Location

Location ANSS

2016/12/06 15:41:37 36.120 -96.702 5.0 3.5 Oklahoma

Focal Mechanism

 USGS/SLU Moment Tensor Solution
 ENS  2016/12/06 15:41:37:0  36.12  -96.70   5.0 3.5 Oklahoma
 
 Stations used:
   GS.OK030 GS.OK031 GS.OK033 GS.OK034 GS.OK045 GS.OK046 
   GS.OK048 GS.OK052 GS.OK053 
 
 Filtering commands used:
   cut o DIST/3.3 -20 o DIST/3.3 +40
   rtr
   taper w 0.1
   hp c 0.04 n 3 
   lp c 0.17 n 3 
 
 Best Fitting Double Couple
  Mo = 6.92e+20 dyne-cm
  Mw = 3.16 
  Z  = 3 km
  Plane   Strike  Dip  Rake
   NP1      252    74   -143
   NP2      150    55   -20
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   6.92e+20     12      17
    N   0.00e+00     50     272
    P  -6.92e+20     37     116

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     5.17e+20
       Mxy     3.63e+20
       Mxz     2.82e+20
       Myy    -2.94e+20
       Myz    -2.57e+20
       Mzz    -2.22e+20
                                                     
                                                     
                                                     
                                                     
                     ###########                     
                 ############### T ####              
              ---###############   #######           
             ---###########################          
           -----#############################        
          ------##############################       
         -------###############################      
        --------#####################-----------     
        ---------############-------------------     
       ----------######--------------------------    
       -----------#------------------------------    
       ---------###------------------------------    
       ------######------------------------------    
        --##########------------------   -------     
        ##############---------------- P -------     
         ##############---------------   ------      
          ###############---------------------       
           ###############-------------------        
             ################--------------          
              #################-----------           
                 ###################---              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -2.22e+20   2.82e+20   2.57e+20 
  2.82e+20   5.17e+20  -3.63e+20 
  2.57e+20  -3.63e+20  -2.94e+20 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20161206154137/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 = 150
      DIP = 55
     RAKE = -20
       MW = 3.16
       HS = 3.0

The NDK file is 20161206154137.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others
SLU
 USGS/SLU Moment Tensor Solution
 ENS  2016/12/06 15:41:37:0  36.12  -96.70   5.0 3.5 Oklahoma
 
 Stations used:
   GS.OK030 GS.OK031 GS.OK033 GS.OK034 GS.OK045 GS.OK046 
   GS.OK048 GS.OK052 GS.OK053 
 
 Filtering commands used:
   cut o DIST/3.3 -20 o DIST/3.3 +40
   rtr
   taper w 0.1
   hp c 0.04 n 3 
   lp c 0.17 n 3 
 
 Best Fitting Double Couple
  Mo = 6.92e+20 dyne-cm
  Mw = 3.16 
  Z  = 3 km
  Plane   Strike  Dip  Rake
   NP1      252    74   -143
   NP2      150    55   -20
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   6.92e+20     12      17
    N   0.00e+00     50     272
    P  -6.92e+20     37     116

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     5.17e+20
       Mxy     3.63e+20
       Mxz     2.82e+20
       Myy    -2.94e+20
       Myz    -2.57e+20
       Mzz    -2.22e+20
                                                     
                                                     
                                                     
                                                     
                     ###########                     
                 ############### T ####              
              ---###############   #######           
             ---###########################          
           -----#############################        
          ------##############################       
         -------###############################      
        --------#####################-----------     
        ---------############-------------------     
       ----------######--------------------------    
       -----------#------------------------------    
       ---------###------------------------------    
       ------######------------------------------    
        --##########------------------   -------     
        ##############---------------- P -------     
         ##############---------------   ------      
          ###############---------------------       
           ###############-------------------        
             ################--------------          
              #################-----------           
                 ###################---              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -2.22e+20   2.82e+20   2.57e+20 
  2.82e+20   5.17e+20  -3.63e+20 
  2.57e+20  -3.63e+20  -2.94e+20 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20161206154137/index.html
	

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 -20 o DIST/3.3 +40
rtr
taper w 0.1
hp c 0.04 n 3 
lp c 0.17 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   155    55     5   2.90 0.5321
WVFGRD96    2.0   155    35    -5   3.15 0.5884
WVFGRD96    3.0   150    55   -20   3.16 0.5920
WVFGRD96    4.0    40    15   -70   3.38 0.5599
WVFGRD96    5.0    30    15   -85   3.44 0.5445
WVFGRD96    6.0    15    80    75   3.49 0.5200
WVFGRD96    7.0    20    80    75   3.54 0.4923
WVFGRD96    8.0   200    90   -80   3.63 0.4553
WVFGRD96    9.0   325    80   -30   3.33 0.4186
WVFGRD96   10.0   215    20   -60   3.57 0.4156
WVFGRD96   11.0   220    20   -55   3.59 0.4132
WVFGRD96   12.0   240    20   -40   3.65 0.4231
WVFGRD96   13.0   240    25   -35   3.64 0.4333
WVFGRD96   14.0   245    25   -30   3.65 0.4491
WVFGRD96   15.0   255    30   -20   3.67 0.4610
WVFGRD96   16.0   255    30   -15   3.65 0.4711
WVFGRD96   17.0   260    30   -10   3.66 0.4767
WVFGRD96   18.0   265    35    -5   3.67 0.4784
WVFGRD96   19.0   265    35     0   3.64 0.4770
WVFGRD96   20.0   270    40     5   3.66 0.4824
WVFGRD96   21.0   270    40     5   3.67 0.4818
WVFGRD96   22.0   275    40    10   3.68 0.4848
WVFGRD96   23.0   150    55   -30   3.55 0.4891
WVFGRD96   24.0   150    55   -30   3.56 0.5007
WVFGRD96   25.0   150    55   -30   3.57 0.5087
WVFGRD96   26.0   150    55   -30   3.57 0.5154
WVFGRD96   27.0   150    55   -30   3.58 0.5207
WVFGRD96   28.0   150    55   -30   3.58 0.5184
WVFGRD96   29.0   150    50   -30   3.60 0.5221

The best solution is

WVFGRD96    3.0   150    55   -20   3.16 0.5920

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 -20 o DIST/3.3 +40
rtr
taper w 0.1
hp c 0.04 n 3 
lp c 0.17 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:

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 Tue Dec 6 12:20:46 CST 2016