Location

2011/04/05 07:05:25 44.617 -112.098 5.0 4.1 Montana

Arrival Times (from USGS)

Felt Map

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2011/04/05 07:05:25:0 44.62 -112.10 5.0 4.1 Montana Stations used: IW.DLMT IW.FLWY IW.IMW IW.LOHW IW.MOOW IW.REDW IW.SNOW US.AHID US.BOZ US.BW06 US.DUG US.EGMT US.HLID US.HWUT US.LKWY US.MSO US.NEW US.RLMT UU.BGU UU.CTU UU.HVU UU.MPU UU.NLU UU.SPU UU.TMU WY.YFT WY.YMR Filtering commands used: hp c 0.02 n 3 lp c 0.06 n 3 Best Fitting Double Couple Mo = 5.01e+22 dyne-cm Mw = 4.40 Z = 11 km Plane Strike Dip Rake NP1 300 85 -20 NP2 32 70 -175 Principal Axes: Axis Value Plunge Azimuth T 5.01e+22 10 347 N 0.00e+00 69 107 P -5.01e+22 18 254 Moment Tensor: (dyne-cm) Component Value Mxx 4.29e+22 Mxy -2.22e+22 Mxz 1.26e+22 Myy -3.99e+22 Myz 1.20e+22 Mzz -2.98e+21 # ########## ##### T ############## ######## ##############--- ##########################---- ############################------ -###########################-------- ------#######################--------- -----------##################----------- --------------##############------------ -------------------#########-------------- ----------------------#####--------------- -------------------------#---------------- --- -------------------###-------------- -- P ------------------#######---------- -- -----------------###########------- -------------------###############---- -----------------################### --------------#################### ----------#################### -------##################### ###################### ############## Global CMT Convention Moment Tensor: R T P -2.98e+21 1.26e+22 -1.20e+22 1.26e+22 4.29e+22 2.22e+22 -1.20e+22 2.22e+22 -3.99e+22 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20110405070525/index.html

Preferred Solution

The preferred solution from an analysis of the surface-wave spectral amplitude radiation pattern, waveform inversion and first motion observations is

      STK = 300
      DIP = 85
     RAKE = -20
       MW = 4.40
       HS = 11.0

The NDK file is 20110405070525.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others

SLU GCMT

USGS/SLU Moment Tensor Solution ENS 2011/04/05 07:05:25:0 44.62 -112.10 5.0 4.1 Montana Stations used: IW.DLMT IW.FLWY IW.IMW IW.LOHW IW.MOOW IW.REDW IW.SNOW US.AHID US.BOZ US.BW06 US.DUG US.EGMT US.HLID US.HWUT US.LKWY US.MSO US.NEW US.RLMT UU.BGU UU.CTU UU.HVU UU.MPU UU.NLU UU.SPU UU.TMU WY.YFT WY.YMR Filtering commands used: hp c 0.02 n 3 lp c 0.06 n 3 Best Fitting Double Couple Mo = 5.01e+22 dyne-cm Mw = 4.40 Z = 11 km Plane Strike Dip Rake NP1 300 85 -20 NP2 32 70 -175 Principal Axes: Axis Value Plunge Azimuth T 5.01e+22 10 347 N 0.00e+00 69 107 P -5.01e+22 18 254 Moment Tensor: (dyne-cm) Component Value Mxx 4.29e+22 Mxy -2.22e+22 Mxz 1.26e+22 Myy -3.99e+22 Myz 1.20e+22 Mzz -2.98e+21 # ########## ##### T ############## ######## ##############--- ##########################---- ############################------ -###########################-------- ------#######################--------- -----------##################----------- --------------##############------------ -------------------#########-------------- ----------------------#####--------------- -------------------------#---------------- --- -------------------###-------------- -- P ------------------#######---------- -- -----------------###########------- -------------------###############---- -----------------################### --------------#################### ----------#################### -------##################### ###################### ############## Global CMT Convention Moment Tensor: R T P -2.98e+21 1.26e+22 -1.20e+22 1.26e+22 4.29e+22 2.22e+22 -1.20e+22 2.22e+22 -3.99e+22 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20110405070525/index.html

April 5, 2011, WESTERN MONTANA, MW=4.6 Howard Koss Meredith Nettles CENTROID-MOMENT-TENSOR SOLUTION GCMT EVENT: S201104050705A DATA: II IU CU G GE IC TA US CI BK LD SURFACE WAVES: 129S, 188C, T= 50 TIMESTAMP: Q-20110406152325 CENTROID LOCATION: ORIGIN TIME: 07:05:30.0 0.5 LAT:44.69N 0.03;LON:112.05W 0.04 DEP: 12.0 FIX;TRIANG HDUR: 0.5 MOMENT TENSOR: SCALE 10**23 D-CM RR=-0.177 0.042; TT= 0.815 0.042 PP=-0.638 0.037; RT= 0.018 0.135 RP=-0.387 0.122; TP= 0.326 0.036 PRINCIPAL AXES: 1.(T) VAL= 0.889;PLG= 4;AZM=167 2.(N) 0.019; 62; 70 3.(P) -0.908; 28; 259 BEST DBLE.COUPLE:M0= 8.99*10**22 NP1: STRIKE=299;DIP=68;SLIP= -18 NP2: STRIKE= 36;DIP=74;SLIP=-157 ########### ################### #####################-- #######################---- #---###################------ ------------###########-------- ----------------######--------- ---------------------#----------- ---------------------##---------- --- --------------#####-------- --- P -------------########------ -- -----------############--- ---------------##############-- ------------################# ---------################## ----################### ############ #### ######## T

Magnitudes

ML Magnitude

(a) ML computed using the IASPEI formula for Horizontal components; (b) 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.

(a) ML computed using the IASPEI formula for Vertical components (research); (b) 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.

Context

The next figure presents the focal mechanism for this earthquake (red) in the context of other events (blue) in the SLU Moment Tensor Catalog which are within ± 0.5 degrees of the new event. This comparison is shown in the left panel of the figure. 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).

Waveform Inversion

The focal mechanism was determined using broadband seismic waveforms. The location of the event and the and stations used for 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 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 0.06 n 3

The results of this grid search from 0.5 to 19 km depth are as follow:

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    0.5   120    90     5   4.00 0.3968
WVFGRD96    1.0   300    90     0   4.03 0.4326
WVFGRD96    2.0   120    90     5   4.14 0.5513
WVFGRD96    3.0   300    85   -10   4.19 0.5997
WVFGRD96    4.0   300    85   -20   4.23 0.6370
WVFGRD96    5.0   295    75   -25   4.28 0.6740
WVFGRD96    6.0   295    75   -25   4.30 0.7059
WVFGRD96    7.0   295    75   -20   4.32 0.7307
WVFGRD96    8.0   295    75   -25   4.36 0.7546
WVFGRD96    9.0   295    75   -25   4.38 0.7651
WVFGRD96   10.0   300    85   -20   4.38 0.7686
WVFGRD96   11.0   300    85   -20   4.40 0.7699
WVFGRD96   12.0   300    85   -15   4.40 0.7667
WVFGRD96   13.0   300    85   -15   4.41 0.7610
WVFGRD96   14.0   120    90    15   4.42 0.7505
WVFGRD96   15.0   300    90   -15   4.43 0.7418
WVFGRD96   16.0   120    90    15   4.44 0.7311
WVFGRD96   17.0   120    90    15   4.45 0.7186
WVFGRD96   18.0   300    90   -15   4.45 0.7050
WVFGRD96   19.0   300    90   -15   4.46 0.6904
WVFGRD96   20.0   300    90   -15   4.47 0.6754
WVFGRD96   21.0   300    90   -15   4.47 0.6596
WVFGRD96   22.0   120    85    15   4.48 0.6441
WVFGRD96   23.0   120    85    15   4.48 0.6281
WVFGRD96   24.0   120    85    15   4.49 0.6118
WVFGRD96   25.0   300    90   -15   4.49 0.5930
WVFGRD96   26.0   120    85    15   4.49 0.5794
WVFGRD96   27.0   120    85    10   4.49 0.5633
WVFGRD96   28.0   120    85   -10   4.49 0.5498
WVFGRD96   29.0   120    85   -10   4.50 0.5381

The best solution is

WVFGRD96   11.0   300    85   -20   4.40 0.7699

The mechanism correspond 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 and because the velocity model used in the predictions may not be perfect. 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 0.06 n 3

Figure 3. Waveform comparison for selected depth

Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to thewavefroms. 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.

Discussion

Acknowledgements

Thanks also to the many seismic network operators whose dedication make this effort possible: University of Nevada Reno, University of Alaska, University of Washington, Oregon State University, University of Utah, Montana Bureas of Mines, UC Berkely, Caltech, UC San Diego, Saint Louis University, University of Memphis, Lamont Doherty Earth Observatory, the Iris stations and the Transportable Array of EarthScope.

Velocity Model

The WUS model used for the waveform synthetic seismograms and for the surface wave eigenfunctions and dispersion is as follows:

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

Quality Control

Here we tabulate the reasons for not using certain digital data sets

The following stations did not have a valid response files:

Last Changed Sun Dec 6 19:41:46 CST 2015