Location

Location ANSS

The ANSS event ID is usp000jn74 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usp000jn74/executive.

2012/06/25 04:04:56 47.349 -113.135 23.8 3.4 Montana

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2012/06/25 04:04:56:0 47.35 -113.14 23.8 3.4 Montana Stations used: IW.FXWY MB.JTMT US.BOZ US.EGMT US.MSO WY.YMR WY.YPP WY.YUF Filtering commands used: hp c 0.02 n 3 lp c 0.08 n 3 Best Fitting Double Couple Mo = 1.58e+21 dyne-cm Mw = 3.40 Z = 21 km Plane Strike Dip Rake NP1 189 46 -80 NP2 355 45 -100 Principal Axes: Axis Value Plunge Azimuth T 1.58e+21 0 272 N 0.00e+00 7 2 P -1.58e+21 83 179 Moment Tensor: (dyne-cm) Component Value Mxx -2.19e+19 Mxy -5.61e+19 Mxz 1.94e+20 Myy 1.58e+21 Myz -1.70e+19 Mzz -1.56e+21 ############## #########-----######## ##########---------######### #########-------------######## ##########---------------######### ##########-----------------######### ##########-------------------######### ##########--------------------########## ##########---------------------######### ########----------------------########## T ########----------------------########## ########---------- ---------########## ##########---------- P ---------########## #########---------- ---------######### #########----------------------######### ########---------------------######### ########--------------------######## #######-------------------######## ######-----------------####### ######---------------####### #####------------##### ##---------### Global CMT Convention Moment Tensor: R T P -1.56e+21 1.94e+20 1.70e+19 1.94e+20 -2.19e+19 5.61e+19 1.70e+19 5.61e+19 1.58e+21 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20120625040456/index.html

Preferred Solution

      STK = -5
      DIP = 45
     RAKE = -100
       MW = 3.40
       HS = 21.0

The NDK file is 20120625040456.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

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:

hp c 0.02 n 3
lp c 0.08 n 3

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    0.5   175    40    90   2.88 0.2370
WVFGRD96    1.0    85    80    10   2.94 0.2513
WVFGRD96    2.0    85    75    15   3.07 0.3077
WVFGRD96    3.0    85    75    15   3.14 0.3103
WVFGRD96    4.0    80    70    -5   3.15 0.2781
WVFGRD96    5.0   285    25    -5   3.15 0.2923
WVFGRD96    6.0   280    25   -10   3.17 0.3266
WVFGRD96    7.0   275    25   -15   3.18 0.3525
WVFGRD96    8.0   280    20    -5   3.25 0.3675
WVFGRD96    9.0    20    90   -65   3.25 0.3820
WVFGRD96   10.0   205    80    60   3.27 0.3952
WVFGRD96   11.0    30    60   -70   3.31 0.4165
WVFGRD96   12.0    25    55   -70   3.31 0.4412
WVFGRD96   13.0    15    50   -80   3.32 0.4627
WVFGRD96   14.0    15    50   -80   3.33 0.4815
WVFGRD96   15.0    10    45   -85   3.34 0.4972
WVFGRD96   16.0     5    45   -90   3.35 0.5100
WVFGRD96   17.0   185    45   -85   3.35 0.5205
WVFGRD96   18.0   190    45   -80   3.37 0.5282
WVFGRD96   19.0   190    45   -80   3.38 0.5348
WVFGRD96   20.0   190    45   -80   3.39 0.5387
WVFGRD96   21.0    -5    45  -100   3.40 0.5405
WVFGRD96   22.0   195    45   -75   3.41 0.5404
WVFGRD96   23.0   195    45   -75   3.42 0.5387
WVFGRD96   24.0   195    45   -75   3.43 0.5354
WVFGRD96   25.0   195    45   -75   3.43 0.5302
WVFGRD96   26.0   200    45   -70   3.44 0.5247
WVFGRD96   27.0   200    45   -70   3.45 0.5184
WVFGRD96   28.0   205    45   -65   3.46 0.5115
WVFGRD96   29.0   205    45   -65   3.47 0.5041

The best solution is

WVFGRD96   21.0    -5    45  -100   3.40 0.5405

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

hp c 0.02 n 3
lp c 0.08 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)

 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