Location

SLU Location

To check the ANSS location or to compare the observed P-wave first motions to the moment tensor solution, P- and S-wave first arrival times were manually read together with the P-wave first motions. The subsequent output of the program elocate is given in the file elocate.txt. The first motion plot is shown below.

Location ANSS

The ANSS event ID is ok2021gurr and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/ok2021gurr/executive.

2021/04/07 16:51:49 35.059 -96.317 28.6 3.61 Oklahoma

Focal Mechanism

 USGS/SLU Moment Tensor Solution
 ENS  2021/04/07 16:51:49:0  35.06  -96.32  28.6 3.6 Oklahoma
 
 Stations used:
   GS.OK048 N4.TUL3 O2.ARC2 O2.CHAN O2.CRES O2.DRIP O2.DRUM 
   O2.DUST O2.ERNS O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 
   O2.PW18 O2.SC13 O2.SMNL O2.STIG OK.CHOK OK.DEOK OK.QUOK 
 
 Filtering commands used:
   cut o DIST/3.5 -10 o DIST/3.5 +10
   rtr
   taper w 0.1
   hp c 0.5 n 3 
   lp c 0.50 n 3 
 
 Best Fitting Double Couple
  Mo = 8.81e+20 dyne-cm
  Mw = 3.23 
  Z  = 29 km
  Plane   Strike  Dip  Rake
   NP1      237    86   -150
   NP2      145    60    -5
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   8.81e+20     17       7
    N   0.00e+00     60     245
    P  -8.81e+20     24     105

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     7.36e+20
       Mxy     2.91e+20
       Mxz     3.37e+20
       Myy    -6.70e+20
       Myz    -2.83e+20
       Mzz    -6.65e+19
                                                     
                                                     
                                                     
                                                     
                     ########   ###                  
                 ############ T #######              
              --#############   ##########           
             ---###########################          
           -----#############################        
          ------###########################---       
         -------########################-------      
        ---------####################-----------     
        ---------################---------------     
       -----------############-------------------    
       ------------########----------------------    
       -------------#####------------------------    
       --------------#--------------------   ----    
        -----------###-------------------- P ---     
        --------#######-------------------   ---     
         -----###########----------------------      
          --###############-------------------       
           ##################----------------        
             ##################------------          
              #####################-------           
                 ######################              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -6.65e+19   3.37e+20   2.83e+20 
  3.37e+20   7.36e+20  -2.91e+20 
  2.83e+20  -2.91e+20  -6.70e+20 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210407165149/index.html
        

Preferred Solution

The preferred solution from an analysis of the surface-wave spectral amplitude radiation pattern, waveform inversion or first motion observations is

      STK = 145
      DIP = 60
     RAKE = -5
       MW = 3.23
       HS = 29.0

The NDK file is 20210407165149.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to those provided by others. The purpose is to look for major differences and also to note slight differences that might be inherent to the processing procedure. For completeness the USGS/SLU solution is repeated from above.
SLU
SLUFM
 USGS/SLU Moment Tensor Solution
 ENS  2021/04/07 16:51:49:0  35.06  -96.32  28.6 3.6 Oklahoma
 
 Stations used:
   GS.OK048 N4.TUL3 O2.ARC2 O2.CHAN O2.CRES O2.DRIP O2.DRUM 
   O2.DUST O2.ERNS O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 
   O2.PW18 O2.SC13 O2.SMNL O2.STIG OK.CHOK OK.DEOK OK.QUOK 
 
 Filtering commands used:
   cut o DIST/3.5 -10 o DIST/3.5 +10
   rtr
   taper w 0.1
   hp c 0.5 n 3 
   lp c 0.50 n 3 
 
 Best Fitting Double Couple
  Mo = 8.81e+20 dyne-cm
  Mw = 3.23 
  Z  = 29 km
  Plane   Strike  Dip  Rake
   NP1      237    86   -150
   NP2      145    60    -5
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   8.81e+20     17       7
    N   0.00e+00     60     245
    P  -8.81e+20     24     105

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     7.36e+20
       Mxy     2.91e+20
       Mxz     3.37e+20
       Myy    -6.70e+20
       Myz    -2.83e+20
       Mzz    -6.65e+19
                                                     
                                                     
                                                     
                                                     
                     ########   ###                  
                 ############ T #######              
              --#############   ##########           
             ---###########################          
           -----#############################        
          ------###########################---       
         -------########################-------      
        ---------####################-----------     
        ---------################---------------     
       -----------############-------------------    
       ------------########----------------------    
       -------------#####------------------------    
       --------------#--------------------   ----    
        -----------###-------------------- P ---     
        --------#######-------------------   ---     
         -----###########----------------------      
          --###############-------------------       
           ##################----------------        
             ##################------------          
              #####################-------           
                 ######################              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -6.65e+19   3.37e+20   2.83e+20 
  3.37e+20   7.36e+20  -2.91e+20 
  2.83e+20  -2.91e+20  -6.70e+20 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210407165149/index.html
	


First motions and takeoff angles from an elocate run.

Magnitudes

Given the availability of digital waveforms for determination of the moment tensor, this section documents the added processing leading to mLg, if appropriate to the region, and ML by application of the respective IASPEI formulae. As a research study, the linear distance term of the IASPEI formula for ML is adjusted to remove a linear distance trend in residuals to give a regionally defined ML. The defined ML uses horizontal component recordings, but the same procedure is applied to the vertical components since there may be some interest in vertical component ground motions. Residual plots versus distance may indicate interesting features of ground motion scaling in some distance ranges. A residual plot of the regionalized magnitude is given as a function of distance and azimuth, since data sets may transcend different wave propagation provinces.

mLg Magnitude


Left: mLg computed using the IASPEI formula. Center: mLg residuals versus epicentral distance ; the values used for the trimmed mean magnitude estimate are indicated. Right: residuals as a function of distance and azimuth.

ML Magnitude


Left: ML computed using the IASPEI formula for Horizontal components. Center: 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. Right: Residuals from new relation as a function of distance and azimuth.


Left: ML computed using the IASPEI formula for Vertical components (research). Center: 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. Right: Residuals from new relation as a function of distance and azimuth.

Context

The left panel of the next figure presents the focal mechanism for this earthquake (red) in the context of other nearby events (blue) in the SLU Moment Tensor Catalog. 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). Thus context plot is useful for assessing the appropriateness of the moment tensor of this event.

Waveform Inversion using wvfgrd96

The focal mechanism was determined using broadband seismic waveforms. The location of the event (star) and the stations used for (red) 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's 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/3.5 -10 o DIST/3.5 +10
rtr
taper w 0.1
hp c 0.5 n 3 
lp c 0.50 n 3 
The results of this grid search are as follow:

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0   280     0  -105   2.65 0.1415
WVFGRD96    2.0    55    55   -25   2.83 0.1297
WVFGRD96    3.0   170    60    55   2.94 0.1884
WVFGRD96    4.0   175    55    65   2.97 0.2374
WVFGRD96    5.0   175    50    60   2.98 0.2607
WVFGRD96    6.0   170    55    50   3.00 0.2716
WVFGRD96    7.0   165    50    35   2.99 0.2731
WVFGRD96    8.0   170    45    40   3.07 0.2830
WVFGRD96    9.0   165    55    40   3.12 0.3142
WVFGRD96   10.0   165    55    40   3.15 0.3259
WVFGRD96   11.0   160    55    35   3.18 0.3433
WVFGRD96   12.0   160    55    30   3.20 0.3553
WVFGRD96   13.0   155    55    25   3.21 0.3618
WVFGRD96   14.0   155    55    20   3.22 0.3815
WVFGRD96   15.0   155    55    25   3.23 0.3777
WVFGRD96   16.0   155    55    20   3.24 0.4026
WVFGRD96   17.0   155    55    20   3.24 0.4015
WVFGRD96   18.0   150    55    15   3.24 0.3989
WVFGRD96   19.0   150    55    15   3.24 0.4109
WVFGRD96   20.0   150    55    15   3.23 0.3949
WVFGRD96   21.0   150    50    15   3.23 0.3878
WVFGRD96   22.0   150    55    10   3.21 0.3659
WVFGRD96   23.0   150    55    10   3.20 0.3502
WVFGRD96   24.0   145    60    -5   3.19 0.3263
WVFGRD96   25.0   140    65   -20   3.21 0.3564
WVFGRD96   26.0   140    60   -15   3.21 0.3623
WVFGRD96   27.0   140    60   -10   3.22 0.3933
WVFGRD96   28.0   140    60   -10   3.23 0.4092
WVFGRD96   29.0   145    60    -5   3.23 0.4159
WVFGRD96   30.0   145    60    -5   3.23 0.4008
WVFGRD96   31.0   145    60    -5   3.22 0.3955
WVFGRD96   32.0   140    65   -20   3.20 0.3752
WVFGRD96   33.0   140    65   -20   3.20 0.3957
WVFGRD96   34.0   140    65   -20   3.19 0.3929
WVFGRD96   35.0   140    65   -25   3.19 0.3958
WVFGRD96   36.0   140    60   -20   3.18 0.4043
WVFGRD96   37.0   140    60   -20   3.18 0.3999
WVFGRD96   38.0   140    60   -20   3.18 0.3982
WVFGRD96   39.0   135    60   -20   3.21 0.3821
WVFGRD96   40.0   330    60    -5   3.26 0.3389
WVFGRD96   41.0   140    60   -25   3.31 0.2990
WVFGRD96   42.0   150    70     5   3.32 0.2795
WVFGRD96   43.0   150    70    10   3.34 0.2573
WVFGRD96   44.0   330    70    -5   3.35 0.2726
WVFGRD96   45.0   330    70    -5   3.36 0.2671
WVFGRD96   46.0   335    70     5   3.37 0.2670
WVFGRD96   47.0   150    65    10   3.37 0.2338
WVFGRD96   48.0   155    55    30   3.39 0.2143
WVFGRD96   49.0   155    55    30   3.40 0.2214

The best solution is

WVFGRD96   29.0   145    60    -5   3.23 0.4159

The mechanism corresponding 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, the velocity model used in the predictions may not be perfect and the epicentral parameters may be be off. 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/3.5 -10 o DIST/3.5 +10
rtr
taper w 0.1
hp c 0.5 n 3 
lp c 0.50 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. The time scale is relative to the first trace sample.

Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to the waveforms. 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.

Velocity Model

The WUS.model used for the waveform synthetic seismograms and for the surface wave eigenfunctions and dispersion is as follows (The format is in the model96 format of Computer Programs in Seismology).

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    
Last Changed Wed Apr 24 10:07:01 PM CDT 2024