The ANSS event ID is usp000dw3e and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usp000dw3e/executive.
2005/07/28 02:29:30 45.371 -112.603 5.0 3.5 Montana
USGS/SLU Moment Tensor Solution
ENS 2005/07/28 02:29:30:0 45.37 -112.60 5.0 3.5 Montana
Stations used:
US.BOZ US.HLID US.HWUT US.LAO US.MSO US.REDW
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 0.10 n 3
br c 0.12 0.25 n 4 p 2
Best Fitting Double Couple
Mo = 1.82e+21 dyne-cm
Mw = 3.44
Z = 11 km
Plane Strike Dip Rake
NP1 109 55 -93
NP2 295 35 -85
Principal Axes:
Axis Value Plunge Azimuth
T 1.82e+21 10 201
N 0.00e+00 3 111
P -1.82e+21 79 5
Moment Tensor: (dyne-cm)
Component Value
Mxx 1.47e+21
Mxy 5.94e+20
Mxz -6.17e+20
Myy 2.35e+20
Myz -1.44e+20
Mzz -1.70e+21
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#--------------------------#########
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#------------------ -------------#####
###----------------- P --------------#####
####---------------- ---------------####
######---------------------------------###
########-------------------------------###
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### T ################
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Global CMT Convention Moment Tensor:
R T P
-1.70e+21 -6.17e+20 1.44e+20
-6.17e+20 1.47e+21 -5.94e+20
1.44e+20 -5.94e+20 2.35e+20
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20050728022930/index.html
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STK = 295
DIP = 35
RAKE = -85
MW = 3.44
HS = 11.0
The NDK file is 20050728022930.ndk The waveform inversion is preferred.
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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.
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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 0.10 n 3 br c 0.12 0.25 n 4 p 2The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 1.0 0 90 0 3.16 0.4555
WVFGRD96 2.0 200 85 0 3.16 0.4879
WVFGRD96 3.0 290 85 -10 3.22 0.4596
WVFGRD96 4.0 285 80 -50 3.33 0.4800
WVFGRD96 5.0 285 85 -65 3.37 0.5829
WVFGRD96 6.0 110 90 65 3.35 0.6607
WVFGRD96 7.0 115 85 60 3.34 0.7020
WVFGRD96 8.0 115 85 60 3.41 0.7220
WVFGRD96 9.0 115 85 55 3.41 0.7340
WVFGRD96 10.0 300 30 -80 3.44 0.7450
WVFGRD96 11.0 295 35 -85 3.44 0.7500
WVFGRD96 12.0 295 35 -85 3.43 0.7446
WVFGRD96 13.0 165 60 35 3.43 0.7422
WVFGRD96 14.0 165 60 35 3.43 0.7370
WVFGRD96 15.0 165 60 30 3.45 0.7305
WVFGRD96 16.0 165 60 30 3.46 0.7217
WVFGRD96 17.0 165 65 30 3.46 0.7114
WVFGRD96 18.0 165 65 30 3.47 0.7007
WVFGRD96 19.0 165 65 25 3.50 0.6887
WVFGRD96 20.0 165 65 25 3.51 0.6747
WVFGRD96 21.0 165 65 25 3.52 0.6585
WVFGRD96 22.0 105 85 65 3.47 0.6444
WVFGRD96 23.0 105 85 70 3.47 0.6339
WVFGRD96 24.0 105 85 70 3.48 0.6237
WVFGRD96 25.0 105 85 70 3.49 0.6127
WVFGRD96 26.0 105 85 70 3.50 0.6010
WVFGRD96 27.0 105 85 75 3.51 0.5895
WVFGRD96 28.0 310 10 110 3.51 0.5743
WVFGRD96 29.0 310 5 110 3.52 0.5628
The best solution is
WVFGRD96 11.0 295 35 -85 3.44 0.7500
The mechanism corresponding to the best fit is
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The best fit as a function of depth is given in the following figure:
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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 0.10 n 3 br c 0.12 0.25 n 4 p 2
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| 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. |
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| 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:
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.
The following figure shows the stations used in the grid search for the best focal mechanism to fit the surface-wave spectral amplitudes of the Love and Rayleigh waves.
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The surface-wave determined focal mechanism is shown here.
NODAL PLANES
STK= 327.59
DIP= 60.50
RAKE= -61.66
OR
STK= 100.00
DIP= 40.00
RAKE= -129.99
DEPTH = 12.0 km
Mw = 3.53
Best Fit 0.8919 - P-T axis plot gives solutions with FIT greater than FIT90
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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.
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.
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| 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. |
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| 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. |
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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