Location
SLU Location
The program elocate was used with the CUS model to locate the earthquake using readings from nearby stations. The purpose was to check the ANSS location, which is essentailly the same, but primarily to get the takeoff angles for the first motion plot. The output of elocate is given by elocate.txt. The first motion data is compared to the final solution below.
ANSS Location
2010/10/11 13:33:40 35.306 -92.315 5.0 3.80 Arkansas
Arrival Times (from USGS)
Arrival time list
Felt Map
USGS Felt map for this earthquake
USGS Felt reports main page
Focal Mechanism
USGS/SLU Moment Tensor Solution
ENS 2010/10/11 13:33:40:0 35.31 -92.32 5.0 3.8 Arkansas
Stations used:
AG.FCAR AG.LCAR AG.WLAR IU.WCI NM.BLO NM.MGMO NM.MPH
NM.OLIL NM.PBMO NM.SIUC NM.SLM NM.UALR NM.USIN NM.UTMT
TA.135A TA.137A TA.138A TA.139A TA.237A TA.238A TA.239A
TA.338A TA.339A TA.O36A TA.P35A TA.P36A TA.Q34A TA.Q35A
TA.Q36A TA.Q37A TA.R34A TA.R35A TA.R36A TA.S33A TA.S34A
TA.S35A TA.S36A TA.T33A TA.T34A TA.T35A TA.T36A TA.T37A
TA.TUL1 TA.U33A TA.U34A TA.V33A TA.V34A TA.V35A TA.W33A
TA.W34A TA.W35A TA.W36A TA.W37A TA.W38A TA.X33A TA.X34A
TA.X35A TA.X36A TA.X37A TA.X38A TA.Y33A TA.Y34A TA.Y35A
TA.Y36A TA.Y38A TA.Y39A TA.Z34A TA.Z35A TA.Z37A TA.Z38A
TA.Z39A US.HDIL US.KSU1 US.MIAR US.OXF US.WMOK
Filtering commands used:
hp c 0.02 n 3
lp c 0.08 n 3
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 1.26e+22 dyne-cm
Mw = 4.00
Z = 5 km
Plane Strike Dip Rake
NP1 202 80 165
NP2 295 75 10
Principal Axes:
Axis Value Plunge Azimuth
T 1.26e+22 18 158
N 0.00e+00 72 351
P -1.26e+22 4 249
Moment Tensor: (dyne-cm)
Component Value
Mxx 8.28e+21
Mxy -8.12e+21
Mxz -3.07e+21
Myy -9.37e+21
Myz 2.11e+21
Mzz 1.09e+21
##############
##################----
###################---------
###################-----------
####################--------------
####################----------------
------##############------------------
--------------######--------------------
----------------------------------------
-------------------#####------------------
-------------------#########--------------
------------------#############-----------
-----------------################---------
-------------###################-----
P ------------######################---
-----------########################-
------------########################
----------########################
--------############ #######
-------############ T ######
---############# ###
##############
Global CMT Convention Moment Tensor:
R T P
1.09e+21 -3.07e+21 -2.11e+21
-3.07e+21 8.28e+21 8.12e+21
-2.11e+21 8.12e+21 -9.37e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20101011133340/index.html
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Preferred Solution
The preferred solution from an analysis of the surface-wave spectral amplitude radiation pattern, waveform inversion and first motion observations is
STK = 295
DIP = 75
RAKE = 10
MW = 4.00
HS = 5.0
The initial solution using without a microseism filter was
WVFGRD96 5.0 115 85 -5 3.98 0.5236
. Since this had few Rayleigh waves, a microseism filter was applied to show more Rayleigh wave data. There are only slight differences between the solutions. The addition of more Rayleigh-wave data makes the solution more convincing.
The surface-wave study was performed to get good Love wave dispersion to the new positions of the TA array. Also not ehte large amplitude for stations in Texas due to shallow structure.
Moment Tensor Comparison
The following compares this source inversion to others
| SLU |
SLUFM |
USGS/SLU Moment Tensor Solution
ENS 2010/10/11 13:33:40:0 35.31 -92.32 5.0 3.8 Arkansas
Stations used:
AG.FCAR AG.LCAR AG.WLAR IU.WCI NM.BLO NM.MGMO NM.MPH
NM.OLIL NM.PBMO NM.SIUC NM.SLM NM.UALR NM.USIN NM.UTMT
TA.135A TA.137A TA.138A TA.139A TA.237A TA.238A TA.239A
TA.338A TA.339A TA.O36A TA.P35A TA.P36A TA.Q34A TA.Q35A
TA.Q36A TA.Q37A TA.R34A TA.R35A TA.R36A TA.S33A TA.S34A
TA.S35A TA.S36A TA.T33A TA.T34A TA.T35A TA.T36A TA.T37A
TA.TUL1 TA.U33A TA.U34A TA.V33A TA.V34A TA.V35A TA.W33A
TA.W34A TA.W35A TA.W36A TA.W37A TA.W38A TA.X33A TA.X34A
TA.X35A TA.X36A TA.X37A TA.X38A TA.Y33A TA.Y34A TA.Y35A
TA.Y36A TA.Y38A TA.Y39A TA.Z34A TA.Z35A TA.Z37A TA.Z38A
TA.Z39A US.HDIL US.KSU1 US.MIAR US.OXF US.WMOK
Filtering commands used:
hp c 0.02 n 3
lp c 0.08 n 3
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 1.26e+22 dyne-cm
Mw = 4.00
Z = 5 km
Plane Strike Dip Rake
NP1 202 80 165
NP2 295 75 10
Principal Axes:
Axis Value Plunge Azimuth
T 1.26e+22 18 158
N 0.00e+00 72 351
P -1.26e+22 4 249
Moment Tensor: (dyne-cm)
Component Value
Mxx 8.28e+21
Mxy -8.12e+21
Mxz -3.07e+21
Myy -9.37e+21
Myz 2.11e+21
Mzz 1.09e+21
##############
##################----
###################---------
###################-----------
####################--------------
####################----------------
------##############------------------
--------------######--------------------
----------------------------------------
-------------------#####------------------
-------------------#########--------------
------------------#############-----------
-----------------################---------
-------------###################-----
P ------------######################---
-----------########################-
------------########################
----------########################
--------############ #######
-------############ T ######
---############# ###
##############
Global CMT Convention Moment Tensor:
R T P
1.09e+21 -3.07e+21 -2.11e+21
-3.07e+21 8.28e+21 8.12e+21
-2.11e+21 8.12e+21 -9.37e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20101011133340/index.html
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First motions and takeoff angles from an elocate run.
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Waveform Inversion
The focal mechanism was determined using broadband seismic waveforms. The location of the event and the
and stations used for 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 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 0.08 n 3
br c 0.12 0.25 n 4 p 2
The results of this grid search from 0.5 to 19 km depth are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 0.5 290 65 -20 3.94 0.4832
WVFGRD96 1.0 290 65 -20 3.95 0.5032
WVFGRD96 2.0 290 70 -20 3.97 0.5278
WVFGRD96 3.0 295 85 0 3.96 0.5446
WVFGRD96 4.0 295 85 5 3.98 0.5535
WVFGRD96 5.0 295 75 10 4.00 0.5556
WVFGRD96 6.0 295 75 10 4.01 0.5539
WVFGRD96 7.0 295 70 10 4.02 0.5502
WVFGRD96 8.0 295 70 5 4.03 0.5457
WVFGRD96 9.0 295 70 5 4.03 0.5420
WVFGRD96 10.0 295 70 10 4.04 0.5387
WVFGRD96 11.0 295 70 10 4.05 0.5349
WVFGRD96 12.0 295 75 10 4.05 0.5313
WVFGRD96 13.0 295 75 10 4.05 0.5276
WVFGRD96 14.0 295 75 10 4.06 0.5237
WVFGRD96 15.0 295 80 15 4.06 0.5202
WVFGRD96 16.0 295 80 15 4.07 0.5162
WVFGRD96 17.0 115 90 -15 4.07 0.5100
WVFGRD96 18.0 295 85 15 4.08 0.5074
WVFGRD96 19.0 115 90 -15 4.09 0.5007
WVFGRD96 20.0 295 85 15 4.10 0.4973
WVFGRD96 21.0 295 85 15 4.11 0.4909
WVFGRD96 22.0 115 90 -15 4.11 0.4834
WVFGRD96 23.0 115 90 -15 4.12 0.4765
WVFGRD96 24.0 115 90 -15 4.12 0.4690
WVFGRD96 25.0 115 90 -15 4.13 0.4614
WVFGRD96 26.0 115 90 -15 4.14 0.4537
WVFGRD96 27.0 295 90 15 4.14 0.4459
WVFGRD96 28.0 295 90 15 4.15 0.4378
WVFGRD96 29.0 295 90 15 4.15 0.4299
The best solution is
WVFGRD96 5.0 295 75 10 4.00 0.5556
The mechanism correspond 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 and because the velocity model used in the predictions may not be perfect.
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 0.08 n 3
br c 0.12 0.25 n 4 p 2
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Figure 3. Waveform comparison for selected depth
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Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to thewavefroms.
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= 25.00
DIP= 90.00
RAKE= -160.00
OR
STK= 295.00
DIP= 70.00
RAKE= -0.01
DEPTH = 7.0 km
Mw = 4.14
Best Fit 0.8437 - P-T axis plot gives solutions with FIT greater than FIT90
First motion data
The P-wave first motion data for focal mechanism studies are as follow:
Sta Az Dist First motion
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
Broadband station distribution
The distribution of broadband stations with azimuth and distance is
Listing of broadband stations used
Waveform comparison for this mechanism
Since the analysis of the surface-wave radiation patterns uses only spectral
amplitudes and because the surfave-wave radiation patterns have a 180 degree symmetry, each surface-wave solution consists of four possible focal mechanisms corresponding to the interchange of the P- and T-axes and a roation of the mechanism by 180 degrees. To select one mechanism, P-wave first motion can be used. This was not possible in this case because all the P-wave first motions were
emergent ( a feature of the P-wave wave takeoff angle, the station location and the mechanism). The other way to select among the mechanisms is to compute
forward synthetics and compare the observed and predicted waveforms.
The fits to the waveforms with the given mechanism are show below:
This figure shows the fit to the three components of motion (Z - vertical, R-radial and T - transverse). For each station and component, the
observed traces is shown in red and the model predicted trace in blue. The traces represent filtered ground velocity in units of meters/sec (the peak value is printed adjacent to each trace; each pair of traces to plotted to the same scale to emphasize the difference in levels). Both synthetic and observed traces have been filtered using the SAC commands:
Discussion
The Future
Should the national backbone of the
USGS Advanced National Seismic System (ANSS)
be implemented with an interstation separation of 300 km, it is very likely that
an earthquake such as this would have been recorded at distances on the order of
100-200 km. This means that the closest station would have information on
source depth and mechanism that was lacking here.
Acknowledgements
Dr. Harley Benz, USGS, provided the USGS USNSN digital data.
The digital data used in this study were provided by Natural Resources Canada through their AUTODRM site http://www.seismo.nrcan.gc.ca/nwfa/autodrm/autodrm_req_e.php, and IRIS using their BUD interface.
Thanks also to the many seismic network operators whose dedication make this effort possible: University of Alaska, University of Washington, Oregon State University, University of Utah, Montana Bureas of Mines, UC Berkely, Caltech, UC San Diego, Saint L ouis University, Universityof Memphis, Lamont Doehrty Earth Observatory, Boston College, the Iris stations and the Transportable Array of EarthScope.
Appendix A
Spectra fit plots to each station
Velocity Model
The CUS used for the waveform synthetic seismograms and for the surface wave eigenfunctions and dispersion is as follows:
MODEL.01
CUS Model with Q from simple gamma values
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
1.0000 5.0000 2.8900 2.5000 0.172E-02 0.387E-02 0.00 0.00 1.00 1.00
9.0000 6.1000 3.5200 2.7300 0.160E-02 0.363E-02 0.00 0.00 1.00 1.00
10.0000 6.4000 3.7000 2.8200 0.149E-02 0.336E-02 0.00 0.00 1.00 1.00
20.0000 6.7000 3.8700 2.9020 0.000E-04 0.000E-04 0.00 0.00 1.00 1.00
0.0000 8.1500 4.7000 3.3640 0.194E-02 0.431E-02 0.00 0.00 1.00 1.00
Quality Control
Here we tabulate the reasons for not using certain digital data sets
The following stations did not have a valid response files:
DATE=Fri Oct 15 12:00:04 CDT 2010
Last Changed 2010/10/11
