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 nm605762 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/nm605762/executive.

2005/06/02 11:35:10 36.150 -89.474 15.0 4 Tennessee

Focal Mechanism

 USGS/SLU Moment Tensor Solution
 ENS  2005/06/02 11:35:10:0  36.15  -89.47  15.0 4.0 Tennessee
 
 Stations used:
   NM.BLO NM.FVM NM.MPH NM.OLIL NM.PLAL NM.PVMO NM.SLM NM.UALR 
   NM.USIN NM.UTMT US.LRAL US.OXF US.WVT 
 
 Filtering commands used:
   cut o DIST/3.3 -40 o DIST/3.3 +50
   rtr
   taper w 0.1
   hp c 0.03 n 3 
   lp c 0.10 n 3 
 
 Best Fitting Double Couple
  Mo = 7.00e+21 dyne-cm
  Mw = 3.83 
  Z  = 15 km
  Plane   Strike  Dip  Rake
   NP1      145    70    60
   NP2       24    36   144
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   7.00e+21     55      17
    N   0.00e+00     28     156
    P  -7.00e+21     19     257

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     1.81e+21
       Mxy    -7.06e+20
       Mxz     3.64e+21
       Myy    -5.70e+21
       Myz     3.12e+21
       Mzz     3.90e+21
                                                     
                                                     
                                                     
                                                     
                     ##############                  
                 #####################-              
              --#######################---           
             ---########################---          
           ------########################----        
          -------############   ##########----       
         ---------########### T ##########-----      
        -----------##########   ##########------     
        -----------#######################------     
       -------------######################-------    
       --------------#####################-------    
       ---------------####################-------    
       ---   -----------#################--------    
        -- P ------------################-------     
        --   --------------#############--------     
         -------------------###########--------      
          --------------------########--------       
           ---------------------####---------        
             ------------------------------          
              ------------------#####-----           
                 -----------###########              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  3.90e+21   3.64e+21  -3.12e+21 
  3.64e+21   1.81e+21   7.06e+20 
 -3.12e+21   7.06e+20  -5.70e+21 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20050602113510/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 = 70
     RAKE = 60
       MW = 3.83
       HS = 15.0

The NDK file is 20050602113510.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  2005/06/02 11:35:10:0  36.15  -89.47  15.0 4.0 Tennessee
 
 Stations used:
   NM.BLO NM.FVM NM.MPH NM.OLIL NM.PLAL NM.PVMO NM.SLM NM.UALR 
   NM.USIN NM.UTMT US.LRAL US.OXF US.WVT 
 
 Filtering commands used:
   cut o DIST/3.3 -40 o DIST/3.3 +50
   rtr
   taper w 0.1
   hp c 0.03 n 3 
   lp c 0.10 n 3 
 
 Best Fitting Double Couple
  Mo = 7.00e+21 dyne-cm
  Mw = 3.83 
  Z  = 15 km
  Plane   Strike  Dip  Rake
   NP1      145    70    60
   NP2       24    36   144
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   7.00e+21     55      17
    N   0.00e+00     28     156
    P  -7.00e+21     19     257

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     1.81e+21
       Mxy    -7.06e+20
       Mxz     3.64e+21
       Myy    -5.70e+21
       Myz     3.12e+21
       Mzz     3.90e+21
                                                     
                                                     
                                                     
                                                     
                     ##############                  
                 #####################-              
              --#######################---           
             ---########################---          
           ------########################----        
          -------############   ##########----       
         ---------########### T ##########-----      
        -----------##########   ##########------     
        -----------#######################------     
       -------------######################-------    
       --------------#####################-------    
       ---------------####################-------    
       ---   -----------#################--------    
        -- P ------------################-------     
        --   --------------#############--------     
         -------------------###########--------      
          --------------------########--------       
           ---------------------####---------        
             ------------------------------          
              ------------------#####-----           
                 -----------###########              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  3.90e+21   3.64e+21  -3.12e+21 
  3.64e+21   1.81e+21   7.06e+20 
 -3.12e+21   7.06e+20  -5.70e+21 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20050602113510/index.html
	


First motions and takeoff angles from an elocate run.

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 0.03 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   335    50    80   3.65 0.3572
WVFGRD96    2.0   330    60    75   3.74 0.3353
WVFGRD96    3.0   320    70    65   3.72 0.3198
WVFGRD96    4.0   130    85   -65   3.68 0.3459
WVFGRD96    5.0   315    90    65   3.68 0.3724
WVFGRD96    6.0   320    85    65   3.69 0.3955
WVFGRD96    7.0   320    85    65   3.69 0.4142
WVFGRD96    8.0   320    80    65   3.70 0.4290
WVFGRD96    9.0   155    65    70   3.74 0.4444
WVFGRD96   10.0   150    65    70   3.78 0.4680
WVFGRD96   11.0   155    60    75   3.81 0.4866
WVFGRD96   12.0   155    60    75   3.82 0.5013
WVFGRD96   13.0   155    60    75   3.82 0.5102
WVFGRD96   14.0   145    70    60   3.82 0.5163
WVFGRD96   15.0   145    70    60   3.83 0.5198
WVFGRD96   16.0   145    70    60   3.84 0.5195
WVFGRD96   17.0   150    70    65   3.84 0.5165
WVFGRD96   18.0   150    70    65   3.85 0.5109
WVFGRD96   19.0   150    70    65   3.86 0.5030
WVFGRD96   20.0   150    70    65   3.89 0.4960
WVFGRD96   21.0   150    70    65   3.90 0.4852
WVFGRD96   22.0   150    75    65   3.90 0.4731
WVFGRD96   23.0   150    75    70   3.91 0.4628
WVFGRD96   24.0   150    75    70   3.91 0.4513
WVFGRD96   25.0   150    75    70   3.92 0.4383
WVFGRD96   26.0   155    75    75   3.92 0.4245
WVFGRD96   27.0   155    80    80   3.92 0.4130
WVFGRD96   28.0   155    80    75   3.93 0.4020
WVFGRD96   29.0   155    80    75   3.93 0.3911

The best solution is

WVFGRD96   15.0   145    70    60   3.83 0.5198

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 0.03 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 Sun Apr 14 10:40:09 AM CDT 2024