Location

2005/07/27 15:51:46 45.39N 112.62W 5 4.2 Montana

Arrival Times (from USGS)

Arrival time list

Felt Map

USGS Felt map for this earthquake

USGS Felt reports page for Intermountain Western US

Focal Mechanism

 SLU Moment Tensor Solution
 2005/07/27 15:51:46 45.39N 112.62W 5 4.2 Montana
 
 Best Fitting Double Couple
    Mo = 1.05e+22 dyne-cm
    Mw = 3.98 
    Z  = 12 km
     Plane   Strike  Dip  Rake
      NP1      102    74   -143
      NP2      360    55   -20
 Principal Axes:
   Axis    Value   Plunge  Azimuth
     T   1.05e+22     12     227
     N   0.00e+00     50     122
     P  -1.05e+22     37     326



 Moment Tensor: (dyne-cm)
    Component  Value
       Mxx     7.85e+14
       Mxy     8.06e+21
       Mxz    -5.64e+21
       Myy     3.37e+21
       Myz     1.22e+21
       Mzz    -3.37e+21
                                                     
                                                     
                                                     
                                                     
                     ---------#####                  
                 --------------########              
              -------------------#########           
             ---------------------#########          
           --------   -------------##########        
          --------- P -------------###########       
         ----------   --------------###########      
        ----------------------------############     
        -----------------------------###########     
       ###---------------------------############    
       ######------------------------############    
       ##########--------------------############    
       ###############---------------############    
        ######################-------##########-     
        ############################------------     
         ###########################-----------      
          ###   ###################-----------       
           ## T ###################----------        
                ##################---------          
              ###################---------           
                 ##############--------              
                     #########-----                  
                                                     
                                                     
                                                     

 Harvard Convention
 Moment Tensor:
      R          T          F
 -3.37e+21  -5.64e+21  -1.22e+21 
 -5.64e+21   7.85e+14  -8.06e+21 
 -1.22e+21  -8.06e+21   3.37e+21 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/NEW/20050727155146/index.html
	

The focal mechanism was determined using broadband seismic waveforms. The location of the event and the station distribution are given in Figure 1.
Figure 1. Location of broadband stations used to obtain focal mechanism

Preferred Solution

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

      STK = 360
      DIP = 55
     RAKE = -20
       MW = 3.98
       HS = 12

The source parameters determined by both techniques are virtually the same. The parameters given here are those of the waveform fit.

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 3
lp c 0.14 3
br c 0.12 0.2 n 8 p 2
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   190    70    20   3.45 0.2553
WVFGRD96    1.0   185    85     0   3.51 0.2882
WVFGRD96    2.0   185    90     0   3.66 0.3861
WVFGRD96    3.0   185    90     0   3.76 0.4366
WVFGRD96    4.0   185    90     0   3.80 0.4135
WVFGRD96    5.0   185    90     5   3.83 0.3701
WVFGRD96    6.0   100    80    25   3.85 0.3793
WVFGRD96    7.0   360    50   -20   3.86 0.4350
WVFGRD96    8.0   360    50   -20   3.92 0.4817
WVFGRD96    9.0   360    50   -20   3.94 0.5147
WVFGRD96   10.0   360    50   -20   3.95 0.5345
WVFGRD96   11.0   360    55   -20   3.97 0.5444
WVFGRD96   12.0   360    55   -20   3.98 0.5485
WVFGRD96   13.0   360    55   -20   3.99 0.5475
WVFGRD96   14.0   360    55   -15   3.99 0.5443
WVFGRD96   15.0   360    55   -15   4.00 0.5388
WVFGRD96   16.0    10    55     0   4.01 0.5347
WVFGRD96   17.0    10    55     0   4.02 0.5297
WVFGRD96   18.0    10    55     0   4.02 0.5230
WVFGRD96   19.0    10    60     0   4.04 0.5150

The best solution is

WVFGRD96   12.0   360    55   -20   3.98 0.5485

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 3
lp c 0.14 3
br c 0.12 0.2 n 8 p 2
Figure 3. Waveform comparison for depth of 8 km
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


  NODAL PLANES 

  
  STK=      99.99
  DIP=      79.99
 RAKE=    -145.00
  
             OR
  
  STK=       3.06
  DIP=      55.61
 RAKE=     -12.15
 
 
DEPTH = 10.0 km
 
Mw = 4.03
Best Fit 0.8458 - 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(deg)    Dist(km)   First motion
MSO       328  190 eP_-
HLID      216  248 iP_C
REDW      147  265 iP_D
AHID      157  316 eP_+
BW06      139  381 eP_X
WALA      347  420 -12345
HWUT      168  429 eP_X

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.

The velocity model used for the search is a modified Utah model .

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 distributiuon

Sta Az(deg)    Dist(km)   
MSO	  328	  190
HLID	  216	  248
REDW	  147	  265
AHID	  157	  316
BW06	  139	  381
WALA	  347	  420
HWUT	  168	  429
LAO	   71	  516
PNT	  312	  686
LON	  285	  727
TTW	  294	  742
SLEB	  330	  762
EDM	  357	  873
TPH	  207	  898
LLLB	  313	  902
WDC	  240	  969
SDCO	  143	 1035
DAC	  204	 1095
GSC	  199	 1175
ISA	  207	 1188
SAO	  221	 1210
CBKS	  120	 1290
MWC	  202	 1323
ULM	   61	 1362
GLA	  189	 1383
BAR	  195	 1453
TUC	  173	 1460
KSU1	  112	 1491
MNTX	  155	 1644
YKW3	  357	 1916
LTX	  153	 1947
CCM	  107	 1949
FVM	  106	 2014
NATX	  128	 2167
USIN	  103	 2225
OXF	  113	 2310
WCI	  101	 2316
LRAL	  113	 2586
NHSC	  105	 3087
PAL	   85	 3154
DWPF	  114	 3348

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 velocity model used for the waveform fit is a modified Utah model .

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 3
lp c 0.14 3
br c 0.12 0.2 n 8 p 2

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.

Appendix A

The figures below show the observed spectral amplitudes (units of cm-sec) at each station and the theoretical predictions as a function of period for the mechanism given above. The modified Utah model earth model was used to define the Green's functions. For each station, the Love and Rayleigh wave spectrail amplitudes are plotted with the same scaling so that one can get a sense fo the effects of the effects of the focal mechanism and depth on the excitation of each.

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 Wed Jul 27 18:36:06 CDT 2005