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 nm608392 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/nm608392/executive.
2011/02/18 04:59:50 35.257 -92.370 5.0 3.9 Arkansas
USGS/SLU Moment Tensor Solution
ENS 2011/02/18 04:59:50:0 35.26 -92.37 5.0 3.9 Arkansas
Stations used:
AG.FCAR AG.HHAR AG.LCAR AG.WHAR AG.WLAR NM.MGMO NM.MPH
NM.OLIL NM.PBMO NM.PVMO NM.SIUC NM.SLM NM.UALR NM.USIN
NM.UTMT NM.X102 NM.X201 TA.137A TA.138A TA.139A TA.141A
TA.238A TA.240A TA.O38A TA.O39A TA.P40A TA.Q39A TA.Q40A
TA.R35A TA.R36A TA.R37A TA.R40A TA.S34A TA.S35A TA.S36A
TA.S38A TA.S39A TA.S40A TA.T34A TA.T35A TA.T36A TA.T37A
TA.T38A TA.T40A TA.TUL1 TA.U34A TA.U35A TA.U36A TA.U38A
TA.U39A TA.U40A TA.V33A TA.V34A TA.V35A TA.V36A TA.V37A
TA.V38A TA.V39A TA.W34A TA.W35A TA.W36A TA.W37B TA.W39A
TA.W40A TA.X34A TA.X36A TA.X37A TA.X38A TA.X39A TA.X40A
TA.Y36A TA.Y37A TA.Y38A TA.Y39A TA.Y40A TA.Z38A TA.Z39A
TA.Z40A US.KSU1 US.LRAL US.MIAR US.OXF
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
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 7.00e+21 dyne-cm
Mw = 3.83
Z = 4 km
Plane Strike Dip Rake
NP1 202 85 -160
NP2 110 70 -5
Principal Axes:
Axis Value Plunge Azimuth
T 7.00e+21 11 334
N 0.00e+00 69 214
P -7.00e+21 17 68
Moment Tensor: (dyne-cm)
Component Value
Mxx 4.56e+21
Mxy -4.89e+21
Mxz 3.76e+20
Myy -4.17e+21
Myz -2.40e+21
Mzz -3.92e+20
##############
# T ##############----
#### #############--------
####################----------
#####################-------------
#####################---------------
#####################------------- -
-####################-------------- P --
---##################-------------- --
------###############---------------------
--------############----------------------
-----------########-----------------------
--------------#####-----------------------
-----------------#----------------------
----------------########----------------
---------------#######################
-------------#######################
-----------#######################
---------#####################
-------#####################
----##################
##############
Global CMT Convention Moment Tensor:
R T P
-3.92e+20 3.76e+20 2.40e+21
3.76e+20 4.56e+21 4.89e+21
2.40e+21 4.89e+21 -4.17e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20110218045950/index.html
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STK = 110
DIP = 70
RAKE = -5
MW = 3.83
HS = 4.0
The NDK file is 20110218045950.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 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 0.5 110 90 25 3.65 0.5500
WVFGRD96 1.0 285 75 -35 3.72 0.5801
WVFGRD96 2.0 110 55 0 3.79 0.6298
WVFGRD96 3.0 110 60 -5 3.83 0.6587
WVFGRD96 4.0 110 70 -5 3.83 0.6630
WVFGRD96 5.0 110 75 -5 3.85 0.6513
WVFGRD96 6.0 290 90 10 3.85 0.6286
WVFGRD96 7.0 295 75 5 3.85 0.6176
WVFGRD96 8.0 295 70 5 3.87 0.6117
WVFGRD96 9.0 295 70 5 3.89 0.6032
WVFGRD96 10.0 295 65 5 3.91 0.5936
WVFGRD96 11.0 295 65 5 3.92 0.5791
WVFGRD96 12.0 295 60 5 3.94 0.5646
WVFGRD96 13.0 290 65 5 3.94 0.5516
WVFGRD96 14.0 290 65 5 3.95 0.5403
WVFGRD96 15.0 290 65 5 3.96 0.5297
WVFGRD96 16.0 290 65 5 3.96 0.5198
WVFGRD96 17.0 290 65 5 3.97 0.5114
WVFGRD96 18.0 290 65 5 3.98 0.5032
WVFGRD96 19.0 290 65 5 3.98 0.4955
WVFGRD96 20.0 290 60 5 4.00 0.4874
WVFGRD96 21.0 290 60 5 4.01 0.4799
WVFGRD96 22.0 290 60 5 4.01 0.4727
WVFGRD96 23.0 290 60 5 4.02 0.4657
WVFGRD96 24.0 290 60 5 4.03 0.4588
WVFGRD96 25.0 290 60 5 4.03 0.4522
WVFGRD96 26.0 290 55 5 4.04 0.4457
WVFGRD96 27.0 290 55 5 4.05 0.4402
WVFGRD96 28.0 290 55 5 4.06 0.4346
WVFGRD96 29.0 290 55 5 4.06 0.4293
The best solution is
WVFGRD96 4.0 110 70 -5 3.83 0.6630
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 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 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