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 nm608790 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/nm608790/executive.
2011/04/08 14:56:32 35.261 -92.362 6.2 3.9 Arkansas
USGS/SLU Moment Tensor Solution
ENS 2011/04/08 14:56:32:0 35.26 -92.36 6.2 3.9 Arkansas
Stations used:
AG.FCAR AG.HHAR AG.LCAR AG.WHAR AG.WLAR NM.MGMO NM.MPH
NM.OLIL NM.PLAL NM.SLM NM.UALR NM.USIN NM.X201 TA.O36A
TA.O38A TA.TUL1 TA.U34A TA.V34A TA.W34A TA.W40A TA.Z37A
TA.Z38A TA.Z39A US.KSU1 US.MIAR
Filtering commands used:
hp c 0.02 n 3
lp c 0.10 n 3
Best Fitting Double Couple
Mo = 7.76e+21 dyne-cm
Mw = 3.86
Z = 4 km
Plane Strike Dip Rake
NP1 211 85 -165
NP2 120 75 -5
Principal Axes:
Axis Value Plunge Azimuth
T 7.76e+21 7 345
N 0.00e+00 74 229
P -7.76e+21 14 77
Moment Tensor: (dyne-cm)
Component Value
Mxx 6.72e+21
Mxy -3.59e+21
Mxz 4.93e+20
Myy -6.38e+21
Myz -2.03e+21
Mzz -3.38e+20
T ###########
#### ###############
#######################-----
#######################-------
#######################-----------
#######################-------------
--#####################---------------
-----##################------------- -
-------##############--------------- P -
----------###########---------------- --
-------------#######----------------------
---------------####-----------------------
------------------------------------------
----------------####--------------------
---------------#########----------------
-------------###############----------
-----------#######################--
---------#########################
------########################
----########################
######################
##############
Global CMT Convention Moment Tensor:
R T P
-3.38e+20 4.93e+20 2.03e+21
4.93e+20 6.72e+21 3.59e+21
2.03e+21 3.59e+21 -6.38e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20110408145632/index.html
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STK = 120
DIP = 75
RAKE = -5
MW = 3.86
HS = 4.0
The NDK file is 20110408145632.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:
hp c 0.02 n 3 lp c 0.10 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 0.5 260 10 -20 3.97 0.4334
WVFGRD96 1.0 295 90 -30 3.60 0.4626
WVFGRD96 2.0 120 60 5 3.74 0.5619
WVFGRD96 3.0 120 70 0 3.79 0.6209
WVFGRD96 4.0 120 75 -5 3.86 0.6439
WVFGRD96 5.0 120 85 -5 3.88 0.6382
WVFGRD96 6.0 300 85 5 3.90 0.6151
WVFGRD96 7.0 300 75 10 3.91 0.5859
WVFGRD96 8.0 300 70 10 3.94 0.5604
WVFGRD96 9.0 300 65 10 3.96 0.5322
WVFGRD96 10.0 300 60 10 3.99 0.5076
WVFGRD96 11.0 300 60 10 4.00 0.4805
WVFGRD96 12.0 300 60 10 4.01 0.4552
WVFGRD96 13.0 300 55 10 4.02 0.4332
WVFGRD96 14.0 300 55 10 4.03 0.4153
WVFGRD96 15.0 300 55 10 4.04 0.4012
WVFGRD96 16.0 300 55 10 4.05 0.3898
WVFGRD96 17.0 300 55 10 4.05 0.3802
WVFGRD96 18.0 300 55 10 4.06 0.3717
WVFGRD96 19.0 300 55 10 4.07 0.3640
WVFGRD96 20.0 300 50 10 4.09 0.3576
WVFGRD96 21.0 300 50 10 4.09 0.3504
WVFGRD96 22.0 300 50 10 4.10 0.3439
WVFGRD96 23.0 300 45 10 4.11 0.3381
WVFGRD96 24.0 300 45 10 4.11 0.3327
WVFGRD96 25.0 300 45 10 4.12 0.3280
WVFGRD96 26.0 305 45 25 4.12 0.3244
WVFGRD96 27.0 305 45 25 4.13 0.3220
WVFGRD96 28.0 305 45 25 4.13 0.3196
WVFGRD96 29.0 305 45 25 4.14 0.3173
The best solution is
WVFGRD96 4.0 120 75 -5 3.86 0.6439
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 0.10 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 CUS.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 CUS Model with Q from simple gamma values 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 1.0000 5.0000 2.8900 2.5000 0.172E-02 0.387E-02 0.00 0.00 1.00 1.00 9.0000 6.1000 3.5200 2.7300 0.160E-02 0.363E-02 0.00 0.00 1.00 1.00 10.0000 6.4000 3.7000 2.8200 0.149E-02 0.336E-02 0.00 0.00 1.00 1.00 20.0000 6.7000 3.8700 2.9020 0.000E-04 0.000E-04 0.00 0.00 1.00 1.00 0.0000 8.1500 4.7000 3.3640 0.194E-02 0.431E-02 0.00 0.00 1.00 1.00