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 usp000h78h and the event page is at
https://earthquake.usgs.gov/earthquakes/eventpage/usp000h78h/executive.
2010/02/13 05:30:55 35.530 -97.272 8.1 3.2 Oklahoma
Focal Mechanism
USGS/SLU Moment Tensor Solution
ENS 2010/02/13 05:30:55:0 35.53 -97.27 8.1 3.2 Oklahoma
Stations used:
GS.OK001 GS.OK002 GS.OK003 GS.OK004 GS.OK005 GS.OK006
Filtering commands used:
hp c 0.50 n 2
lp c 1.00 n 2
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 7.16e+20 dyne-cm
Mw = 3.17
Z = 5 km
Plane Strike Dip Rake
NP1 57 80 -170
NP2 325 80 -10
Principal Axes:
Axis Value Plunge Azimuth
T 7.16e+20 0 191
N 0.00e+00 76 100
P -7.16e+20 14 281
Moment Tensor: (dyne-cm)
Component Value
Mxx 6.67e+20
Mxy 2.58e+20
Mxz -3.33e+19
Myy -6.24e+20
Myz 1.66e+20
Mzz -4.25e+19
##############
######################
----########################
-------#######################
-----------#######################
-------------#####################--
----------------##################----
------------------###############-------
- ----------------###########---------
-- P -----------------#######-------------
-- ------------------####---------------
------------------------#-----------------
---------------------#####----------------
-----------------#########--------------
--------------#############-------------
----------#################-----------
----#######################---------
###########################-------
##########################----
##########################--
###### #############
## T #########
Global CMT Convention Moment Tensor:
R T P
-4.25e+19 -3.33e+19 -1.66e+20
-3.33e+19 6.67e+20 -2.58e+20
-1.66e+20 -2.58e+20 -6.24e+20
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20100213053055/index.html
|
Preferred Solution
The preferred solution from an analysis of the surface-wave spectral amplitude radiation pattern, waveform inversion or first motion observations is
STK = 325
DIP = 80
RAKE = -10
MW = 3.17
HS = 5.0
The NDK file is 20100213053055.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 2010/02/13 05:30:55:0 35.53 -97.27 8.1 3.2 Oklahoma
Stations used:
GS.OK001 GS.OK002 GS.OK003 GS.OK004 GS.OK005 GS.OK006
Filtering commands used:
hp c 0.50 n 2
lp c 1.00 n 2
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 7.16e+20 dyne-cm
Mw = 3.17
Z = 5 km
Plane Strike Dip Rake
NP1 57 80 -170
NP2 325 80 -10
Principal Axes:
Axis Value Plunge Azimuth
T 7.16e+20 0 191
N 0.00e+00 76 100
P -7.16e+20 14 281
Moment Tensor: (dyne-cm)
Component Value
Mxx 6.67e+20
Mxy 2.58e+20
Mxz -3.33e+19
Myy -6.24e+20
Myz 1.66e+20
Mzz -4.25e+19
##############
######################
----########################
-------#######################
-----------#######################
-------------#####################--
----------------##################----
------------------###############-------
- ----------------###########---------
-- P -----------------#######-------------
-- ------------------####---------------
------------------------#-----------------
---------------------#####----------------
-----------------#########--------------
--------------#############-------------
----------#################-----------
----#######################---------
###########################-------
##########################----
##########################--
###### #############
## T #########
Global CMT Convention Moment Tensor:
R T P
-4.25e+19 -3.33e+19 -1.66e+20
-3.33e+19 6.67e+20 -2.58e+20
-1.66e+20 -2.58e+20 -6.24e+20
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20100213053055/index.html
|
First motions plotted with waveform inversion
nodal planes. Take-off angles are from WUS model and
elocate run.
|
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.
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.
|
|
Location of broadband stations used for waveform inversion
|
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 0.50 n 2
lp c 1.00 n 2
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 0.5 150 90 0 2.42 0.2947
WVFGRD96 1.0 20 80 0 2.47 0.3078
WVFGRD96 2.0 290 55 -25 2.73 0.1387
WVFGRD96 3.0 325 80 -20 3.03 0.2812
WVFGRD96 4.0 325 80 -15 3.13 0.4226
WVFGRD96 5.0 325 80 -10 3.17 0.4562
WVFGRD96 6.0 325 75 -5 3.18 0.4549
WVFGRD96 7.0 325 65 0 3.19 0.4430
WVFGRD96 8.0 330 60 0 3.23 0.4255
WVFGRD96 9.0 330 65 0 3.29 0.4370
WVFGRD96 10.0 330 65 0 3.32 0.4253
WVFGRD96 11.0 330 65 0 3.34 0.4072
WVFGRD96 12.0 330 70 5 3.36 0.3641
WVFGRD96 13.0 335 70 5 3.36 0.3139
WVFGRD96 14.0 140 90 -30 3.38 0.2995
WVFGRD96 15.0 340 55 15 3.23 0.1142
WVFGRD96 16.0 340 25 20 3.12 0.0631
WVFGRD96 17.0 345 25 25 3.12 0.0608
WVFGRD96 18.0 335 30 5 3.10 0.0457
WVFGRD96 19.0 110 75 0 3.22 0.0370
The best solution is
WVFGRD96 5.0 325 80 -10 3.17 0.4562
The mechanism corresponding to the best fit is
|
|
Figure 1. Waveform inversion focal mechanism
|
The best fit as a function of depth is given in the following figure:
|
|
Figure 2. Depth sensitivity for waveform mechanism
|
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 0.50 n 2
lp c 1.00 n 2
br c 0.12 0.25 n 4 p 2
|
|
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.
|
|
|
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:
- 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 11:23:29 AM CDT 2024
