.6675
WVFGRD96 17.0 145 60 15 3.73 0.6479
WVFGRD96 18.0 145 60 15 3.74 0.6290
WVFGRD96 19.0 145 60 15 3.75 0.6087
WVFGRD96 20.0 150 55 20 3.75 0.5913
WVFGRD96 21.0 150 55 20 3.76 0.5730
WVFGRD96 22.0 150 55 20 3.77 0.5550
WVFGRD96 23.0 150 55 20 3.78 0.5381
WVFGRD96 24.0 155 50 25 3.78 0.5220
WVFGRD96 25.0 155 50 25 3.79 0.5063
WVFGRD96 26.0 155 50 25 3.79 0.4912
WVFGRD96 27.0 155 50 25 3.80 0.4764
WVFGRD96 28.0 155 50 25 3.81 0.4618
WVFGRD96 29.0 155 50 30 3.81 0.4484
The best solution is
WVFGRD96 9.0 140 60 5 3.65 0.7741
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 -30 o DIST/3.3 +40 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.08 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