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 usp000jakf and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usp000jakf/executive.
2011/11/08 19:05:17 35.526 -96.770 3.0 3.5 Oklahoma
USGS/SLU Moment Tensor Solution
ENS 2011/11/08 19:05:17:0 35.53 -96.77 3.0 3.5 Oklahoma
Stations used:
TA.S38A TA.T35A TA.T36A TA.T39A TA.TUL1 TA.U35A TA.U40A
TA.V35A TA.V36A TA.V37A TA.V40A TA.W35A TA.W40A TA.WHTX
TA.X35A TA.X36A TA.X37A TA.X38A TA.Y35A TA.Y36A TA.Y37A
TA.Y40A US.KSU1 US.WMOK
Filtering commands used:
hp c 0.02 n 3
lp c 0.10 n 3
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 2.02e+21 dyne-cm
Mw = 3.47
Z = 8 km
Plane Strike Dip Rake
NP1 135 80 25
NP2 40 65 169
Principal Axes:
Axis Value Plunge Azimuth
T 2.02e+21 25 0
N 0.00e+00 63 155
P -2.02e+21 10 266
Moment Tensor: (dyne-cm)
Component Value
Mxx 1.66e+21
Mxy -1.46e+20
Mxz 7.91e+20
Myy -1.95e+21
Myz 3.42e+20
Mzz 2.92e+20
##############
########## #########
############# T ###########-
-############# ###########--
----##########################----
------#########################-----
--------#######################-------
-----------####################---------
------------###################---------
---------------################-----------
- -------------############-------------
- P --------------##########--------------
- ----------------#######---------------
---------------------###----------------
----------------------------------------
--------------------####--------------
----------------##########----------
-------------##############-------
--------####################--
-###########################
######################
##############
Global CMT Convention Moment Tensor:
R T P
2.92e+20 7.91e+20 -3.42e+20
7.91e+20 1.66e+21 1.46e+20
-3.42e+20 1.46e+20 -1.95e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20111108190517/index.html
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STK = 135
DIP = 80
RAKE = 25
MW = 3.47
HS = 8.0
The NDK file is 20111108190517.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 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 -20 3.09 0.2761
WVFGRD96 1.0 130 90 0 3.12 0.3068
WVFGRD96 2.0 130 80 -10 3.27 0.4587
WVFGRD96 3.0 135 90 -5 3.31 0.5119
WVFGRD96 4.0 315 85 5 3.35 0.5331
WVFGRD96 5.0 130 90 -15 3.41 0.5372
WVFGRD96 6.0 315 75 10 3.42 0.5349
WVFGRD96 7.0 135 80 20 3.44 0.5372
WVFGRD96 8.0 135 80 25 3.47 0.5393
WVFGRD96 9.0 135 80 25 3.49 0.5377
WVFGRD96 10.0 135 80 25 3.50 0.5352
WVFGRD96 11.0 140 70 25 3.50 0.5322
WVFGRD96 12.0 140 70 25 3.52 0.5281
WVFGRD96 13.0 140 70 25 3.53 0.5230
WVFGRD96 14.0 140 70 25 3.54 0.5167
WVFGRD96 15.0 140 65 25 3.56 0.5096
WVFGRD96 16.0 140 65 25 3.57 0.5018
WVFGRD96 17.0 135 75 20 3.58 0.4947
WVFGRD96 18.0 135 75 20 3.59 0.4883
WVFGRD96 19.0 135 75 20 3.60 0.4811
WVFGRD96 20.0 135 75 20 3.61 0.4736
WVFGRD96 21.0 135 75 20 3.62 0.4654
WVFGRD96 22.0 135 80 25 3.63 0.4568
WVFGRD96 23.0 135 80 25 3.64 0.4480
WVFGRD96 24.0 135 80 25 3.65 0.4384
WVFGRD96 25.0 135 80 25 3.66 0.4284
WVFGRD96 26.0 135 85 30 3.66 0.4187
WVFGRD96 27.0 135 85 30 3.67 0.4081
WVFGRD96 28.0 135 85 30 3.67 0.3974
WVFGRD96 29.0 135 85 35 3.68 0.3868
The best solution is
WVFGRD96 8.0 135 80 25 3.47 0.5393
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 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