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 usp000h65q and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usp000h65q/executive.
2010/01/15 15:18:26 35.576 -97.250 8.0 3.8 Oklahoma
USGS/SLU Moment Tensor Solution
ENS 2010/01/15 15:18:26:0 35.58 -97.25 8.0 3.8 Oklahoma
Stations used:
NM.MGMO NM.UALR TA.133A TA.135A TA.234A TA.ABTX TA.P31A
TA.P32A TA.P33A TA.Q30A TA.Q31A TA.Q32A TA.Q33A TA.R30A
TA.R31A TA.R32A TA.R33A TA.S29A TA.S30A TA.S31A TA.S32A
TA.S33A TA.T29A TA.T30A TA.T31A TA.T32A TA.T33A TA.TUL1
TA.U30A TA.U31A TA.U32A TA.U33A TA.U34A TA.V32A TA.V33A
TA.V34A TA.W31A TA.W33A TA.W34A TA.WHTX TA.X30A TA.X33A
TA.X34A TA.Y31A TA.Y33A TA.Y34A TA.Z31A TA.Z32A TA.Z33A
TA.Z34A TA.Z35A US.AMTX US.KSU1 US.WMOK
Filtering commands used:
cut o DIST/3.3 -20 o DIST/3.3 +50
rtr
taper w 0.1
hp c 0.03 n 3
lp c 0.10 n 3
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 6.76e+21 dyne-cm
Mw = 3.82
Z = 8 km
Plane Strike Dip Rake
NP1 233 85 155
NP2 325 65 5
Principal Axes:
Axis Value Plunge Azimuth
T 6.76e+21 21 186
N 0.00e+00 65 43
P -6.76e+21 14 282
Moment Tensor: (dyne-cm)
Component Value
Mxx 5.59e+21
Mxy 1.88e+21
Mxz -2.55e+21
Myy -6.04e+21
Myz 1.32e+21
Mzz 4.51e+20
##############
######################
------######################
----------####################
---------------##################-
------------------#############-----
--------------------#########---------
- -------------------####-------------
- P --------------------#---------------
-- ------------------####---------------
--------------------########--------------
------------------###########-------------
----------------##############------------
------------##################----------
----------####################----------
-------#######################--------
----##########################------
-############################-----
############ ############---
########### T ############--
######## ###########
##############
Global CMT Convention Moment Tensor:
R T P
4.51e+20 -2.55e+21 -1.32e+21
-2.55e+21 5.59e+21 -1.88e+21
-1.32e+21 -1.88e+21 -6.04e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20100115151826/index.html
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STK = 325
DIP = 65
RAKE = 5
MW = 3.82
HS = 8.0
The NDK file is 20100115151826.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 -20 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.10 n 3 br c 0.12 0.25 n 4 p 2The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 1.0 325 90 15 3.42 0.3550
WVFGRD96 2.0 325 90 0 3.60 0.5929
WVFGRD96 3.0 145 90 5 3.66 0.6818
WVFGRD96 4.0 325 85 -10 3.70 0.7261
WVFGRD96 5.0 325 70 -5 3.74 0.7473
WVFGRD96 6.0 325 65 5 3.77 0.7593
WVFGRD96 7.0 325 70 5 3.79 0.7661
WVFGRD96 8.0 325 65 5 3.82 0.7691
WVFGRD96 9.0 325 65 5 3.84 0.7683
WVFGRD96 10.0 325 65 5 3.85 0.7660
WVFGRD96 11.0 325 70 5 3.86 0.7623
WVFGRD96 12.0 325 70 5 3.87 0.7589
WVFGRD96 13.0 325 70 5 3.88 0.7541
WVFGRD96 14.0 325 80 15 3.89 0.7489
WVFGRD96 15.0 325 85 15 3.90 0.7428
WVFGRD96 16.0 325 80 15 3.92 0.7368
WVFGRD96 17.0 325 80 15 3.93 0.7296
WVFGRD96 18.0 325 85 15 3.94 0.7217
WVFGRD96 19.0 325 85 15 3.95 0.7135
WVFGRD96 20.0 325 80 10 3.95 0.7053
WVFGRD96 21.0 325 80 10 3.96 0.6958
WVFGRD96 22.0 325 80 10 3.97 0.6870
WVFGRD96 23.0 325 80 10 3.98 0.6767
WVFGRD96 24.0 325 80 10 3.99 0.6666
WVFGRD96 25.0 325 80 10 3.99 0.6553
WVFGRD96 26.0 325 80 10 4.00 0.6430
WVFGRD96 27.0 325 70 -5 4.01 0.6327
WVFGRD96 28.0 325 70 -5 4.02 0.6222
WVFGRD96 29.0 330 65 5 4.03 0.6131
The best solution is
WVFGRD96 8.0 325 65 5 3.82 0.7691
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 -20 o DIST/3.3 +50 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.10 n 3 br c 0.12 0.25 n 4 p 2
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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