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 nm608446 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/nm608446/executive.
2011/02/21 16:17:32 35.265 -92.385 6.0 3.4 Arkansas
USGS/SLU Moment Tensor Solution
ENS 2011/02/21 16:17:32:0 35.26 -92.39 6.0 3.4 Arkansas
Stations used:
AG.WHAR NM.X102 NM.X201 TA.U40A TA.V38A TA.V39A TA.W39A
TA.W40A TA.X40A
Filtering commands used:
hp c 0.05 n 3
lp c 0.10 n 3
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 9.12e+20 dyne-cm
Mw = 3.24
Z = 3 km
Plane Strike Dip Rake
NP1 227 74 -143
NP2 125 55 -20
Principal Axes:
Axis Value Plunge Azimuth
T 9.12e+20 12 352
N 0.00e+00 50 247
P -9.12e+20 37 91
Moment Tensor: (dyne-cm)
Component Value
Mxx 8.56e+20
Mxy -1.02e+20
Mxz 1.95e+20
Myy -5.63e+20
Myz -4.64e+20
Mzz -2.93e+20
### ########
####### T ############
########## ###############
#############################-
##########################--------
-#######################------------
--#####################---------------
----#################-------------------
-----##############---------------------
-------###########------------------------
--------########----------------- ------
---------#####------------------- P ------
-----------##-------------------- ------
----------##----------------------------
---------#####--------------------------
-------#########----------------------
-----#############------------------
---###################------------
##############################
############################
######################
##############
Global CMT Convention Moment Tensor:
R T P
-2.93e+20 1.95e+20 4.64e+20
1.95e+20 8.56e+20 1.02e+20
4.64e+20 1.02e+20 -5.63e+20
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20110221161732/index.html
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STK = 125
DIP = 55
RAKE = -20
MW = 3.24
HS = 3.0
The NDK file is 20110221161732.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 0.05 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 0.5 305 70 -35 3.05 0.4960
WVFGRD96 1.0 305 65 -30 3.08 0.5080
WVFGRD96 2.0 125 50 -15 3.19 0.5389
WVFGRD96 3.0 125 55 -20 3.24 0.5477
WVFGRD96 4.0 130 65 -15 3.24 0.5394
WVFGRD96 5.0 130 75 -15 3.24 0.5160
WVFGRD96 6.0 130 85 -15 3.24 0.4895
WVFGRD96 7.0 130 90 -15 3.26 0.4644
WVFGRD96 8.0 310 75 15 3.26 0.4507
WVFGRD96 9.0 310 60 15 3.27 0.4421
WVFGRD96 10.0 315 50 15 3.30 0.4392
WVFGRD96 11.0 310 55 15 3.32 0.4351
WVFGRD96 12.0 310 55 15 3.33 0.4292
WVFGRD96 13.0 310 50 15 3.34 0.4235
WVFGRD96 14.0 310 50 15 3.36 0.4184
WVFGRD96 15.0 310 50 15 3.37 0.4128
WVFGRD96 16.0 310 50 15 3.37 0.4077
WVFGRD96 17.0 310 50 15 3.38 0.4038
WVFGRD96 18.0 310 50 15 3.39 0.4002
WVFGRD96 19.0 310 50 15 3.40 0.3968
WVFGRD96 20.0 310 45 20 3.42 0.3941
WVFGRD96 21.0 310 45 20 3.43 0.3897
WVFGRD96 22.0 310 45 20 3.44 0.3861
WVFGRD96 23.0 310 40 25 3.45 0.3829
WVFGRD96 24.0 310 40 25 3.45 0.3797
WVFGRD96 25.0 305 40 25 3.46 0.3770
WVFGRD96 26.0 305 40 25 3.47 0.3743
WVFGRD96 27.0 300 40 25 3.48 0.3721
WVFGRD96 28.0 300 40 25 3.49 0.3696
WVFGRD96 29.0 300 40 25 3.49 0.3673
The best solution is
WVFGRD96 3.0 125 55 -20 3.24 0.5477
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 0.05 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