The ANSS event ID is us7000mx7h and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/us7000mx7h/executive.
2024/07/05 10:46:38 47.289 -113.214 10.0 3.9 Montana
USGS/SLU Moment Tensor Solution
ENS 2024/07/05 10:46:38:0 47.29 -113.21 10.0 3.9 Montana
Stations used:
IW.DLMT IW.PLID MB.ECMT MB.FCMT MB.GBMT MB.HRY MB.JTMT
MB.LDM MB.LRM MB.SRMT US.BMO US.BOZ US.EGMT US.HLID US.MSO
US.NEW US.RLMT UW.AGNW UW.BRAN UW.DAVN UW.LBRT UW.LMONT
UW.LNO UW.TUCA UW.WOLL WW.BILL WW.IRMR WY.YFT WY.YHB WY.YHL
WY.YMR WY.YNE 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 0.08 n 3
Best Fitting Double Couple
Mo = 6.76e+21 dyne-cm
Mw = 3.82
Z = 24 km
Plane Strike Dip Rake
NP1 40 75 -25
NP2 137 66 -164
Principal Axes:
Axis Value Plunge Azimuth
T 6.76e+21 6 90
N 0.00e+00 61 191
P -6.76e+21 28 357
Moment Tensor: (dyne-cm)
Component Value
Mxx -5.24e+21
Mxy 3.24e+20
Mxz -2.81e+21
Myy 6.67e+21
Myz 8.76e+20
Mzz -1.43e+21
--------------
--------- ----------
------------ P ------------#
#------------ ------------##
###--------------------------#####
#####------------------------#######
######-----------------------#########
########---------------------###########
#########-------------------############
###########-----------------###########
############---------------############ T
##############-----------##############
###############---------##################
################-----###################
##################-#####################
################---###################
#############-------################
##########------------############
######------------------######
#---------------------------
----------------------
--------------
Global CMT Convention Moment Tensor:
R T P
-1.43e+21 -2.81e+21 -8.76e+20
-2.81e+21 -5.24e+21 -3.24e+20
-8.76e+20 -3.24e+20 6.67e+21
Details of the solution is found at
http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20240705104638/index.html
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STK = 40
DIP = 75
RAKE = -25
MW = 3.82
HS = 24.0
The NDK file is 20240705104638.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 0.08 n 3The results of this grid search are as follow:
DEPTH STK DIP RAKE MW FIT
WVFGRD96 1.0 165 50 65 3.31 0.2757
WVFGRD96 2.0 160 50 60 3.44 0.3848
WVFGRD96 3.0 230 75 -15 3.40 0.4159
WVFGRD96 4.0 225 85 25 3.44 0.4522
WVFGRD96 5.0 225 80 25 3.48 0.4950
WVFGRD96 6.0 225 80 25 3.51 0.5367
WVFGRD96 7.0 225 80 25 3.55 0.5768
WVFGRD96 8.0 225 80 30 3.60 0.6146
WVFGRD96 9.0 225 80 30 3.62 0.6431
WVFGRD96 10.0 225 80 25 3.64 0.6678
WVFGRD96 11.0 225 80 25 3.66 0.6892
WVFGRD96 12.0 225 80 25 3.68 0.7070
WVFGRD96 13.0 225 80 25 3.69 0.7219
WVFGRD96 14.0 40 80 -25 3.71 0.7338
WVFGRD96 15.0 40 80 -25 3.72 0.7470
WVFGRD96 16.0 40 75 -25 3.74 0.7580
WVFGRD96 17.0 40 75 -25 3.75 0.7688
WVFGRD96 18.0 40 75 -25 3.76 0.7777
WVFGRD96 19.0 40 75 -25 3.77 0.7851
WVFGRD96 20.0 40 75 -25 3.79 0.7908
WVFGRD96 21.0 40 75 -25 3.80 0.7956
WVFGRD96 22.0 40 75 -25 3.81 0.7998
WVFGRD96 23.0 40 75 -25 3.81 0.8024
WVFGRD96 24.0 40 75 -25 3.82 0.8036
WVFGRD96 25.0 40 75 -25 3.83 0.8034
WVFGRD96 26.0 40 75 -25 3.84 0.8015
WVFGRD96 27.0 40 75 -25 3.84 0.7979
WVFGRD96 28.0 40 75 -25 3.85 0.7931
WVFGRD96 29.0 40 75 -25 3.86 0.7864
WVFGRD96 30.0 40 75 -25 3.86 0.7775
WVFGRD96 31.0 40 75 -25 3.87 0.7672
WVFGRD96 32.0 40 75 -25 3.87 0.7554
WVFGRD96 33.0 40 75 -25 3.88 0.7419
WVFGRD96 34.0 40 75 -25 3.88 0.7282
WVFGRD96 35.0 40 75 -25 3.89 0.7134
WVFGRD96 36.0 40 75 -25 3.89 0.6997
WVFGRD96 37.0 40 75 -20 3.90 0.6874
WVFGRD96 38.0 40 75 -20 3.91 0.6773
WVFGRD96 39.0 40 75 -20 3.92 0.6703
WVFGRD96 40.0 35 65 -30 3.97 0.6687
WVFGRD96 41.0 35 65 -30 3.98 0.6658
WVFGRD96 42.0 35 65 -30 3.99 0.6627
WVFGRD96 43.0 40 70 -25 3.99 0.6598
WVFGRD96 44.0 40 70 -25 3.99 0.6570
WVFGRD96 45.0 40 65 -25 4.01 0.6537
WVFGRD96 46.0 40 70 -25 4.01 0.6497
WVFGRD96 47.0 40 70 -25 4.01 0.6455
WVFGRD96 48.0 40 70 -20 4.01 0.6409
WVFGRD96 49.0 40 70 -20 4.02 0.6367
WVFGRD96 50.0 40 70 -20 4.03 0.6336
WVFGRD96 51.0 40 75 -20 4.03 0.6309
WVFGRD96 52.0 40 75 -20 4.03 0.6267
WVFGRD96 53.0 40 75 -20 4.04 0.6229
WVFGRD96 54.0 40 75 -20 4.04 0.6210
WVFGRD96 55.0 40 75 -20 4.04 0.6175
WVFGRD96 56.0 40 75 -20 4.05 0.6142
WVFGRD96 57.0 40 75 -20 4.05 0.6132
WVFGRD96 58.0 40 75 -20 4.06 0.6095
WVFGRD96 59.0 40 80 -15 4.06 0.6076
The best solution is
WVFGRD96 24.0 40 75 -25 3.82 0.8036
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 0.08 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