Location

Location SLU

Becasue the station OK040 was very close to the ANSS location, the program elocate was used to relocate the event in order to chack the azimuths to the nearest station. The ANSS solution and the SLU solutions are virtually the same. The comparison between the waveform inversion mechanism and the first motions is shown below in the comparison. The results are given in the file elocate.txt.

Location ANSS

2016/09/07 02:26:50 36.433 -96.900 6.9 3.5 Oklahoma

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2016/09/07 02:26:50:0 36.43 -96.90 6.9 3.5 Oklahoma Stations used: GS.OK029 GS.OK030 GS.OK031 GS.OK033 GS.OK044 OK.BCOK TA.TUL1 Filtering commands used: cut o DIST/3.3 -10 o DIST/3.3 +30 rtr taper w 0.1 hp c 0.05 n 3 lp c 0.12 n 3 Best Fitting Double Couple Mo = 6.46e+20 dyne-cm Mw = 3.14 Z = 3 km Plane Strike Dip Rake NP1 320 90 10 NP2 230 80 180 Principal Axes: Axis Value Plunge Azimuth T 6.46e+20 7 185 N 0.00e+00 80 320 P -6.46e+20 7 95 Moment Tensor: (dyne-cm) Component Value Mxx 6.26e+20 Mxy 1.10e+20 Mxz -7.21e+19 Myy -6.26e+20 Myz -8.59e+19 Mzz -9.80e+12 ############## ###################### -########################### ---########################### -------#######################---- ---------###################-------- ------------##############------------ ---------------#########---------------- ----------------######------------------ -------------------#---------------------- ------------------##------------------- ----------------######----------------- P --------------#########---------------- -----------#############---------------- ---------################--------------- -------###################------------ ----#######################--------- --#########################------- ###########################--- ###########################- ######## ########### #### T ####### Global CMT Convention Moment Tensor: R T P -9.80e+12 -7.21e+19 8.59e+19 -7.21e+19 6.26e+20 -1.10e+20 8.59e+19 -1.10e+20 -6.26e+20 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20160907022650/index.html

Preferred Solution

The preferred solution from an analysis of the surface-wave spectral amplitude radiation pattern, waveform inversion and first motion observations is

      STK = 320
      DIP = 90
     RAKE = 10
       MW = 3.14
       HS = 3.0

The NDK file is 20160907022650.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others

SLU SLUFM

USGS/SLU Moment Tensor Solution ENS 2016/09/07 02:26:50:0 36.43 -96.90 6.9 3.5 Oklahoma Stations used: GS.OK029 GS.OK030 GS.OK031 GS.OK033 GS.OK044 OK.BCOK TA.TUL1 Filtering commands used: cut o DIST/3.3 -10 o DIST/3.3 +30 rtr taper w 0.1 hp c 0.05 n 3 lp c 0.12 n 3 Best Fitting Double Couple Mo = 6.46e+20 dyne-cm Mw = 3.14 Z = 3 km Plane Strike Dip Rake NP1 320 90 10 NP2 230 80 180 Principal Axes: Axis Value Plunge Azimuth T 6.46e+20 7 185 N 0.00e+00 80 320 P -6.46e+20 7 95 Moment Tensor: (dyne-cm) Component Value Mxx 6.26e+20 Mxy 1.10e+20 Mxz -7.21e+19 Myy -6.26e+20 Myz -8.59e+19 Mzz -9.80e+12 ############## ###################### -########################### ---########################### -------#######################---- ---------###################-------- ------------##############------------ ---------------#########---------------- ----------------######------------------ -------------------#---------------------- ------------------##------------------- ----------------######----------------- P --------------#########---------------- -----------#############---------------- ---------################--------------- -------###################------------ ----#######################--------- --#########################------- ###########################--- ###########################- ######## ########### #### T ####### Global CMT Convention Moment Tensor: R T P -9.80e+12 -7.21e+19 8.59e+19 -7.21e+19 6.26e+20 -1.10e+20 8.59e+19 -1.10e+20 -6.26e+20 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20160907022650/index.html

First motions and takeoff angles from an elocate run.

Magnitudes

mLg Magnitude

(a) mLg computed using the IASPEI formula; (b) mLg residuals ; the values used for the trimmed mean are indicated.

ML Magnitude

(a) ML computed using the IASPEI formula for Horizontal components; (b) 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.

(a) ML computed using the IASPEI formula for Vertical components (research); (b) 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.

Context

The next figure presents the focal mechanism for this earthquake (red) in the context of other events (blue) in the SLU Moment Tensor Catalog which are within ± 0.5 degrees of the new event. This comparison is shown in the left panel of the figure. 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).

Waveform Inversion using wvfgrd96

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.

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 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 -10 o DIST/3.3 +30
rtr
taper w 0.1
hp c 0.05 n 3 
lp c 0.12 n 3

The results of this grid search from 0.5 to 19 km depth are as follow:

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0   320    85   -15   2.93 0.5108
WVFGRD96    2.0   320    70     5   3.08 0.5896
WVFGRD96    3.0   320    90    10   3.14 0.6059
WVFGRD96    4.0   140    90   -15   3.19 0.5827
WVFGRD96    5.0   315    80     5   3.20 0.5542
WVFGRD96    6.0   320    85    15   3.25 0.5276
WVFGRD96    7.0   320    85    15   3.28 0.4981
WVFGRD96    8.0   320    80    15   3.32 0.4686
WVFGRD96    9.0   320    75    20   3.35 0.4465
WVFGRD96   10.0   320    75    15   3.36 0.4243
WVFGRD96   11.0   320    75    15   3.39 0.4015
WVFGRD96   12.0   315    70    10   3.39 0.3862
WVFGRD96   13.0   315    70    10   3.41 0.3705
WVFGRD96   14.0   315    70     5   3.42 0.3530
WVFGRD96   15.0   315    70     5   3.43 0.3396
WVFGRD96   16.0   335    20    75   3.57 0.3282
WVFGRD96   17.0   325    20    65   3.59 0.3279
WVFGRD96   18.0   320    20    60   3.60 0.3307
WVFGRD96   19.0   315    20    55   3.62 0.3319
WVFGRD96   20.0   310    20    50   3.63 0.3344
WVFGRD96   21.0   310    20    50   3.64 0.3353
WVFGRD96   22.0   300    25    40   3.65 0.3369
WVFGRD96   23.0   300    25    40   3.66 0.3370
WVFGRD96   24.0   300    25    35   3.66 0.3369
WVFGRD96   25.0   300    25    35   3.67 0.3379
WVFGRD96   26.0   300    25    35   3.67 0.3393
WVFGRD96   27.0   300    25    35   3.68 0.3402
WVFGRD96   28.0   230    45   -15   3.66 0.3443
WVFGRD96   29.0   230    45   -15   3.67 0.3602

The best solution is

WVFGRD96    3.0   320    90    10   3.14 0.6059

The mechanism correspond 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 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

cut o DIST/3.3 -10 o DIST/3.3 +30
rtr
taper w 0.1
hp c 0.05 n 3 
lp c 0.12 n 3

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.

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.

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.

Discussion

Acknowledgements

Thanks also to the many seismic network operators whose dedication make this effort possible: University of Nevada Reno, University of Alaska, University of Washington, Oregon State University, University of Utah, Montana Bureas of Mines, UC Berkely, Caltech, UC San Diego, Saint Louis University, University of Memphis, Lamont Doherty Earth Observatory, the Iris stations and the Transportable Array of EarthScope.

Velocity Model

The WUS.model used for the waveform synthetic seismograms and for the surface wave eigenfunctions and dispersion is as follows:

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

Quality Control

Here we tabulate the reasons for not using certain digital data sets

The following stations did not have a valid response files:

Last Changed Wed Sep 7 16:03:24 CDT 2016