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 usp000h7ax and the event page is at
https://earthquake.usgs.gov/earthquakes/eventpage/usp000h7ax/executive.
2010/02/15 03:32:25 35.557 -97.298 3.3 3.0 Oklahoma
Focal Mechanism
USGS/SLU Moment Tensor Solution
ENS 2010/02/15 03:32:25:0 35.56 -97.30 3.3 3.0 Oklahoma
Stations used:
GS.OK001 GS.OK003 GS.OK004 GS.OK005 GS.OK006 TA.V34A
TA.W34A
Filtering commands used:
rtr
hp c 0.5 n 3
lp c 2.00 n 3
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 5.82e+20 dyne-cm
Mw = 3.11
Z = 7 km
Plane Strike Dip Rake
NP1 222 61 132
NP2 340 50 40
Principal Axes:
Axis Value Plunge Azimuth
T 5.82e+20 53 185
N 0.00e+00 36 17
P -5.82e+20 6 283
Moment Tensor: (dyne-cm)
Component Value
Mxx 1.76e+20
Mxy 1.43e+20
Mxz -2.92e+20
Myy -5.45e+20
Myz 3.70e+19
Mzz 3.68e+20
##############
---------#############
---------------#############
------------------###---------
--------------------##------------
------------------######------------
-----------------#########------------
--------------############------------
P ------------###############-----------
-----------#################-----------
------------###################-----------
-----------#####################----------
----------######################----------
--------#######################---------
-------########### ##########---------
------########### T ##########--------
----############ ##########-------
---#########################------
-########################-----
#######################-----
###################---
##############
Global CMT Convention Moment Tensor:
R T P
3.68e+20 -2.92e+20 -3.70e+19
-2.92e+20 1.76e+20 -1.43e+20
-3.70e+19 -1.43e+20 -5.45e+20
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20100215033225/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 = 340
DIP = 50
RAKE = 40
MW = 3.11
HS = 7.0
The NDK file is 20100215033225.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 |
SLUFM |
USGS/SLU Moment Tensor Solution
ENS 2010/02/15 03:32:25:0 35.56 -97.30 3.3 3.0 Oklahoma
Stations used:
GS.OK001 GS.OK003 GS.OK004 GS.OK005 GS.OK006 TA.V34A
TA.W34A
Filtering commands used:
rtr
hp c 0.5 n 3
lp c 2.00 n 3
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 5.82e+20 dyne-cm
Mw = 3.11
Z = 7 km
Plane Strike Dip Rake
NP1 222 61 132
NP2 340 50 40
Principal Axes:
Axis Value Plunge Azimuth
T 5.82e+20 53 185
N 0.00e+00 36 17
P -5.82e+20 6 283
Moment Tensor: (dyne-cm)
Component Value
Mxx 1.76e+20
Mxy 1.43e+20
Mxz -2.92e+20
Myy -5.45e+20
Myz 3.70e+19
Mzz 3.68e+20
##############
---------#############
---------------#############
------------------###---------
--------------------##------------
------------------######------------
-----------------#########------------
--------------############------------
P ------------###############-----------
-----------#################-----------
------------###################-----------
-----------#####################----------
----------######################----------
--------#######################---------
-------########### ##########---------
------########### T ##########--------
----############ ##########-------
---#########################------
-########################-----
#######################-----
###################---
##############
Global CMT Convention Moment Tensor:
R T P
3.68e+20 -2.92e+20 -3.70e+19
-2.92e+20 1.76e+20 -1.43e+20
-3.70e+19 -1.43e+20 -5.45e+20
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20100215033225/index.html
|
The first motion plot is not very satisfying. I plot the observed Z
components about the P-arrival pick. The takeoff angles and picks are
in the elocate.txt file. At these short distances there is sensitivity
of the take-off angles and azimuths to the location. The nodal planes
are sensitive to the distance weighting. So this may be an apparent
inconsistency in the comparison of observed and predicted first
motions.
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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:
rtr
hp c 0.5 n 3
lp c 2.00 n 3
br c 0.12 0.25 n 4 p 2
The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 0.5 55 75 25 2.08 0.1149
WVFGRD96 1.0 55 30 -20 2.22 0.1464
WVFGRD96 2.0 65 40 0 2.63 0.2466
WVFGRD96 3.0 45 50 75 2.73 0.2339
WVFGRD96 4.0 355 85 -30 2.96 0.3653
WVFGRD96 5.0 335 50 25 3.01 0.7015
WVFGRD96 6.0 335 50 30 3.06 0.6848
WVFGRD96 7.0 340 50 40 3.11 0.7090
WVFGRD96 8.0 340 50 45 3.16 0.5723
WVFGRD96 9.0 345 80 80 3.12 0.3753
WVFGRD96 10.0 345 80 75 3.14 0.3641
WVFGRD96 11.0 325 70 -75 3.04 0.1580
WVFGRD96 12.0 330 75 -70 3.03 0.1451
WVFGRD96 13.0 335 75 -70 2.97 0.0826
WVFGRD96 14.0 70 45 30 2.82 0.0251
WVFGRD96 15.0 70 50 25 2.84 0.0242
WVFGRD96 16.0 70 50 25 2.84 0.0214
WVFGRD96 17.0 20 80 30 2.83 0.0086
WVFGRD96 18.0 180 60 -30 2.82 0.0084
WVFGRD96 19.0 195 10 55 2.73 0.0077
WVFGRD96 20.0 190 65 -50 2.80 0.0073
WVFGRD96 21.0 20 40 -70 2.80 0.0059
WVFGRD96 22.0 30 45 -65 2.80 0.0055
WVFGRD96 23.0 295 65 45 2.80 0.0060
WVFGRD96 24.0 5 45 -30 2.84 0.0052
WVFGRD96 25.0 180 55 75 2.83 0.0054
WVFGRD96 26.0 175 55 65 2.86 0.0059
WVFGRD96 27.0 315 65 -60 2.77 0.0047
WVFGRD96 28.0 300 70 -55 2.85 0.0076
WVFGRD96 29.0 295 65 -50 2.89 0.0078
The best solution is
WVFGRD96 7.0 340 50 40 3.11 0.7090
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
rtr
hp c 0.5 n 3
lp c 2.00 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.
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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.
Velocity Model
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
Last Changed Sat Apr 27 03:34:49 PM CDT 2024
