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 us7000e9qy and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/us7000e9qy/executive.

2021/06/04 15:25:00 43.008 -98.733 5.0 3.7 S. Dakota

Focal Mechanism

 USGS/SLU Moment Tensor Solution
 ENS  2021/06/04 15:25:00:0  43.01  -98.73   5.0 3.7 S. Dakota
 
 Stations used:
   N4.BGNE N4.E28B N4.F33B N4.K30B N4.L34B N4.N35B N4.SUSD 
   US.ECSD US.OGNE 
 
 Filtering commands used:
   cut o DIST/3.3 -40 o DIST/3.3 +50
   rtr
   taper w 0.1
   hp c 0.04 n 3 
   lp c 0.10 n 3 
 
 Best Fitting Double Couple
  Mo = 4.03e+21 dyne-cm
  Mw = 3.67 
  Z  = 8 km
  Plane   Strike  Dip  Rake
   NP1      215    60   -50
   NP2      336    48   -138
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   4.03e+21      7     278
    N   0.00e+00     34      12
    P  -4.03e+21     55     178

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx    -1.23e+21
       Mxy    -4.89e+20
       Mxz     1.94e+21
       Myy     3.90e+21
       Myz    -5.21e+20
       Mzz    -2.67e+21
                                                     
                                                     
                                                     
                                                     
                     --------------                  
                 ########--------------              
              ##############-------#######           
             ##############################          
           ##################---#############        
          #################-------############       
         ################----------############      
        ###############-------------############     
          ############---------------###########     
        T ###########-----------------###########    
          ##########-------------------##########    
       ############--------------------##########    
       ###########----------------------#########    
        #########-----------------------########     
        #########----------   ----------########     
         #######----------- P ----------#######      
          ######-----------   ----------######       
           #####------------------------#####        
             ###-----------------------####          
              ##----------------------####           
                 --------------------##              
                     --------------                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -2.67e+21   1.94e+21   5.21e+20 
  1.94e+21  -1.23e+21   4.89e+20 
  5.21e+20   4.89e+20   3.90e+21 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210604152500/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 = 215
      DIP = 60
     RAKE = -50
       MW = 3.67
       HS = 8.0

The NDK file is 20210604152500.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  2021/06/04 15:25:00:0  43.01  -98.73   5.0 3.7 S. Dakota
 
 Stations used:
   N4.BGNE N4.E28B N4.F33B N4.K30B N4.L34B N4.N35B N4.SUSD 
   US.ECSD US.OGNE 
 
 Filtering commands used:
   cut o DIST/3.3 -40 o DIST/3.3 +50
   rtr
   taper w 0.1
   hp c 0.04 n 3 
   lp c 0.10 n 3 
 
 Best Fitting Double Couple
  Mo = 4.03e+21 dyne-cm
  Mw = 3.67 
  Z  = 8 km
  Plane   Strike  Dip  Rake
   NP1      215    60   -50
   NP2      336    48   -138
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   4.03e+21      7     278
    N   0.00e+00     34      12
    P  -4.03e+21     55     178

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx    -1.23e+21
       Mxy    -4.89e+20
       Mxz     1.94e+21
       Myy     3.90e+21
       Myz    -5.21e+20
       Mzz    -2.67e+21
                                                     
                                                     
                                                     
                                                     
                     --------------                  
                 ########--------------              
              ##############-------#######           
             ##############################          
           ##################---#############        
          #################-------############       
         ################----------############      
        ###############-------------############     
          ############---------------###########     
        T ###########-----------------###########    
          ##########-------------------##########    
       ############--------------------##########    
       ###########----------------------#########    
        #########-----------------------########     
        #########----------   ----------########     
         #######----------- P ----------#######      
          ######-----------   ----------######       
           #####------------------------#####        
             ###-----------------------####          
              ##----------------------####           
                 --------------------##              
                     --------------                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -2.67e+21   1.94e+21   5.21e+20 
  1.94e+21  -1.23e+21   4.89e+20 
  5.21e+20   4.89e+20   3.90e+21 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210604152500/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/3.3 -40 o DIST/3.3 +50
rtr
taper w 0.1
hp c 0.04 n 3 
lp c 0.10 n 3 
The results of this grid search are as follow:

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0    70    25    30   3.69 0.4883
WVFGRD96    2.0    65    40    40   3.63 0.4960
WVFGRD96    3.0    85    30    75   3.67 0.4826
WVFGRD96    4.0   225    50   -20   3.58 0.5009
WVFGRD96    5.0   215    55   -50   3.64 0.5597
WVFGRD96    6.0   210    55   -60   3.67 0.6054
WVFGRD96    7.0   210    55   -60   3.67 0.6262
WVFGRD96    8.0   215    60   -50   3.67 0.6332
WVFGRD96    9.0   215    60   -50   3.67 0.6322
WVFGRD96   10.0   215    60   -50   3.70 0.6265
WVFGRD96   11.0   215    60   -50   3.70 0.6150
WVFGRD96   12.0   215    65   -40   3.71 0.5992
WVFGRD96   13.0   220    65   -45   3.71 0.5817
WVFGRD96   14.0   220    65   -45   3.71 0.5628
WVFGRD96   15.0   220    65   -40   3.72 0.5423
WVFGRD96   16.0   220    65   -40   3.72 0.5209
WVFGRD96   17.0   220    65   -40   3.72 0.4995
WVFGRD96   18.0   220    65   -40   3.73 0.4790
WVFGRD96   19.0   225    65   -40   3.73 0.4604
WVFGRD96   20.0   225    65   -40   3.75 0.4422
WVFGRD96   21.0   225    65   -40   3.75 0.4291
WVFGRD96   22.0   225    65   -40   3.76 0.4179
WVFGRD96   23.0   225    65   -40   3.77 0.4092
WVFGRD96   24.0   225    65   -40   3.77 0.4040
WVFGRD96   25.0   225    65   -40   3.78 0.3998
WVFGRD96   26.0   225    65   -40   3.79 0.3960
WVFGRD96   27.0   225    65   -40   3.80 0.3922
WVFGRD96   28.0   225    65   -40   3.80 0.3878
WVFGRD96   29.0   230    60   -40   3.80 0.3851

The best solution is

WVFGRD96    8.0   215    60   -50   3.67 0.6332

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/3.3 -40 o DIST/3.3 +50
rtr
taper w 0.1
hp c 0.04 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. 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 CUS.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
CUS Model with Q from simple gamma values
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
  1.0000  5.0000  2.8900  2.5000 0.172E-02 0.387E-02 0.00  0.00  1.00  1.00 
  9.0000  6.1000  3.5200  2.7300 0.160E-02 0.363E-02 0.00  0.00  1.00  1.00 
 10.0000  6.4000  3.7000  2.8200 0.149E-02 0.336E-02 0.00  0.00  1.00  1.00 
 20.0000  6.7000  3.8700  2.9020 0.000E-04 0.000E-04 0.00  0.00  1.00  1.00 
  0.0000  8.1500  4.7000  3.3640 0.194E-02 0.431E-02 0.00  0.00  1.00  1.00 
Last Changed Wed Apr 24 11:12:34 PM CDT 2024