The ANSS event ID is us6000jke7 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/us6000jke7/executive.
2023/01/30 19:28:52 45.745 -110.597 20.1 3.8 Montana
USGS/SLU Moment Tensor Solution
ENS 2023/01/30 19:28:52:0 45.74 -110.60 20.1 3.8 Montana
Stations used:
IE.BCYI IW.DLMT IW.IMW IW.LOHW IW.MOOW IW.PLID IW.TPAW
MB.BUT MB.FCMT MB.GBMT MB.JTMT US.BOZ US.EGMT US.HLID
US.MSO US.RLMT WW.TYLR WY.YDD WY.YHB WY.YHL WY.YMP WY.YMR
WY.YNE WY.YNM WY.YPP
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 = 5.50e+21 dyne-cm
Mw = 3.76
Z = 17 km
Plane Strike Dip Rake
NP1 333 58 -116
NP2 195 40 -55
Principal Axes:
Axis Value Plunge Azimuth
T 5.50e+21 10 81
N 0.00e+00 22 347
P -5.50e+21 66 193
Moment Tensor: (dyne-cm)
Component Value
Mxx -7.16e+20
Mxy 6.46e+20
Mxz 2.13e+21
Myy 5.15e+21
Myz 1.38e+21
Mzz -4.43e+21
----------####
####-----#############
##########-#################
#########-----################
#########---------################
#########------------###############
#########--------------###############
#########-----------------##############
########-------------------##########
#########--------------------######### T #
#########--------------------######### #
########----------------------############
########-----------------------###########
#######---------- ----------##########
#######---------- P -----------#########
#######--------- -----------########
######-----------------------#######
######----------------------######
#####---------------------####
#####-------------------####
###------------------#
#-------------
Global CMT Convention Moment Tensor:
R T P
-4.43e+21 2.13e+21 -1.38e+21
2.13e+21 -7.16e+20 -6.46e+20
-1.38e+21 -6.46e+20 5.15e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20230130192852/index.html
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STK = 195
DIP = 40
RAKE = -55
MW = 3.76
HS = 17.0
The NDK file is 20230130192852.ndk The waveform inversion is preferred.
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.
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.
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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 0.07 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 1.0 45 85 5 3.28 0.2076
WVFGRD96 2.0 160 45 -90 3.50 0.2672
WVFGRD96 3.0 40 85 -10 3.43 0.2532
WVFGRD96 4.0 215 75 -40 3.51 0.2565
WVFGRD96 5.0 220 35 -5 3.54 0.2859
WVFGRD96 6.0 215 30 -20 3.57 0.3220
WVFGRD96 7.0 210 30 -30 3.58 0.3517
WVFGRD96 8.0 200 25 -45 3.67 0.3815
WVFGRD96 9.0 195 30 -50 3.68 0.4164
WVFGRD96 10.0 195 35 -55 3.71 0.4486
WVFGRD96 11.0 190 35 -60 3.72 0.4765
WVFGRD96 12.0 190 35 -60 3.73 0.4972
WVFGRD96 13.0 195 40 -55 3.74 0.5126
WVFGRD96 14.0 195 40 -55 3.74 0.5233
WVFGRD96 15.0 195 40 -55 3.75 0.5297
WVFGRD96 16.0 195 40 -55 3.76 0.5329
WVFGRD96 17.0 195 40 -55 3.76 0.5334
WVFGRD96 18.0 195 40 -55 3.77 0.5315
WVFGRD96 19.0 195 40 -55 3.78 0.5274
WVFGRD96 20.0 200 45 -45 3.78 0.5216
WVFGRD96 21.0 205 45 -40 3.79 0.5170
WVFGRD96 22.0 205 45 -40 3.80 0.5093
WVFGRD96 23.0 205 45 -40 3.81 0.5006
WVFGRD96 24.0 205 45 -40 3.81 0.4907
WVFGRD96 25.0 205 45 -40 3.82 0.4797
WVFGRD96 26.0 205 45 -40 3.82 0.4683
WVFGRD96 27.0 205 45 -40 3.83 0.4561
WVFGRD96 28.0 205 45 -40 3.83 0.4434
WVFGRD96 29.0 205 50 -40 3.84 0.4304
The best solution is
WVFGRD96 17.0 195 40 -55 3.76 0.5334
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 0.07 n 3
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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 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