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 usc000pdy4 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usc000pdy4/executive.
2014/04/10 07:33:57 35.775 -97.483 7.0 4 Oklahoma
USGS/SLU Moment Tensor Solution
ENS 2014/04/10 07:33:57:0 35.78 -97.48 7.0 4.0 Oklahoma
Stations used:
AG.CCAR AG.HHAR AG.LCAR AG.WHAR AG.WLAR GS.OK025 GS.OK026
GS.OK027 N4.N35B N4.P38B N4.R32B N4.R40B N4.S39B N4.T35B
N4.U38B N4.Z35B N4.Z38B NM.UALR OK.CROK OK.FNO OK.KAY1
OK.U32A OK.X34A OK.X37A TA.ABTX TA.KSCO TA.MSTX TA.TUL1
TA.U40A TA.W39A TA.WHTX TA.X40A US.CBKS US.KSU1 US.MIAR
US.WMOK
Filtering commands used:
cut a -30 a 180
rtr
taper w 0.1
hp c 0.02 n 3
lp c 0.06 n 3
Best Fitting Double Couple
Mo = 1.26e+22 dyne-cm
Mw = 4.00
Z = 5 km
Plane Strike Dip Rake
NP1 300 70 -25
NP2 39 67 -158
Principal Axes:
Axis Value Plunge Azimuth
T 1.26e+22 2 350
N 0.00e+00 58 84
P -1.26e+22 32 259
Moment Tensor: (dyne-cm)
Component Value
Mxx 1.19e+22
Mxy -3.88e+21
Mxz 1.58e+21
Myy -8.43e+21
Myz 5.42e+21
Mzz -3.42e+21
## T #########
###### #############
###########################-
############################--
##############################----
-----#########################------
-------------##################-------
-------------------############---------
----------------------########----------
--------------------------####------------
------------------------------------------
----- --------------------###-----------
----- P ------------------#######---------
---- -----------------##########------
----------------------##############----
-------------------#################--
----------------####################
-------------#####################
--------######################
---#########################
######################
##############
Global CMT Convention Moment Tensor:
R T P
-3.42e+21 1.58e+21 -5.42e+21
1.58e+21 1.19e+22 3.88e+21
-5.42e+21 3.88e+21 -8.43e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20140410073357/index.html
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STK = 300
DIP = 70
RAKE = -25
MW = 4.00
HS = 5.0
The NDK file is 20140410073357.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 a -30 a 180 rtr taper w 0.1 hp c 0.02 n 3 lp c 0.06 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 1.0 300 70 -25 3.79 0.3562
WVFGRD96 2.0 300 65 -25 3.90 0.4504
WVFGRD96 3.0 300 65 -25 3.96 0.4984
WVFGRD96 4.0 300 70 -25 3.98 0.5163
WVFGRD96 5.0 300 70 -25 4.00 0.5186
WVFGRD96 6.0 300 75 -15 4.01 0.5174
WVFGRD96 7.0 305 85 5 4.03 0.5137
WVFGRD96 8.0 300 75 -15 4.06 0.5109
WVFGRD96 9.0 305 85 10 4.07 0.5013
WVFGRD96 10.0 130 80 30 4.08 0.4907
WVFGRD96 11.0 130 80 30 4.09 0.4859
WVFGRD96 12.0 130 80 30 4.10 0.4801
WVFGRD96 13.0 130 85 30 4.11 0.4761
WVFGRD96 14.0 130 85 30 4.12 0.4723
WVFGRD96 15.0 130 85 30 4.13 0.4679
WVFGRD96 16.0 130 85 30 4.14 0.4623
WVFGRD96 17.0 130 85 30 4.15 0.4562
WVFGRD96 18.0 130 85 30 4.15 0.4494
WVFGRD96 19.0 130 85 25 4.16 0.4424
WVFGRD96 20.0 130 85 25 4.17 0.4367
WVFGRD96 21.0 130 85 30 4.18 0.4292
WVFGRD96 22.0 130 85 30 4.19 0.4224
WVFGRD96 23.0 130 85 30 4.19 0.4158
WVFGRD96 24.0 130 85 30 4.20 0.4087
WVFGRD96 25.0 130 80 25 4.20 0.4007
WVFGRD96 26.0 130 80 25 4.20 0.3938
WVFGRD96 27.0 130 80 25 4.21 0.3867
WVFGRD96 28.0 130 80 25 4.22 0.3803
WVFGRD96 29.0 130 80 25 4.22 0.3746
The best solution is
WVFGRD96 5.0 300 70 -25 4.00 0.5186
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 a -30 a 180 rtr taper w 0.1 hp c 0.02 n 3 lp c 0.06 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 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