Location
SLU Location
To check the ANSS location or to compare the observed P-wave first motions to the moment tensor solution, P- and S-wave first arrival times were manually read together with the P-wave first motions. The subsequent output of the program elocate is given in the file elocate.txt. The first motion plot is shown below.
Location ANSS
The ANSS event ID is usp000hn24 and the event page is at
https://earthquake.usgs.gov/earthquakes/eventpage/usp000hn24/executive.
2010/10/13 14:06:29 35.192 -97.320 13.0 4.4 Oklahoma
Focal Mechanism
USGS/SLU Moment Tensor Solution
ENS 2010/10/13 14:06:29:0 35.19 -97.32 13.0 4.4 Oklahoma
Stations used:
AG.WLAR NM.MGMO NM.UALR TA.129A TA.131A TA.133A TA.134A
TA.135A TA.137A TA.139A TA.230A TA.231A TA.232A TA.233A
TA.234A TA.236A TA.332A TA.333A TA.334A TA.335A TA.434A
TA.435B TA.436A TA.P33A TA.P34A TA.P35A TA.Q30A TA.Q31A
TA.Q32A TA.Q33A TA.Q34A TA.Q35A TA.Q36A TA.Q37A TA.R29A
TA.R30A TA.R31A TA.R33A TA.R35A TA.R36A TA.S28A TA.S29A
TA.S30A TA.S31A TA.S32A TA.S34A TA.S35A TA.S36A TA.T29A
TA.T30A TA.T31A TA.T32A TA.T33A TA.T34A TA.T35A TA.T36A
TA.T37A TA.TUL1 TA.U29A TA.U30A TA.U31A TA.U32A TA.U33A
TA.U34A TA.V29A TA.V32A TA.V33A TA.V34A TA.V35A TA.W31A
TA.W32A TA.W33A TA.W34A TA.W35A TA.W36A TA.W37A TA.W38A
TA.WHTX TA.X32A TA.X33A TA.X34A TA.X35A TA.X36A TA.X37A
TA.X38A TA.Y33A TA.Y34A TA.Y35A TA.Y36A TA.Y37A TA.Y38A
TA.Y39A TA.Z29A TA.Z31A TA.Z32A TA.Z33A TA.Z34A TA.Z36A
TA.Z39A US.CBKS US.KSU1 US.MIAR US.WMOK
Filtering commands used:
hp c 0.02 n 3
lp c 0.06 n 3
Best Fitting Double Couple
Mo = 3.94e+22 dyne-cm
Mw = 4.33
Z = 14 km
Plane Strike Dip Rake
NP1 29 85 170
NP2 120 80 5
Principal Axes:
Axis Value Plunge Azimuth
T 3.94e+22 11 344
N 0.00e+00 79 183
P -3.94e+22 4 75
Moment Tensor: (dyne-cm)
Component Value
Mxx 3.26e+22
Mxy -1.98e+22
Mxz 6.20e+21
Myy -3.37e+22
Myz -4.28e+21
Mzz 1.17e+21
###########
#### T ##############-
####### #############-----
#######################-------
#########################---------
#########################-----------
---######################-------------
------###################-------------
--------################-------------- P
------------############---------------
---------------########-------------------
------------------####--------------------
------------------------------------------
-------------------####-----------------
------------------#########-------------
----------------##############--------
-------------######################-
-----------#######################
--------######################
------######################
-#####################
##############
Global CMT Convention Moment Tensor:
R T P
1.17e+21 6.20e+21 4.28e+21
6.20e+21 3.26e+22 1.98e+22
4.28e+21 1.98e+22 -3.37e+22
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20101013140629/index.html
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Preferred Solution
The preferred solution from an analysis of the surface-wave spectral amplitude radiation pattern, waveform inversion or first motion observations is
STK = 120
DIP = 80
RAKE = 5
MW = 4.33
HS = 14.0
The NDK file is 20101013140629.ndk
The waveform inversion is preferred.
Moment Tensor Comparison
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.
| SLU |
GCMT |
SLUFM |
USGS/SLU Moment Tensor Solution
ENS 2010/10/13 14:06:29:0 35.19 -97.32 13.0 4.4 Oklahoma
Stations used:
AG.WLAR NM.MGMO NM.UALR TA.129A TA.131A TA.133A TA.134A
TA.135A TA.137A TA.139A TA.230A TA.231A TA.232A TA.233A
TA.234A TA.236A TA.332A TA.333A TA.334A TA.335A TA.434A
TA.435B TA.436A TA.P33A TA.P34A TA.P35A TA.Q30A TA.Q31A
TA.Q32A TA.Q33A TA.Q34A TA.Q35A TA.Q36A TA.Q37A TA.R29A
TA.R30A TA.R31A TA.R33A TA.R35A TA.R36A TA.S28A TA.S29A
TA.S30A TA.S31A TA.S32A TA.S34A TA.S35A TA.S36A TA.T29A
TA.T30A TA.T31A TA.T32A TA.T33A TA.T34A TA.T35A TA.T36A
TA.T37A TA.TUL1 TA.U29A TA.U30A TA.U31A TA.U32A TA.U33A
TA.U34A TA.V29A TA.V32A TA.V33A TA.V34A TA.V35A TA.W31A
TA.W32A TA.W33A TA.W34A TA.W35A TA.W36A TA.W37A TA.W38A
TA.WHTX TA.X32A TA.X33A TA.X34A TA.X35A TA.X36A TA.X37A
TA.X38A TA.Y33A TA.Y34A TA.Y35A TA.Y36A TA.Y37A TA.Y38A
TA.Y39A TA.Z29A TA.Z31A TA.Z32A TA.Z33A TA.Z34A TA.Z36A
TA.Z39A US.CBKS US.KSU1 US.MIAR US.WMOK
Filtering commands used:
hp c 0.02 n 3
lp c 0.06 n 3
Best Fitting Double Couple
Mo = 3.94e+22 dyne-cm
Mw = 4.33
Z = 14 km
Plane Strike Dip Rake
NP1 29 85 170
NP2 120 80 5
Principal Axes:
Axis Value Plunge Azimuth
T 3.94e+22 11 344
N 0.00e+00 79 183
P -3.94e+22 4 75
Moment Tensor: (dyne-cm)
Component Value
Mxx 3.26e+22
Mxy -1.98e+22
Mxz 6.20e+21
Myy -3.37e+22
Myz -4.28e+21
Mzz 1.17e+21
###########
#### T ##############-
####### #############-----
#######################-------
#########################---------
#########################-----------
---######################-------------
------###################-------------
--------################-------------- P
------------############---------------
---------------########-------------------
------------------####--------------------
------------------------------------------
-------------------####-----------------
------------------#########-------------
----------------##############--------
-------------######################-
-----------#######################
--------######################
------######################
-#####################
##############
Global CMT Convention Moment Tensor:
R T P
1.17e+21 6.20e+21 4.28e+21
6.20e+21 3.26e+22 1.98e+22
4.28e+21 1.98e+22 -3.37e+22
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20101013140629/index.html
|
October 13, 2010, OKLAHOMA, MW=4.4
Meredith Nettles
Goran Ekstrom
CENTROID-MOMENT-TENSOR SOLUTION
GCMT EVENT: S201010131406A
DATA: TA US IU II CU G
SURFACE WAVES: 285S, 377C, T= 40
TIMESTAMP: Q-20101014143127
CENTROID LOCATION:
ORIGIN TIME: 14:06:31.7 0.2
LAT:35.21N 0.01;LON: 97.28W 0.02
DEP: 12.0 FIX;TRIANG HDUR: 1.0
MOMENT TENSOR: SCALE 10**22 D-CM
RR=-0.032 0.139; TT= 3.830 0.108
PP=-3.800 0.144; RT= 0.847 0.313
RP=-0.261 0.365; TP= 2.310 0.119
PRINCIPAL AXES:
1.(T) VAL= 4.596;PLG= 9;AZM=345
2.(N) -0.100; 79; 130
3.(P) -4.497; 6; 254
BEST DBLE.COUPLE:M0= 4.55*10**22
NP1: STRIKE= 29;DIP=79;SLIP= 178
NP2: STRIKE=120;DIP=88;SLIP= 11
########
#### T ##########--
###### ##########----
####################-------
#####################--------
----#################----------
-------#############-----------
-----------#########-------------
--------------######-------------
-----------------##--------------
--------------####------------
P -------------########--------
------------############-----
------------#################
----------#################
------#################
--#################
###########
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First motions and takeoff angles from an elocate run.
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Magnitudes
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.
ML Magnitude
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.
Context
The left panel of the next figure presents the focal mechanism for this earthquake (red) in the context of other nearby events (blue) in the SLU Moment Tensor Catalog. The right panel shows the inferred direction of maximum compressive stress and the type of faulting (green is strike-slip, red is normal, blue is thrust; oblique is shown by a combination of colors). Thus context plot is useful for assessing the appropriateness of the moment tensor of this event.
Waveform Inversion using wvfgrd96
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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Location of broadband stations used for waveform inversion
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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 3
The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 0.5 120 65 0 4.17 0.4012
WVFGRD96 1.0 120 65 0 4.19 0.4196
WVFGRD96 2.0 120 70 0 4.21 0.4487
WVFGRD96 3.0 120 70 0 4.23 0.4688
WVFGRD96 4.0 120 70 0 4.25 0.4843
WVFGRD96 5.0 120 70 5 4.26 0.4973
WVFGRD96 6.0 120 75 10 4.27 0.5092
WVFGRD96 7.0 120 75 10 4.28 0.5198
WVFGRD96 8.0 120 75 10 4.29 0.5285
WVFGRD96 9.0 120 75 5 4.30 0.5356
WVFGRD96 10.0 120 75 10 4.31 0.5422
WVFGRD96 11.0 120 75 5 4.31 0.5461
WVFGRD96 12.0 120 75 5 4.32 0.5487
WVFGRD96 13.0 120 75 5 4.33 0.5498
WVFGRD96 14.0 120 80 5 4.33 0.5506
WVFGRD96 15.0 120 80 5 4.34 0.5501
WVFGRD96 16.0 120 80 5 4.35 0.5489
WVFGRD96 17.0 120 80 5 4.36 0.5472
WVFGRD96 18.0 120 80 5 4.36 0.5447
WVFGRD96 19.0 120 80 5 4.37 0.5419
WVFGRD96 20.0 120 80 5 4.38 0.5387
WVFGRD96 21.0 120 80 5 4.39 0.5339
WVFGRD96 22.0 120 80 5 4.39 0.5288
WVFGRD96 23.0 120 80 5 4.40 0.5230
WVFGRD96 24.0 120 80 5 4.40 0.5167
WVFGRD96 25.0 120 80 5 4.41 0.5102
WVFGRD96 26.0 120 80 5 4.41 0.5032
WVFGRD96 27.0 120 80 5 4.42 0.4959
WVFGRD96 28.0 120 80 5 4.42 0.4885
WVFGRD96 29.0 120 80 5 4.43 0.4810
The best solution is
WVFGRD96 14.0 120 80 5 4.33 0.5506
The mechanism corresponding to the best fit is
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Figure 1. Waveform inversion focal mechanism
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The best fit as a function of depth is given in the following figure:
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Figure 2. Depth sensitivity for waveform mechanism
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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.
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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:
- The origin time and epicentral distance are incorrect
- The velocity model used for the inversion is incorrect
- The velocity model used to define the P-arrival time is not the
same as the velocity model used for the waveform inversion
(assuming that the initial trace alignment is based on the
P arrival time)
Assuming only a mislocation, the time shifts are fit to a functional form:
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.
Surface-Wave Focal Mechanism
The following figure shows the stations used in the grid search for the best focal mechanism to fit the surface-wave spectral amplitudes of the Love and Rayleigh waves.
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Location of broadband stations used to obtain focal mechanism from surface-wave spectral amplitudes
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The surface-wave determined focal mechanism is shown here.
NODAL PLANES
STK= 27.38
DIP= 80.34
RAKE= 164.78
OR
STK= 119.99
DIP= 75.00
RAKE= 10.00
DEPTH = 11.0 km
Mw = 4.37
Best Fit 0.8852 - P-T axis plot gives solutions with FIT greater than FIT90
Surface-wave analysis
Surface wave analysis was performed using codes from
Computer Programs in Seismology, specifically the
multiple filter analysis program do_mft and the surface-wave
radiation pattern search program srfgrd96.
Data preparation
Digital data were collected, instrument response removed and traces converted
to Z, R an T components. Multiple filter analysis was applied to the Z and T traces to obtain the Rayleigh- and Love-wave spectral amplitudes, respectively.
These were input to the search program which examined all depths between 1 and 25 km
and all possible mechanisms.
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Best mechanism fit as a function of depth. The preferred depth is given above. Lower hemisphere projection
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Pressure-tension axis trends. Since the surface-wave spectra search does not distinguish between P and T axes and since there is a 180 ambiguity in strike, all possible P and T axes are plotted. First motion data and waveforms will be used to select the preferred mechanism. The purpose of this plot is to provide an idea of the
possible range of solutions. The P and T-axes for all mechanisms with goodness of fit greater than 0.9 FITMAX (above) are plotted here.
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Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to the Love and Rayleigh wave radiation patterns.
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. Because of the symmetry of the spectral amplitude rediation patterns, only strikes from 0-180 degrees are sampled.
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Love-wave radiation patterns
Rayleigh-wave radiation patterns
