2000/11/10 19:14:05 46.40N 111.38W 1 4.0 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

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 = 190
      DIP = 80
     RAKE = 50
       MW = 3.79
       HS = 13

This event was not recorded by many stations. The preferred solution is the waveform inversion solution. There were very few spectral amplitude data. The moment is well constrained. The focal is similar to the 2000/04/08 and 2000/05/24 earthquakes.

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 0.10 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   345    80    -5   3.19 0.2115
WVFGRD96    1.0   345    80     0   3.24 0.2314
WVFGRD96    2.0   350    70    15   3.41 0.3438
WVFGRD96    3.0   350    70     5   3.46 0.4102
WVFGRD96    4.0   350    70    -5   3.51 0.4642
WVFGRD96    5.0   350    70    -5   3.55 0.5000
WVFGRD96    6.0   350    70   -10   3.59 0.5176
WVFGRD96    7.0   350    75     0   3.62 0.5209
WVFGRD96    8.0   355    70    -5   3.61 0.5184
WVFGRD96    9.0   190    80    65   3.78 0.5157
WVFGRD96   10.0   190    80    60   3.77 0.5213
WVFGRD96   11.0   190    80    60   3.79 0.5257
WVFGRD96   12.0   190    80    55   3.77 0.5282
WVFGRD96   13.0   190    80    55   3.79 0.5293
WVFGRD96   14.0   190    80    55   3.80 0.5284
WVFGRD96   15.0   190    80    55   3.81 0.5262
WVFGRD96   16.0   195    80    55   3.81 0.5237
WVFGRD96   17.0   195    80    50   3.80 0.5212
WVFGRD96   18.0   195    80    50   3.81 0.5178
WVFGRD96   19.0   195    80    55   3.84 0.5144

The best solution is

WVFGRD96   13.0   190    80    55   3.79 0.5293

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 0.10 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


  STK=     179.99
  DIP=      75.00
 RAKE=      45.00
  STK=      75.48
  DIP=      46.93
 RAKE=     159.24
DEPTH = 13.0 km
Mw = 3.84
Best Fit 0.8976 - 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
BOZ       193   86 eP_X
LKWY      159  218 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)   
BOZ	  193	   86
LKWY	  159	  218
HLID	  218	  396
AHID	  177	  405
HWUT	  182	  533
HAWA	  273	  627
WVOR	  235	  727

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 0.10 3
br c 0.12 0.2 n 8 p 2


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.


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 Mon Jun 13 13:12:37 CDT 2005