Location

Location SLU

Because of the small size of this event, the moment tensor solution is very sensitive fo the frequency band used. The small size means that it is difficult to focus on short periods. The program elocate was used to locate the event and to define takeoff angles for a first motion plot. This effort served two purposes: the relocation agrees with the ANSS epicenter so that the distances and azimuths to the stations are validated; the first motion plot agrees with the RMT solution. Thus there is confidence in the RMT soltuion. The details of the relocation are given in the file < href="elocate.txt"> elocate.txt .

Location ANSS

2016/09/22 06:42:18 36.426 -96.919 2.5 3.2 Oklahoma

Focal Mechanism

 USGS/SLU Moment Tensor Solution
 ENS  2016/09/22 06:42:18:0  36.43  -96.92   2.5 3.2 Oklahoma
 
 Stations used:
   GS.OK025 GS.OK029 GS.OK030 GS.OK033 GS.OK034 GS.OK038 
   GS.OK044 GS.OK047 GS.OK049 GS.OK051 N4.T35B OK.CROK OK.U32A 
 
 Filtering commands used:
   cut o DIST/3.3 -20 o DIST/3.3 +40
   rtr
   taper w 0.1
   hp c 0.03 n 3 
   lp c 0.15 n 3 
 
 Best Fitting Double Couple
  Mo = 2.63e+20 dyne-cm
  Mw = 2.88 
  Z  = 3 km
  Plane   Strike  Dip  Rake
   NP1      100    90     5
   NP2       10    85   180
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   2.63e+20      4     325
    N   0.00e+00     85     100
    P  -2.63e+20      4     235

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     8.96e+19
       Mxy    -2.46e+20
       Mxz     2.26e+19
       Myy    -8.96e+19
       Myz     3.98e+18
       Mzz    -2.00e+12
                                                     
                                                     
                                                     
                                                     
                     ###########---                  
                 ###############-------              
               T ##############-----------           
             #   ##############------------          
           ####################--------------        
          #####################---------------       
         ######################----------------      
        ######################------------------     
        ######################------------------     
       -----##################-------------------    
       ----------------######--------------------    
       ----------------------####----------------    
       ----------------------###############-----    
        --------------------####################     
        --------------------####################     
         -------------------###################      
             --------------###################       
           P --------------##################        
             -------------#################          
              ------------################           
                 --------##############              
                     ----##########                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -2.00e+12   2.26e+19  -3.98e+18 
  2.26e+19   8.96e+19   2.46e+20 
 -3.98e+18   2.46e+20  -8.96e+19 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20160922064218/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 = 100
      DIP = 90
     RAKE = 5
       MW = 2.88
       HS = 3.0

The NDK file is 20160922064218.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  2016/09/22 06:42:18:0  36.43  -96.92   2.5 3.2 Oklahoma
 
 Stations used:
   GS.OK025 GS.OK029 GS.OK030 GS.OK033 GS.OK034 GS.OK038 
   GS.OK044 GS.OK047 GS.OK049 GS.OK051 N4.T35B OK.CROK OK.U32A 
 
 Filtering commands used:
   cut o DIST/3.3 -20 o DIST/3.3 +40
   rtr
   taper w 0.1
   hp c 0.03 n 3 
   lp c 0.15 n 3 
 
 Best Fitting Double Couple
  Mo = 2.63e+20 dyne-cm
  Mw = 2.88 
  Z  = 3 km
  Plane   Strike  Dip  Rake
   NP1      100    90     5
   NP2       10    85   180
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   2.63e+20      4     325
    N   0.00e+00     85     100
    P  -2.63e+20      4     235

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     8.96e+19
       Mxy    -2.46e+20
       Mxz     2.26e+19
       Myy    -8.96e+19
       Myz     3.98e+18
       Mzz    -2.00e+12
                                                     
                                                     
                                                     
                                                     
                     ###########---                  
                 ###############-------              
               T ##############-----------           
             #   ##############------------          
           ####################--------------        
          #####################---------------       
         ######################----------------      
        ######################------------------     
        ######################------------------     
       -----##################-------------------    
       ----------------######--------------------    
       ----------------------####----------------    
       ----------------------###############-----    
        --------------------####################     
        --------------------####################     
         -------------------###################      
             --------------###################       
           P --------------##################        
             -------------#################          
              ------------################           
                 --------##############              
                     ----##########                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -2.00e+12   2.26e+19  -3.98e+18 
  2.26e+19   8.96e+19   2.46e+20 
 -3.98e+18   2.46e+20  -8.96e+19 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20160922064218/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 -20 o DIST/3.3 +40
rtr
taper w 0.1
hp c 0.03 n 3 
lp c 0.15 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    10    90   -15   2.67 0.3890
WVFGRD96    2.0   190    80    10   2.83 0.4547
WVFGRD96    3.0   100    90     5   2.88 0.4627
WVFGRD96    4.0   105    75    20   2.95 0.4584
WVFGRD96    5.0   100    85     5   2.97 0.4470
WVFGRD96    6.0   280    90    -5   3.01 0.4292
WVFGRD96    7.0   280    90    -5   3.05 0.4043
WVFGRD96    8.0   280    90   -10   3.08 0.3738
WVFGRD96    9.0   280    90   -10   3.11 0.3500
WVFGRD96   10.0   280    90   -15   3.13 0.3308
WVFGRD96   11.0   105    85    20   3.16 0.3116
WVFGRD96   12.0   105    85    20   3.17 0.2926
WVFGRD96   13.0   275    70   -10   3.18 0.2793
WVFGRD96   14.0   275    70   -15   3.19 0.2679
WVFGRD96   15.0   185    35     5   3.33 0.2579
WVFGRD96   16.0   190    30     5   3.35 0.2544
WVFGRD96   17.0   190    30     5   3.35 0.2502
WVFGRD96   18.0   190    35     0   3.35 0.2452
WVFGRD96   19.0   180    35   -25   3.33 0.2435
WVFGRD96   20.0   175    35   -25   3.34 0.2463
WVFGRD96   21.0   175    35   -25   3.36 0.2536
WVFGRD96   22.0   170    35   -30   3.37 0.2604
WVFGRD96   23.0   170    35   -30   3.38 0.2698
WVFGRD96   24.0   175    40   -30   3.38 0.2769
WVFGRD96   25.0   180    40   -25   3.39 0.2863
WVFGRD96   26.0   180    40   -30   3.40 0.2935
WVFGRD96   27.0   180    40   -30   3.41 0.2995
WVFGRD96   28.0   180    40   -30   3.41 0.3030
WVFGRD96   29.0   180    40   -30   3.42 0.3050

The best solution is

WVFGRD96    3.0   100    90     5   2.88 0.4627

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 0.03 n 3 
lp c 0.15 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 Thu Sep 22 19:18:35 CDT 2016