Location

Location ANSS

The ANSS event ID is us6000nx10 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/us6000nx10/executive.

2024/10/07 06:54:30 45.225 -112.475 13.7 4.1 Montana

Focal Mechanism

 USGS/SLU Moment Tensor Solution
 ENS  2024/10/07 06:54:30:0  45.22 -112.47  13.7 4.1 Montana
 
 Stations used:
   IE.ARNI IE.BCYI IW.DLMT IW.FXWY IW.IMW IW.LOHW IW.MFID 
   IW.PLID IW.SNOW MB.BCMT MB.BDMT MB.BNMT MB.CBMT MB.CPMT 
   MB.ECMT MB.FCMT MB.GBMT MB.HRY MB.JTMT MB.LDM MB.LIMT 
   MB.LRM MB.ODMT MB.SMMT MB.SRMT MB.SXMT MB.WFMT US.AHID 
   US.BOZ US.HLID US.HWUT US.LKWY US.RLMT UU.BEID UU.HDUT 
   UU.HVU UU.MCU UU.SPU UW.BRAN WW.CTNW WW.IRMR WW.TYLR WY.YDD 
   WY.YFT WY.YHB WY.YHH WY.YHL WY.YMP WY.YMR WY.YNR 
 
 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 0.07 n 3 
 
 Best Fitting Double Couple
  Mo = 1.78e+22 dyne-cm
  Mw = 4.10 
  Z  = 15 km
  Plane   Strike  Dip  Rake
   NP1       92    86   150
   NP2      185    60     5
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   1.78e+22     24      45
    N   0.00e+00     60     265
    P  -1.78e+22     17     143

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx    -2.67e+21
       Mxy     1.52e+22
       Mxz     8.76e+21
       Myy     1.33e+21
       Myz     1.54e+21
       Mzz     1.34e+21
                                                     
                                                     
                                                     
                                                     
                     -------#######                  
                 ----------############              
              -----------#################           
             -----------#############   ###          
           ------------############## T #####        
          -------------##############   ######       
         -------------#########################      
        -------------###########################     
        -------------###########################     
       --------------############################    
       -------------#############################    
       #############----#########################    
       #############-----------------------------    
        ############----------------------------     
        ############----------------------------     
         ############--------------------------      
          ###########-------------------------       
           ##########----------------   -----        
             #########--------------- P ---          
              #########--------------   --           
                 #######---------------              
                     ####----------                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  1.34e+21   8.76e+21  -1.54e+21 
  8.76e+21  -2.67e+21  -1.52e+22 
 -1.54e+21  -1.52e+22   1.33e+21 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20241007065430/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 = 185
      DIP = 60
     RAKE = 5
       MW = 4.10
       HS = 15.0

The NDK file is 20241007065430.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
USGSMWR
 USGS/SLU Moment Tensor Solution
 ENS  2024/10/07 06:54:30:0  45.22 -112.47  13.7 4.1 Montana
 
 Stations used:
   IE.ARNI IE.BCYI IW.DLMT IW.FXWY IW.IMW IW.LOHW IW.MFID 
   IW.PLID IW.SNOW MB.BCMT MB.BDMT MB.BNMT MB.CBMT MB.CPMT 
   MB.ECMT MB.FCMT MB.GBMT MB.HRY MB.JTMT MB.LDM MB.LIMT 
   MB.LRM MB.ODMT MB.SMMT MB.SRMT MB.SXMT MB.WFMT US.AHID 
   US.BOZ US.HLID US.HWUT US.LKWY US.RLMT UU.BEID UU.HDUT 
   UU.HVU UU.MCU UU.SPU UW.BRAN WW.CTNW WW.IRMR WW.TYLR WY.YDD 
   WY.YFT WY.YHB WY.YHH WY.YHL WY.YMP WY.YMR WY.YNR 
 
 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 0.07 n 3 
 
 Best Fitting Double Couple
  Mo = 1.78e+22 dyne-cm
  Mw = 4.10 
  Z  = 15 km
  Plane   Strike  Dip  Rake
   NP1       92    86   150
   NP2      185    60     5
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   1.78e+22     24      45
    N   0.00e+00     60     265
    P  -1.78e+22     17     143

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx    -2.67e+21
       Mxy     1.52e+22
       Mxz     8.76e+21
       Myy     1.33e+21
       Myz     1.54e+21
       Mzz     1.34e+21
                                                     
                                                     
                                                     
                                                     
                     -------#######                  
                 ----------############              
              -----------#################           
             -----------#############   ###          
           ------------############## T #####        
          -------------##############   ######       
         -------------#########################      
        -------------###########################     
        -------------###########################     
       --------------############################    
       -------------#############################    
       #############----#########################    
       #############-----------------------------    
        ############----------------------------     
        ############----------------------------     
         ############--------------------------      
          ###########-------------------------       
           ##########----------------   -----        
             #########--------------- P ---          
              #########--------------   --           
                 #######---------------              
                     ####----------                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  1.34e+21   8.76e+21  -1.54e+21 
  8.76e+21  -2.67e+21  -1.52e+22 
 -1.54e+21  -1.52e+22   1.33e+21 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20241007065430/index.html
	
Regional Moment Tensor (Mwr)
Moment
1.757e+15 N-m
Magnitude
4.10 Mwr
Depth
17.0 km
Percent DC
67%
Half Duration
-
Catalog
US
Data Source
US 1
Contributor
US 1
Nodal Planes
Plane	Strike	Dip	Rake
NP1	184	58	-7
NP2	278	84	-148
Principal Axes
Axis	Value	Plunge	Azimuth
T	1.891e+15	17	47
N	-0.310e+15	58	287
P	-1.581e+15	26	146

        

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.

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 0.03 n 3 
lp c 0.07 n 3 
The results of this grid search are as follow:

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0   180    75   -15   3.66 0.3260
WVFGRD96    2.0   175    65   -25   3.81 0.4364
WVFGRD96    3.0   180    65   -10   3.83 0.4781
WVFGRD96    4.0   180    60    -5   3.87 0.5095
WVFGRD96    5.0   185    60     5   3.89 0.5416
WVFGRD96    6.0   185    55     0   3.92 0.5767
WVFGRD96    7.0   185    55     0   3.94 0.6093
WVFGRD96    8.0   180    50   -10   3.99 0.6400
WVFGRD96    9.0   185    55     5   4.01 0.6654
WVFGRD96   10.0   185    55     5   4.02 0.6868
WVFGRD96   11.0   185    55     5   4.04 0.7035
WVFGRD96   12.0   185    60     5   4.06 0.7153
WVFGRD96   13.0   185    60     5   4.07 0.7249
WVFGRD96   14.0   185    60     5   4.08 0.7299
WVFGRD96   15.0   185    60     5   4.10 0.7327
WVFGRD96   16.0   185    60     0   4.10 0.7323
WVFGRD96   17.0   185    60     0   4.12 0.7305
WVFGRD96   18.0   185    60     0   4.13 0.7264
WVFGRD96   19.0   185    60     0   4.14 0.7203
WVFGRD96   20.0   185    55     0   4.15 0.7135
WVFGRD96   21.0   185    55     0   4.16 0.7060
WVFGRD96   22.0   185    55     0   4.17 0.6968
WVFGRD96   23.0   185    55    -5   4.17 0.6866
WVFGRD96   24.0   185    55    -5   4.18 0.6763
WVFGRD96   25.0   185    55    -5   4.19 0.6653
WVFGRD96   26.0   185    55    -5   4.20 0.6534
WVFGRD96   27.0   185    55    -5   4.20 0.6411
WVFGRD96   28.0   185    55    -5   4.21 0.6284
WVFGRD96   29.0   185    55    -5   4.22 0.6160

The best solution is

WVFGRD96   15.0   185    60     5   4.10 0.7327

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 0.07 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 WUS.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
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    
Last Changed Mon Oct 7 06:52:15 CDT 2024