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 usp000jafa and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usp000jafa/executive.
2011/11/06 15:07:05 35.484 -96.856 5.0 3.8 Oklahoma
USGS/SLU Moment Tensor Solution
ENS 2011/11/06 15:07:05:0 35.48 -96.86 5.0 3.8 Oklahoma
Stations used:
AG.HHAR TA.Q34A TA.Q35A TA.Q36A TA.R34A TA.R35A TA.R36A
TA.R37A TA.R38A TA.S34A TA.S35A TA.S36A TA.S37A TA.S38A
TA.S39A TA.T34A TA.T35A TA.T36A TA.T38A TA.T39A TA.TUL1
TA.U32A TA.U35A TA.U36A TA.U37A TA.U38A TA.U40A TA.V35A
TA.V36A TA.V37A TA.V38A TA.V39A TA.V40A TA.W35A TA.W36A
TA.W37B TA.W38A TA.W39A TA.W40A TA.X35A TA.X36A TA.X38A
TA.X39A TA.Y35A TA.Y36A TA.Y37A TA.Y39A TA.Y40A TA.Z37A
US.KSU1 US.MIAR
Filtering commands used:
hp c 0.02 n 3
lp c 0.06 n 3
Best Fitting Double Couple
Mo = 5.13e+21 dyne-cm
Mw = 3.74
Z = 3 km
Plane Strike Dip Rake
NP1 320 85 -15
NP2 51 75 -175
Principal Axes:
Axis Value Plunge Azimuth
T 5.13e+21 7 7
N 0.00e+00 74 122
P -5.13e+21 14 275
Moment Tensor: (dyne-cm)
Component Value
Mxx 4.96e+21
Mxy 9.70e+20
Mxz 5.10e+20
Myy -4.72e+21
Myz 1.28e+21
Mzz -2.30e+20
######## T ###
############ #######
-###########################
----##########################
--------#########################-
-----------######################---
-------------####################-----
----------------################--------
------------------#############---------
- ----------------##########------------
- P ------------------######--------------
- -------------------###----------------
------------------------#-----------------
--------------------#####---------------
------------------#########-------------
--------------#############-----------
---------###################--------
----########################------
###########################---
###########################-
######################
##############
Global CMT Convention Moment Tensor:
R T P
-2.30e+20 5.10e+20 -1.28e+21
5.10e+20 4.96e+21 -9.70e+20
-1.28e+21 -9.70e+20 -4.72e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20111106150705/index.html
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STK = 320
DIP = 85
RAKE = -15
MW = 3.74
HS = 3.0
The NDK file is 20111106150705.ndk The waveform inversion is preferred.
The following compares this source inversion to those provided by others. The purpose is to look for major differences and also to note slight differences that might be inherent to the processing procedure. For completeness the USGS/SLU solution is repeated from above.
USGS/SLU Moment Tensor Solution
ENS 2011/11/06 15:07:05:0 35.48 -96.86 5.0 3.8 Oklahoma
Stations used:
AG.HHAR TA.Q34A TA.Q35A TA.Q36A TA.R34A TA.R35A TA.R36A
TA.R37A TA.R38A TA.S34A TA.S35A TA.S36A TA.S37A TA.S38A
TA.S39A TA.T34A TA.T35A TA.T36A TA.T38A TA.T39A TA.TUL1
TA.U32A TA.U35A TA.U36A TA.U37A TA.U38A TA.U40A TA.V35A
TA.V36A TA.V37A TA.V38A TA.V39A TA.V40A TA.W35A TA.W36A
TA.W37B TA.W38A TA.W39A TA.W40A TA.X35A TA.X36A TA.X38A
TA.X39A TA.Y35A TA.Y36A TA.Y37A TA.Y39A TA.Y40A TA.Z37A
US.KSU1 US.MIAR
Filtering commands used:
hp c 0.02 n 3
lp c 0.06 n 3
Best Fitting Double Couple
Mo = 5.13e+21 dyne-cm
Mw = 3.74
Z = 3 km
Plane Strike Dip Rake
NP1 320 85 -15
NP2 51 75 -175
Principal Axes:
Axis Value Plunge Azimuth
T 5.13e+21 7 7
N 0.00e+00 74 122
P -5.13e+21 14 275
Moment Tensor: (dyne-cm)
Component Value
Mxx 4.96e+21
Mxy 9.70e+20
Mxz 5.10e+20
Myy -4.72e+21
Myz 1.28e+21
Mzz -2.30e+20
######## T ###
############ #######
-###########################
----##########################
--------#########################-
-----------######################---
-------------####################-----
----------------################--------
------------------#############---------
- ----------------##########------------
- P ------------------######--------------
- -------------------###----------------
------------------------#-----------------
--------------------#####---------------
------------------#########-------------
--------------#############-----------
---------###################--------
----########################------
###########################---
###########################-
######################
##############
Global CMT Convention Moment Tensor:
R T P
-2.30e+20 5.10e+20 -1.28e+21
5.10e+20 4.96e+21 -9.70e+20
-1.28e+21 -9.70e+20 -4.72e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20111106150705/index.html
|
USGS/SLU Regional Moment Solution OKLAHOMA 11/11/06 15:07:06.79 Epicenter: 35.550 -96.837 MW 3.8 USGS/SLU REGIONAL MOMENT TENSOR Depth 5 No. of sta: 27 Moment Tensor; Scale 10**14 Nm Mrr=-0.78 Mtt= 6.61 Mpp=-5.83 Mrt=-1.30 Mrp=-3.29 Mtp=-1.26 Principal axes: T Val= 6.87 Plg= 8 Azm=184 N 0.79 62 78 P -7.66 27 278 Best Double Couple:Mo=7.3*10**14 NP1:Strike= 53 Dip=78 Slip=-155 NP2: 318 65 -14 |
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 0.06 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 0.5 320 80 -25 3.59 0.3964
WVFGRD96 1.0 320 80 -20 3.62 0.4211
WVFGRD96 2.0 320 80 -20 3.71 0.4926
WVFGRD96 3.0 320 85 -15 3.74 0.5097
WVFGRD96 4.0 140 90 15 3.77 0.5068
WVFGRD96 5.0 320 90 -20 3.80 0.4985
WVFGRD96 6.0 320 90 -25 3.82 0.4935
WVFGRD96 7.0 320 90 -30 3.84 0.4932
WVFGRD96 8.0 145 85 35 3.88 0.4975
WVFGRD96 9.0 320 90 -35 3.89 0.4894
WVFGRD96 10.0 145 65 20 3.90 0.4871
WVFGRD96 11.0 145 65 20 3.91 0.4838
WVFGRD96 12.0 145 65 20 3.91 0.4793
WVFGRD96 13.0 145 70 20 3.92 0.4736
WVFGRD96 14.0 145 70 20 3.92 0.4672
WVFGRD96 15.0 145 70 20 3.93 0.4601
WVFGRD96 16.0 145 70 10 3.93 0.4532
WVFGRD96 17.0 140 65 -10 3.94 0.4486
WVFGRD96 18.0 140 65 -10 3.95 0.4434
WVFGRD96 19.0 140 65 -10 3.95 0.4374
WVFGRD96 20.0 140 65 -10 3.96 0.4310
WVFGRD96 21.0 140 75 -20 3.97 0.4255
WVFGRD96 22.0 140 75 -20 3.98 0.4211
WVFGRD96 23.0 140 80 -20 3.98 0.4169
WVFGRD96 24.0 140 80 -20 3.99 0.4124
WVFGRD96 25.0 140 80 -20 4.00 0.4070
WVFGRD96 26.0 140 80 -20 4.01 0.4012
WVFGRD96 27.0 140 80 -20 4.01 0.3949
WVFGRD96 28.0 140 85 -20 4.02 0.3892
WVFGRD96 29.0 140 85 -20 4.03 0.3836
The best solution is
WVFGRD96 3.0 320 85 -15 3.74 0.5097
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 0.06 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