Location

2004/01/07 09:23:46 43.60 -110.35 5.0 4.0 Wyoming

Arrival Times (from USGS)

Arrival time list

Felt Map

USGS Felt map for this earthquake

USGS Felt reports page for Intermountain West

Focal Mechanism

 SLU Moment Tensor Solution
 2004/01/07 09:23:46 43.60 -110.35 5.0 4.0 Wyoming
 
 Best Fitting Double Couple
    Mo = 6.10e+21 dyne-cm
    Mw = 3.79 
    Z  = 17 km
     Plane   Strike  Dip  Rake
      NP1      128    80   -165
      NP2       35    75   -10
 Principal Axes:
   Axis    Value   Plunge  Azimuth
     T   6.10e+21      4     261
     N   0.00e+00     72     159
     P  -6.10e+21     18     352



 Moment Tensor: (dyne-cm)
    Component  Value
       Mxx    -5.27e+21
       Mxy     1.73e+21
       Mxz    -1.80e+21
       Myy     5.80e+21
       Myz    -1.40e+20
       Mzz    -5.29e+20
                                                     
                                                     
                                                     
                                                     
                     ---   --------                  
                 ------- P ------------              
              ----------   -------------##           
             --------------------------####          
           #---------------------------######        
          ###-------------------------########       
         ######----------------------##########      
        #########-------------------############     
        ###########----------------#############     
       ##############-------------###############    
       ################----------################    
          ###############-------#################    
        T ##################---##################    
          ###################-##################     
        ####################-----###############     
         #################----------###########      
          ###############--------------#######       
           ############--------------------##        
             ########----------------------          
              ####------------------------           
                 ----------------------              
                     --------------                  
                                                     
                                                     
                                                     

 Harvard Convention
 Moment Tensor:
      R          T          F
 -5.29e+20  -1.80e+21   1.40e+20 
 -1.80e+21  -5.27e+21  -1.73e+21 
  1.40e+20  -1.73e+21   5.80e+21 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20040107092347/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 = 35
      DIP = 75
     RAKE = -10
       MW = 3.79
       HS = 17.0

The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others
SLU
 SLU Moment Tensor Solution
 2004/01/07 09:23:46 43.60 -110.35 5.0 4.0 Wyoming
 
 Best Fitting Double Couple
    Mo = 6.10e+21 dyne-cm
    Mw = 3.79 
    Z  = 17 km
     Plane   Strike  Dip  Rake
      NP1      128    80   -165
      NP2       35    75   -10
 Principal Axes:
   Axis    Value   Plunge  Azimuth
     T   6.10e+21      4     261
     N   0.00e+00     72     159
     P  -6.10e+21     18     352



 Moment Tensor: (dyne-cm)
    Component  Value
       Mxx    -5.27e+21
       Mxy     1.73e+21
       Mxz    -1.80e+21
       Myy     5.80e+21
       Myz    -1.40e+20
       Mzz    -5.29e+20
                                                     
                                                     
                                                     
                                                     
                     ---   --------                  
                 ------- P ------------              
              ----------   -------------##           
             --------------------------####          
           #---------------------------######        
          ###-------------------------########       
         ######----------------------##########      
        #########-------------------############     
        ###########----------------#############     
       ##############-------------###############    
       ################----------################    
          ###############-------#################    
        T ##################---##################    
          ###################-##################     
        ####################-----###############     
         #################----------###########      
          ###############--------------#######       
           ############--------------------##        
             ########----------------------          
              ####------------------------           
                 ----------------------              
                     --------------                  
                                                     
                                                     
                                                     

 Harvard Convention
 Moment Tensor:
      R          T          F
 -5.29e+20  -1.80e+21   1.40e+20 
 -1.80e+21  -5.27e+21  -1.73e+21 
  1.40e+20  -1.73e+21   5.80e+21 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20040107092347/index.html
	

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:

hp c 0.02 n 3
lp c 0.10 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   115    55   -30   3.16 0.1927
WVFGRD96    1.0   295    90    -5   3.20 0.2019
WVFGRD96    2.0   120    70    -5   3.32 0.2584
WVFGRD96    3.0   205    75    -5   3.41 0.2899
WVFGRD96    4.0   205    70    -5   3.47 0.3136
WVFGRD96    5.0    25    65   -20   3.49 0.3367
WVFGRD96    6.0    25    65   -20   3.52 0.3715
WVFGRD96    7.0    30    70   -20   3.54 0.4032
WVFGRD96    8.0    25    65   -20   3.62 0.4432
WVFGRD96    9.0    30    70   -20   3.63 0.4685
WVFGRD96   10.0    30    70   -15   3.67 0.4926
WVFGRD96   11.0    30    70   -15   3.69 0.5112
WVFGRD96   12.0    30    70   -15   3.71 0.5259
WVFGRD96   13.0    30    70   -15   3.73 0.5371
WVFGRD96   14.0    35    70   -15   3.74 0.5442
WVFGRD96   15.0    35    75   -15   3.76 0.5494
WVFGRD96   16.0    35    75   -15   3.77 0.5530
WVFGRD96   17.0    35    75   -10   3.79 0.5536
WVFGRD96   18.0    35    75   -10   3.80 0.5506
WVFGRD96   19.0   220    75    15   3.79 0.5457
WVFGRD96   20.0   220    75    15   3.80 0.5436
WVFGRD96   21.0   220    75    15   3.81 0.5363
WVFGRD96   22.0   220    75    15   3.82 0.5275
WVFGRD96   23.0   220    75    15   3.82 0.5147
WVFGRD96   24.0   220    70    20   3.82 0.4981
WVFGRD96   25.0   220    75    20   3.82 0.4831
WVFGRD96   26.0   220    75    20   3.83 0.4679
WVFGRD96   27.0   210    55   -20   3.87 0.4535
WVFGRD96   28.0   205    55   -20   3.89 0.4404
WVFGRD96   29.0   205    50   -20   3.89 0.4267

The best solution is

WVFGRD96   17.0    35    75   -10   3.79 0.5536

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 componnet is plotted to the same scale and peak amplitudes are indicated by the numbers to the left of each trace. The number in black at the rightr of each predicted traces 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 bandpass filter used in the processing and for the display was

hp c 0.02 n 3
lp c 0.10 n 3
Figure 3. Waveform comparison for selected depth
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.

Surface-Wave Focal Mechanism

The following figure shows the stations used in the grid search for the best focal mechanism to fit the surface-wave spectral amplitudes of the Love and Rayleigh waves.
Location of broadband stations used to obtain focal mechanism from surface-wave spectral amplitudes

The surface-wave determined focal mechanism is shown here.


  NODAL PLANES 

  
  STK=      35.00
  DIP=      74.99
 RAKE=      19.99
  
             OR
  
  STK=     299.62
  DIP=      70.72
 RAKE=     164.08
 
 
DEPTH = 18.0 km
 
Mw = 3.88
Best Fit 0.8612 - P-T axis plot gives solutions with FIT greater than FIT90

First motion data

The P-wave first motion data for focal mechanism studies are as follow:

Sta Az    Dist   First motion
LKWY      358  107 IPU0
BW06      145  113 IPU0
YMR       338  129 IPU0
HWUT      205  243 IPU0
BOZ       336  249 IPU0
HVU       225  283 IPU0
CTU       200  343 IPU0

Surface-wave analysis

Surface wave analysis was performed using codes from Computer Programs in Seismology, specifically the multiple filter analysis program do_mft and the surface-wave radiation pattern search program srfgrd96.

Data preparation

Digital data were collected, instrument response removed and traces converted to Z, R an T components. Multiple filter analysis was applied to the Z and T traces to obtain the Rayleigh- and Love-wave spectral amplitudes, respectively. These were input to the search program which examined all depths between 1 and 25 km and all possible mechanisms.
Best mechanism fit as a function of depth. The preferred depth is given above. Lower hemisphere projection

Pressure-tension axis trends. Since the surface-wave spectra search does not distinguish between P and T axes and since there is a 180 ambiguity in strike, all possible P and T axes are plotted. First motion data and waveforms will be used to select the preferred mechanism. The purpose of this plot is to provide an idea of the possible range of solutions. The P and T-axes for all mechanisms with goodness of fit greater than 0.9 FITMAX (above) are plotted here.


Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to the Love and Rayleigh wave radiation patterns. 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. Because of the symmetry of the spectral amplitude rediation patterns, only strikes from 0-180 degrees are sampled.

Love-wave radiation patterns

Rayleigh-wave radiation patterns

Broadband station distribution

The distribution of broadband stations with azimuth and distance is
Listing of broadband stations used

Waveform comparison for this mechanism

Since the analysis of the surface-wave radiation patterns uses only spectral amplitudes and because the surfave-wave radiation patterns have a 180 degree symmetry, each surface-wave solution consists of four possible focal mechanisms corresponding to the interchange of the P- and T-axes and a roation of the mechanism by 180 degrees. To select one mechanism, P-wave first motion can be used. This was not possible in this case because all the P-wave first motions were emergent ( a feature of the P-wave wave takeoff angle, the station location and the mechanism). The other way to select among the mechanisms is to compute forward synthetics and compare the observed and predicted waveforms.

The fits to the waveforms with the given mechanism are show below:

This figure shows the fit to the three components of motion (Z - vertical, R-radial and T - transverse). For each station and component, the observed traces is shown in red and the model predicted trace in blue. The traces represent filtered ground velocity in units of meters/sec (the peak value is printed adjacent to each trace; each pair of traces to plotted to the same scale to emphasize the difference in levels). Both synthetic and observed traces have been filtered using the SAC commands:

hp c 0.02 n 3
lp c 0.10 n 3

Discussion

The Future

Should the national backbone of the USGS Advanced National Seismic System (ANSS) be implemented with an interstation separation of 300 km, it is very likely that an earthquake such as this would have been recorded at distances on the order of 100-200 km. This means that the closest station would have information on source depth and mechanism that was lacking here.

Acknowledgements

Dr. Harley Benz, USGS, provided the USGS USNSN digital data. The digital data used in this study were provided by Natural Resources Canada through their AUTODRM site http://www.seismo.nrcan.gc.ca/nwfa/autodrm/autodrm_req_e.php, and IRIS using their BUD interface.

Thanks also to the many seismic network operators whose dedication make this effort possible: University of Alaska, University of Washington, Oregon State University, University of Utah, Montana Bureas of Mines, UC Berkely, Caltech, UC San Diego, Saint L ouis University, Universityof Memphis, Lamont Doehrty Earth Observatory, Boston College, the Iris stations and the Transportable Array of EarthScope.

Appendix A


Spectra fit plots to each station

Velocity Model

The WUS 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

DATE=Sun Aug 10 18:19:09 CDT 2008

Last Changed 2004/01/07