Location

2016/01/02 20:26:40 35.763 -97.367 9.1 3.5 Oklahoma

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  2016/01/02 20:26:40:0  35.76  -97.37   9.1 3.5 Oklahoma
 
 Stations used:
   GS.OK025 GS.OK033 N4.T35B OK.BCOK OK.CCOK OK.CHOK OK.FNO 
   OK.OKCFA 
 
 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 0.20 n 3 
 
 Best Fitting Double Couple
  Mo = 1.05e+21 dyne-cm
  Mw = 3.28 
  Z  = 5 km
  Plane   Strike  Dip  Rake
   NP1      210    85   175
   NP2      300    85     5
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   1.05e+21      7     165
    N   0.00e+00     83     345
    P  -1.05e+21      0     255

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     8.88e+20
       Mxy    -5.26e+20
       Mxz    -1.23e+20
       Myy    -9.04e+20
       Myz     3.38e+19
       Mzz     1.58e+19
                                                     
                                                     
                                                     
                                                     
                     ##############                  
                 #####################-              
              ######################------           
             ######################--------          
           #######################-----------        
          -######################-------------       
         ------################----------------      
        -----------###########------------------     
        --------------#######-------------------     
       -------------------##---------------------    
       --------------------##--------------------    
       -------------------######-----------------    
       ------------------##########--------------    
          --------------##############----------     
        P -------------##################-------     
          ------------#####################----      
          -----------#########################       
           ---------#########################        
             ------########################          
              -----#######################           
                 -##############   ####              
                     ########### T                   
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  1.58e+19  -1.23e+20  -3.38e+19 
 -1.23e+20   8.88e+20   5.26e+20 
 -3.38e+19   5.26e+20  -9.04e+20 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20160102202640/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 = 300
      DIP = 85
     RAKE = 5
       MW = 3.28
       HS = 5.0

The NDK file is 20160102202640.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others
SLU
 USGS/SLU Moment Tensor Solution
 ENS  2016/01/02 20:26:40:0  35.76  -97.37   9.1 3.5 Oklahoma
 
 Stations used:
   GS.OK025 GS.OK033 N4.T35B OK.BCOK OK.CCOK OK.CHOK OK.FNO 
   OK.OKCFA 
 
 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 0.20 n 3 
 
 Best Fitting Double Couple
  Mo = 1.05e+21 dyne-cm
  Mw = 3.28 
  Z  = 5 km
  Plane   Strike  Dip  Rake
   NP1      210    85   175
   NP2      300    85     5
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   1.05e+21      7     165
    N   0.00e+00     83     345
    P  -1.05e+21      0     255

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     8.88e+20
       Mxy    -5.26e+20
       Mxz    -1.23e+20
       Myy    -9.04e+20
       Myz     3.38e+19
       Mzz     1.58e+19
                                                     
                                                     
                                                     
                                                     
                     ##############                  
                 #####################-              
              ######################------           
             ######################--------          
           #######################-----------        
          -######################-------------       
         ------################----------------      
        -----------###########------------------     
        --------------#######-------------------     
       -------------------##---------------------    
       --------------------##--------------------    
       -------------------######-----------------    
       ------------------##########--------------    
          --------------##############----------     
        P -------------##################-------     
          ------------#####################----      
          -----------#########################       
           ---------#########################        
             ------########################          
              -----#######################           
                 -##############   ####              
                     ########### T                   
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  1.58e+19  -1.23e+20  -3.38e+19 
 -1.23e+20   8.88e+20   5.26e+20 
 -3.38e+19   5.26e+20  -9.04e+20 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20160102202640/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

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 0.20 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    30    85    20   2.85 0.3334
WVFGRD96    2.0    25    75   -10   3.06 0.4343
WVFGRD96    3.0   120    90   -15   3.15 0.4818
WVFGRD96    4.0   300    85    15   3.23 0.5160
WVFGRD96    5.0   300    85     5   3.28 0.5252
WVFGRD96    6.0   300    80     5   3.34 0.5145
WVFGRD96    7.0   300    80     5   3.39 0.4894
WVFGRD96    8.0   300    80     5   3.43 0.4499
WVFGRD96    9.0   300    75     5   3.47 0.4060
WVFGRD96   10.0   300    65     0   3.50 0.3619
WVFGRD96   11.0   300    70     0   3.51 0.3186
WVFGRD96   12.0   295    60   -10   3.54 0.2801
WVFGRD96   13.0   305    35     5   3.60 0.2512
WVFGRD96   14.0   285    35   -10   3.62 0.2331
WVFGRD96   15.0   295    35    -5   3.61 0.2198
WVFGRD96   16.0   205    90   -60   3.64 0.2227
WVFGRD96   17.0    25    85    55   3.65 0.2268
WVFGRD96   18.0    25    85    55   3.66 0.2292
WVFGRD96   19.0   120    70   -10   3.54 0.2342
WVFGRD96   20.0   125    65   -10   3.57 0.2436
WVFGRD96   21.0   125    65   -15   3.58 0.2495
WVFGRD96   22.0   125    65   -15   3.59 0.2590
WVFGRD96   23.0   125    65   -15   3.59 0.2633
WVFGRD96   24.0   125    60   -15   3.60 0.2685
WVFGRD96   25.0   125    55   -15   3.61 0.2725
WVFGRD96   26.0   125    55   -15   3.62 0.2721
WVFGRD96   27.0   125    60   -10   3.61 0.2752
WVFGRD96   28.0   125    60   -10   3.61 0.2736
WVFGRD96   29.0   125    70     5   3.60 0.2789

The best solution is

WVFGRD96    5.0   300    85     5   3.28 0.5252

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 0.20 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 Sun Jan 3 10:15:35 CST 2016