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 us10003mqq and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/us10003mqq/executive.
2015/10/10 22:03:05 35.986 -96.803 3.3 4.3 Oklahoma
USGS/SLU Moment Tensor Solution
ENS 2015/10/10 22:03:05:0 35.99 -96.80 3.3 4.3 Oklahoma
Stations used:
AG.FCAR AG.LCAR AG.WHAR AG.WLAR GS.KAN01 GS.KAN06 GS.KAN08
GS.KAN10 GS.KAN11 GS.KAN12 GS.KAN14 GS.KAN16 GS.KAN17
GS.KS20 GS.KS21 GS.OK025 GS.OK029 GS.OK032 N4.237B N4.N33B
N4.P38B N4.R32B N4.S39B N4.T35B N4.T42B N4.U38B N4.Z35B
N4.Z38B NM.MGMO OK.BCOK OK.CCOK OK.CHOK OK.CROK OK.FNO
OK.LOOK OK.OKCFA OK.U32A OK.X34A OK.X37A TA.ABTX TA.TUL1
TA.U40A TA.W39A TA.WHTX TA.X40A US.CBKS US.KSU1 US.MIAR
US.WMOK
Filtering commands used:
cut o DIST/3.3 -30 o DIST/3.3 +70
rtr
taper w 0.1
hp c 0.03 n 3
lp c 0.07 n 3
Best Fitting Double Couple
Mo = 2.60e+22 dyne-cm
Mw = 4.21
Z = 3 km
Plane Strike Dip Rake
NP1 60 90 -175
NP2 330 85 0
Principal Axes:
Axis Value Plunge Azimuth
T 2.60e+22 4 195
N 0.00e+00 85 60
P -2.60e+22 4 285
Moment Tensor: (dyne-cm)
Component Value
Mxx 2.24e+22
Mxy 1.30e+22
Mxz -1.96e+21
Myy -2.24e+22
Myz 1.13e+21
Mzz 0.00e+00
##############
-#####################
-----#######################
--------######################
-----------#######################
-------------#######################
---------------##################-----
----------------#############---------
P -----------------#########------------
------------------#####----------------
----------------------#-------------------
-------------------####-------------------
----------------########------------------
------------############----------------
---------################---------------
-----####################-------------
#########################-----------
#########################---------
########################------
#######################-----
#### ##############-
T ###########
Global CMT Convention Moment Tensor:
R T P
0.00e+00 -1.96e+21 -1.13e+21
-1.96e+21 2.24e+22 -1.30e+22
-1.13e+21 -1.30e+22 -2.24e+22
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20151010220305/index.html
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STK = 330
DIP = 85
RAKE = 0
MW = 4.21
HS = 3.0
The NDK file is 20151010220305.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 2015/10/10 22:03:05:0 35.99 -96.80 3.3 4.3 Oklahoma
Stations used:
AG.FCAR AG.LCAR AG.WHAR AG.WLAR GS.KAN01 GS.KAN06 GS.KAN08
GS.KAN10 GS.KAN11 GS.KAN12 GS.KAN14 GS.KAN16 GS.KAN17
GS.KS20 GS.KS21 GS.OK025 GS.OK029 GS.OK032 N4.237B N4.N33B
N4.P38B N4.R32B N4.S39B N4.T35B N4.T42B N4.U38B N4.Z35B
N4.Z38B NM.MGMO OK.BCOK OK.CCOK OK.CHOK OK.CROK OK.FNO
OK.LOOK OK.OKCFA OK.U32A OK.X34A OK.X37A TA.ABTX TA.TUL1
TA.U40A TA.W39A TA.WHTX TA.X40A US.CBKS US.KSU1 US.MIAR
US.WMOK
Filtering commands used:
cut o DIST/3.3 -30 o DIST/3.3 +70
rtr
taper w 0.1
hp c 0.03 n 3
lp c 0.07 n 3
Best Fitting Double Couple
Mo = 2.60e+22 dyne-cm
Mw = 4.21
Z = 3 km
Plane Strike Dip Rake
NP1 60 90 -175
NP2 330 85 0
Principal Axes:
Axis Value Plunge Azimuth
T 2.60e+22 4 195
N 0.00e+00 85 60
P -2.60e+22 4 285
Moment Tensor: (dyne-cm)
Component Value
Mxx 2.24e+22
Mxy 1.30e+22
Mxz -1.96e+21
Myy -2.24e+22
Myz 1.13e+21
Mzz 0.00e+00
##############
-#####################
-----#######################
--------######################
-----------#######################
-------------#######################
---------------##################-----
----------------#############---------
P -----------------#########------------
------------------#####----------------
----------------------#-------------------
-------------------####-------------------
----------------########------------------
------------############----------------
---------################---------------
-----####################-------------
#########################-----------
#########################---------
########################------
#######################-----
#### ##############-
T ###########
Global CMT Convention Moment Tensor:
R T P
0.00e+00 -1.96e+21 -1.13e+21
-1.96e+21 2.24e+22 -1.30e+22
-1.13e+21 -1.30e+22 -2.24e+22
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20151010220305/index.html
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Regional Moment Tensor (Mwr)
Moment 4.123e+15 N-m
Magnitude 4.34
Depth 5.0 km
Percent DC 85%
Half Duration –
Catalog US (us10003mqq)
Data Source US1
Contributor US1
Nodal Planes
Plane Strike Dip Rake
NP1 331 81 -26
NP2 65 65 -170
Principal Axes
Axis Value Plunge Azimuth
T 3.959 11 21
N 0.310 63 132
P -4.269 25 286
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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 -30 o DIST/3.3 +70 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.07 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 1.0 330 85 0 4.05 0.4347
WVFGRD96 2.0 330 85 -5 4.16 0.5229
WVFGRD96 3.0 330 85 0 4.21 0.5494
WVFGRD96 4.0 330 85 0 4.24 0.5481
WVFGRD96 5.0 330 80 5 4.27 0.5339
WVFGRD96 6.0 330 75 5 4.29 0.5182
WVFGRD96 7.0 330 75 5 4.31 0.5039
WVFGRD96 8.0 330 70 5 4.34 0.4894
WVFGRD96 9.0 330 70 5 4.35 0.4716
WVFGRD96 10.0 330 70 10 4.36 0.4569
WVFGRD96 11.0 330 70 10 4.37 0.4435
WVFGRD96 12.0 330 70 10 4.38 0.4309
WVFGRD96 13.0 330 70 10 4.38 0.4195
WVFGRD96 14.0 330 70 10 4.39 0.4083
WVFGRD96 15.0 330 70 10 4.40 0.3976
WVFGRD96 16.0 330 75 10 4.40 0.3876
WVFGRD96 17.0 330 75 10 4.41 0.3778
WVFGRD96 18.0 330 75 10 4.42 0.3683
WVFGRD96 19.0 330 75 10 4.42 0.3591
WVFGRD96 20.0 330 75 10 4.43 0.3506
WVFGRD96 21.0 330 75 10 4.43 0.3426
WVFGRD96 22.0 330 75 10 4.44 0.3350
WVFGRD96 23.0 330 75 10 4.44 0.3275
WVFGRD96 24.0 330 75 10 4.45 0.3203
WVFGRD96 25.0 330 70 5 4.46 0.3141
WVFGRD96 26.0 330 70 5 4.46 0.3090
WVFGRD96 27.0 330 70 5 4.47 0.3043
WVFGRD96 28.0 330 70 5 4.48 0.3003
WVFGRD96 29.0 330 70 5 4.48 0.2969
The best solution is
WVFGRD96 3.0 330 85 0 4.21 0.5494
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 -30 o DIST/3.3 +70 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.07 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