Location

Location ANSS

The ANSS event ID is usp000h62m and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usp000h62m/executive.

2010/01/13 11:17:55 47.431 -113.174 20.8 3.7 Montana

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2010/01/13 11:17:55:0 47.43 -113.17 20.8 3.7 Montana Stations used: TA.A19A TA.C19A TA.D19A TA.E19A TA.E20A US.BOZ US.MSO US.RLMT Filtering commands used: cut o DIST/3.3 -20 o DIST/3.3 +40 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.07 n 3 Best Fitting Double Couple Mo = 6.10e+21 dyne-cm Mw = 3.79 Z = 23 km Plane Strike Dip Rake NP1 330 53 -106 NP2 175 40 -70 Principal Axes: Axis Value Plunge Azimuth T 6.10e+21 7 71 N 0.00e+00 13 339 P -6.10e+21 76 188 Moment Tensor: (dyne-cm) Component Value Mxx 2.76e+20 Mxy 1.81e+21 Mxz 1.68e+21 Myy 5.37e+21 Myz 8.52e+20 Mzz -5.64e+21 ---########### ###--################# ######-----################# ######---------############### #######------------############### #######---------------############## ########-----------------########### ########-------------------########## T ########--------------------######### #########---------------------############ #########----------------------########### #########-----------------------########## #########---------- ----------########## ########---------- P -----------######## #########--------- -----------######## ########-----------------------####### ########----------------------###### ########---------------------##### #######--------------------### ########-----------------### #######--------------- ######-------- Global CMT Convention Moment Tensor: R T P -5.64e+21 1.68e+21 -8.52e+20 1.68e+21 2.76e+20 -1.81e+21 -8.52e+20 -1.81e+21 5.37e+21 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20100113111755/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 = 175
      DIP = 40
     RAKE = -70
       MW = 3.79
       HS = 23.0

The NDK file is 20100113111755.ndk The waveform inversion is preferred.

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 M_L by application of the respective IASPEI formulae. As a research study, the linear distance term of the IASPEI formula for M_L is adjusted to remove a linear distance trend in residuals to give a regionally defined M_L. The defined M_L 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 -20 o DIST/3.3 +40
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    75    85    -5   3.49 0.5548
WVFGRD96    2.0   255    90     0   3.58 0.6513
WVFGRD96    3.0   255    80   -10   3.64 0.6506
WVFGRD96    4.0   250    60   -25   3.73 0.6578
WVFGRD96    5.0   245    45   -30   3.76 0.6955
WVFGRD96    6.0    75    45     0   3.73 0.7223
WVFGRD96    7.0    75    50     0   3.73 0.7379
WVFGRD96    8.0    80    40    15   3.76 0.7486
WVFGRD96    9.0    80    45    15   3.77 0.7574
WVFGRD96   10.0    80    50    15   3.77 0.7615
WVFGRD96   11.0    80    50    15   3.77 0.7660
WVFGRD96   12.0    80    50    15   3.77 0.7675
WVFGRD96   13.0    75    55     0   3.78 0.7709
WVFGRD96   14.0    75    55     5   3.77 0.7734
WVFGRD96   15.0   235    50   -45   3.80 0.7756
WVFGRD96   16.0   180    35   -75   3.73 0.7844
WVFGRD96   17.0   180    35   -75   3.74 0.7928
WVFGRD96   18.0   175    40   -70   3.75 0.8001
WVFGRD96   19.0   175    40   -70   3.75 0.8065
WVFGRD96   20.0   175    40   -70   3.76 0.8112
WVFGRD96   21.0   175    40   -70   3.78 0.8132
WVFGRD96   22.0   175    40   -70   3.78 0.8154
WVFGRD96   23.0   175    40   -70   3.79 0.8161
WVFGRD96   24.0   175    40   -65   3.80 0.8159
WVFGRD96   25.0   175    40   -65   3.81 0.8145
WVFGRD96   26.0   175    40   -65   3.82 0.8120
WVFGRD96   27.0   175    45   -55   3.84 0.8088
WVFGRD96   28.0   175    45   -55   3.85 0.8049
WVFGRD96   29.0   175    45   -55   3.86 0.8003

The best solution is

WVFGRD96   23.0   175    40   -70   3.79 0.8161

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 -20 o DIST/3.3 +40
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:

The origin time and epicentral distance are incorrect
The velocity model used for the inversion is incorrect
The velocity model used to define the P-arrival time is not the same as the velocity model used for the waveform inversion (assuming that the initial trace alignment is based on the P arrival time)

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 Sat Apr 27 11:02:33 AM CDT 2024