Location

2013/12/07 18:10:24 35.362 -97.344 9.2 4.5 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  2013/12/07 18:10:24:0  35.36  -97.34   9.2 4.5 Oklahoma
 
 Stations used:
   AG.CCAR AG.FCAR AG.LCAR AG.WHAR AG.WLAR IU.CCM NM.MGMO 
   NM.PBMO NM.UALR OK.U32A OK.X37A TA.435B TA.ABTX TA.KSCO 
   TA.MSTX TA.T25A TA.TUL1 TA.U40A TA.W39A TA.W41B TA.WHTX 
   TA.X40A TA.X43A TA.Z41A US.AMTX US.CBKS US.KSU1 US.MIAR 
   US.WMOK 
 
 Filtering commands used:
   cut a -30 a 210
   rtr
   taper w 0.1
   hp c 0.02 n 3 
   lp c 0.06 n 3 
 
 Best Fitting Double Couple
  Mo = 6.61e+22 dyne-cm
  Mw = 4.48 
  Z  = 8 km
  Plane   Strike  Dip  Rake
   NP1      203    81   -160
   NP2      110    70   -10
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   6.61e+22      7     335
    N   0.00e+00     68     227
    P  -6.61e+22     21      68

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     4.58e+22
       Mxy    -4.45e+22
       Mxz    -6.47e+20
       Myy    -3.84e+22
       Myz    -2.39e+22
       Mzz    -7.37e+21
                                                     
                                                     
                                                     
                                                     
                     ##############                  
                 # T ##############----              
              ####   #############--------           
             ###################-----------          
           ####################--------------        
          ####################----------------       
         ####################-------------   --      
        -###################-------------- P ---     
        ---################---------------   ---     
       ------##############----------------------    
       --------###########-----------------------    
       -----------#######------------------------    
       --------------###-------------------------    
        ----------------##----------------------     
        ---------------#########----------------     
         -------------#########################      
          ------------########################       
           ----------########################        
             --------######################          
              ------######################           
                 ---###################              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -7.37e+21  -6.47e+20   2.39e+22 
 -6.47e+20   4.58e+22   4.45e+22 
  2.39e+22   4.45e+22  -3.84e+22 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20131207181024/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 = 110
      DIP = 70
     RAKE = -10
       MW = 4.48
       HS = 8.0

The NDK file is 20131207181024.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others
SLU
USGSMT
 USGS/SLU Moment Tensor Solution
 ENS  2013/12/07 18:10:24:0  35.36  -97.34   9.2 4.5 Oklahoma
 
 Stations used:
   AG.CCAR AG.FCAR AG.LCAR AG.WHAR AG.WLAR IU.CCM NM.MGMO 
   NM.PBMO NM.UALR OK.U32A OK.X37A TA.435B TA.ABTX TA.KSCO 
   TA.MSTX TA.T25A TA.TUL1 TA.U40A TA.W39A TA.W41B TA.WHTX 
   TA.X40A TA.X43A TA.Z41A US.AMTX US.CBKS US.KSU1 US.MIAR 
   US.WMOK 
 
 Filtering commands used:
   cut a -30 a 210
   rtr
   taper w 0.1
   hp c 0.02 n 3 
   lp c 0.06 n 3 
 
 Best Fitting Double Couple
  Mo = 6.61e+22 dyne-cm
  Mw = 4.48 
  Z  = 8 km
  Plane   Strike  Dip  Rake
   NP1      203    81   -160
   NP2      110    70   -10
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   6.61e+22      7     335
    N   0.00e+00     68     227
    P  -6.61e+22     21      68

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     4.58e+22
       Mxy    -4.45e+22
       Mxz    -6.47e+20
       Myy    -3.84e+22
       Myz    -2.39e+22
       Mzz    -7.37e+21
                                                     
                                                     
                                                     
                                                     
                     ##############                  
                 # T ##############----              
              ####   #############--------           
             ###################-----------          
           ####################--------------        
          ####################----------------       
         ####################-------------   --      
        -###################-------------- P ---     
        ---################---------------   ---     
       ------##############----------------------    
       --------###########-----------------------    
       -----------#######------------------------    
       --------------###-------------------------    
        ----------------##----------------------     
        ---------------#########----------------     
         -------------#########################      
          ------------########################       
           ----------########################        
             --------######################          
              ------######################           
                 ---###################              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -7.37e+21  -6.47e+20   2.39e+22 
 -6.47e+20   4.58e+22   4.45e+22 
  2.39e+22   4.45e+22  -3.84e+22 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20131207181024/index.html
	
Regional Moment Tensor (Mwr)

Moment magnitude derived from a moment tensor inversion of complete waveforms at regional distances (less than ~8 degrees), generally used for the analysis of small to moderate size earthquakes (typically Mw 3.5-6.0) crust or upper mantle earthquakes.

Moment
7.36e+15 N-m
Magnitude
4.5
Percent DC
86%
Depth
8.0 km
Updated
2013-12-07 18:23:36 UTC
Author
us
Catalog
us
Contributor
us
Code
us_b000ldeh_mwr
Principal Axes

Axis	Value	Plunge	Azimuth
T	7.613	0	159
N	-0.526	81	69
P	-7.087	9	249
Nodal Planes

Plane	Strike	Dip	Rake
NP1	24	84	-174
NP2	294	84	-6


        

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 a -30 a 210
rtr
taper w 0.1
hp c 0.02 n 3 
lp c 0.06 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    0.5   105    65   -30   4.27 0.4698
WVFGRD96    1.0   110    70   -20   4.26 0.4951
WVFGRD96    2.0   110    70   -20   4.35 0.5928
WVFGRD96    3.0   110    75   -15   4.37 0.6302
WVFGRD96    4.0   110    80   -10   4.39 0.6513
WVFGRD96    5.0   110    75   -10   4.41 0.6617
WVFGRD96    6.0   110    75    -5   4.43 0.6667
WVFGRD96    7.0   110    75    -5   4.45 0.6701
WVFGRD96    8.0   110    70   -10   4.48 0.6748
WVFGRD96    9.0   110    70   -10   4.49 0.6694
WVFGRD96   10.0   110    75   -15   4.51 0.6634
WVFGRD96   11.0   110    75   -15   4.52 0.6571
WVFGRD96   12.0   110    75   -15   4.53 0.6490
WVFGRD96   13.0   110    75   -15   4.54 0.6390
WVFGRD96   14.0   110    75   -15   4.54 0.6275
WVFGRD96   15.0   110    75   -15   4.55 0.6144
WVFGRD96   16.0   110    75   -15   4.56 0.6001
WVFGRD96   17.0   110    75   -15   4.56 0.5850
WVFGRD96   18.0   110    75   -15   4.57 0.5690
WVFGRD96   19.0   110    75   -15   4.57 0.5527
WVFGRD96   20.0   110    75   -15   4.58 0.5366
WVFGRD96   21.0   110    75   -15   4.59 0.5224
WVFGRD96   22.0   110    75   -15   4.59 0.5067
WVFGRD96   23.0   110    75   -15   4.60 0.4904
WVFGRD96   24.0   110    75   -15   4.60 0.4749
WVFGRD96   25.0   110    75   -15   4.61 0.4591
WVFGRD96   26.0   110    80   -20   4.62 0.4435
WVFGRD96   27.0   110    80   -20   4.62 0.4285
WVFGRD96   28.0   110    80   -20   4.63 0.4134
WVFGRD96   29.0   110    80   -20   4.63 0.3980

The best solution is

WVFGRD96    8.0   110    70   -10   4.48 0.6748

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 a -30 a 210
rtr
taper w 0.1
hp c 0.02 n 3 
lp c 0.06 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 7 00:23:48 CST 2015