Location

Location ANSS

2016/12/05 08:58:31 36.036 -96.768 5.0 3.6 Oklahoma

Focal Mechanism

 USGS/SLU Moment Tensor Solution
 ENS  2016/12/05 08:58:31:0  36.04  -96.77   5.0 3.6 Oklahoma
 
 Stations used:
   GS.KAN06 GS.OK025 GS.OK030 GS.OK031 GS.OK033 GS.OK044 
   GS.OK045 GS.OK046 GS.OK048 GS.OK050 N4.T35B 
 
 Filtering commands used:
   cut o DIST/3.3 -30 o DIST/3.3 +50
   rtr
   taper w 0.1
   hp c 0.03 n 3 
   lp c 0.10 n 3 
 
 Best Fitting Double Couple
  Mo = 8.51e+20 dyne-cm
  Mw = 3.22 
  Z  = 3 km
  Plane   Strike  Dip  Rake
   NP1      218    80   170
   NP2      310    80    10
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   8.51e+20     14     174
    N   0.00e+00     76     355
    P  -8.51e+20      0     264

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     7.83e+20
       Mxy    -1.68e+20
       Mxz    -2.00e+20
       Myy    -8.34e+20
       Myz     2.22e+19
       Mzz     5.06e+19
                                                     
                                                     
                                                     
                                                     
                     ##############                  
                 ######################              
              ##########################--           
             #########################-----          
           ----####################----------        
          --------################------------       
         ------------###########---------------      
        ----------------######------------------     
        ------------------###-------------------     
       --------------------##--------------------    
       -------------------#####------------------    
         ---------------#########----------------    
       P --------------############--------------    
         ------------################-----------     
        ------------###################---------     
         ----------#####################-------      
          --------########################----       
           ------##########################--        
             ---###########################          
              -#############   ###########           
                 ########### T ########              
                     #######   ####                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  5.06e+19  -2.00e+20  -2.22e+19 
 -2.00e+20   7.83e+20   1.68e+20 
 -2.22e+19   1.68e+20  -8.34e+20 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20161205085831/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 = 310
      DIP = 80
     RAKE = 10
       MW = 3.22
       HS = 3.0

The NDK file is 20161205085831.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others
SLU
 USGS/SLU Moment Tensor Solution
 ENS  2016/12/05 08:58:31:0  36.04  -96.77   5.0 3.6 Oklahoma
 
 Stations used:
   GS.KAN06 GS.OK025 GS.OK030 GS.OK031 GS.OK033 GS.OK044 
   GS.OK045 GS.OK046 GS.OK048 GS.OK050 N4.T35B 
 
 Filtering commands used:
   cut o DIST/3.3 -30 o DIST/3.3 +50
   rtr
   taper w 0.1
   hp c 0.03 n 3 
   lp c 0.10 n 3 
 
 Best Fitting Double Couple
  Mo = 8.51e+20 dyne-cm
  Mw = 3.22 
  Z  = 3 km
  Plane   Strike  Dip  Rake
   NP1      218    80   170
   NP2      310    80    10
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   8.51e+20     14     174
    N   0.00e+00     76     355
    P  -8.51e+20      0     264

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     7.83e+20
       Mxy    -1.68e+20
       Mxz    -2.00e+20
       Myy    -8.34e+20
       Myz     2.22e+19
       Mzz     5.06e+19
                                                     
                                                     
                                                     
                                                     
                     ##############                  
                 ######################              
              ##########################--           
             #########################-----          
           ----####################----------        
          --------################------------       
         ------------###########---------------      
        ----------------######------------------     
        ------------------###-------------------     
       --------------------##--------------------    
       -------------------#####------------------    
         ---------------#########----------------    
       P --------------############--------------    
         ------------################-----------     
        ------------###################---------     
         ----------#####################-------      
          --------########################----       
           ------##########################--        
             ---###########################          
              -#############   ###########           
                 ########### T ########              
                     #######   ####                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  5.06e+19  -2.00e+20  -2.22e+19 
 -2.00e+20   7.83e+20   1.68e+20 
 -2.22e+19   1.68e+20  -8.34e+20 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20161205085831/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 -30 o DIST/3.3 +50
rtr
taper w 0.1
hp c 0.03 n 3 
lp c 0.10 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   310    90    15   3.03 0.4629
WVFGRD96    2.0   130    80     5   3.16 0.5124
WVFGRD96    3.0   310    80    10   3.22 0.5135
WVFGRD96    4.0   310    80    15   3.26 0.4986
WVFGRD96    5.0   310    75    10   3.30 0.4836
WVFGRD96    6.0   310    75    10   3.33 0.4679
WVFGRD96    7.0   310    80    15   3.35 0.4518
WVFGRD96    8.0   310    75    10   3.39 0.4328
WVFGRD96    9.0   310    75    10   3.41 0.4130
WVFGRD96   10.0   310    70     5   3.43 0.3925
WVFGRD96   11.0   310    75    10   3.44 0.3759
WVFGRD96   12.0   310    75    10   3.46 0.3600
WVFGRD96   13.0   310    75    10   3.47 0.3459
WVFGRD96   14.0   315    75    20   3.47 0.3341
WVFGRD96   15.0   315    80    25   3.48 0.3244
WVFGRD96   16.0   315    80    25   3.49 0.3164
WVFGRD96   17.0   315    80    25   3.50 0.3093
WVFGRD96   18.0   315    80    30   3.51 0.3035
WVFGRD96   19.0   325    70    50   3.55 0.3033
WVFGRD96   20.0   330    70    60   3.57 0.3048
WVFGRD96   21.0   330    70    60   3.58 0.3086
WVFGRD96   22.0   330    70    60   3.59 0.3115
WVFGRD96   23.0   330    70    65   3.61 0.3132
WVFGRD96   24.0   330    70    65   3.61 0.3149
WVFGRD96   25.0   335    65    70   3.63 0.3164
WVFGRD96   26.0   335    65    70   3.63 0.3191
WVFGRD96   27.0   340    65    75   3.64 0.3220
WVFGRD96   28.0   145    40    30   3.57 0.3193
WVFGRD96   29.0   140    45    25   3.58 0.3256

The best solution is

WVFGRD96    3.0   310    80    10   3.22 0.5135

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 -30 o DIST/3.3 +50
rtr
taper w 0.1
hp c 0.03 n 3 
lp c 0.10 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 Mon Dec 5 05:52:21 CST 2016