Location

Location ANSS

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2021/02/05 17:48:43:0 36.31 -97.48 5.0 4.1 Oklahoma Stations used: GS.KS28 GS.OK029 GS.OK038 GS.OK048 GS.OK052 N4.R32B N4.T35B N4.TUL3 N4.U38B O2.ALVA O2.ARC2 O2.CALT O2.CHAN O2.CRES O2.DOVR O2.DRIP O2.DRUM O2.DUST O2.ERNS O2.FREE O2.FW03 O2.FW06 O2.GORE O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 O2.PW18 O2.SC07 O2.SC11 O2.SC13 O2.SC15 O2.SC16 O2.SC19 O2.SC20 O2.SMNL O2.STIG OK.AMES OK.CHOK OK.CROK OK.CSTR OK.DEOK OK.FNO OK.HTCH OK.MOOR OK.NOKA OK.W35A TX.DRZT US.CBKS US.KSU1 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 Best Fitting Double Couple Mo = 1.78e+22 dyne-cm Mw = 4.10 Z = 5 km Plane Strike Dip Rake NP1 45 85 -175 NP2 315 85 -5 Principal Axes: Axis Value Plunge Azimuth T 1.78e+22 0 180 N 0.00e+00 83 90 P -1.78e+22 7 270 Moment Tensor: (dyne-cm) Component Value Mxx 1.78e+22 Mxy 1.35e+20 Mxz -1.25e+19 Myy -1.75e+22 Myz 2.17e+21 Mzz -2.69e+20 ############## ###################### ############################ -############################- ------########################---- ---------####################------- ------------#################--------- ---------------#############------------ -----------------#########-------------- -----------------######---------------- P -------------------##------------------ -------------------##------------------ --------------------######---------------- -----------------#########-------------- ---------------#############------------ ------------#################--------- ---------####################------- ------########################---- -############################- ############################ ######### ########## ##### T ###### Global CMT Convention Moment Tensor: R T P -2.69e+20 -1.25e+19 -2.17e+21 -1.25e+19 1.78e+22 -1.35e+20 -2.17e+21 -1.35e+20 -1.75e+22 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210205174843/index.html

Preferred Solution

      STK = 315
      DIP = 85
     RAKE = -5
       MW = 4.10
       HS = 5.0

The NDK file is 20210205174843.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others

SLU

USGSMWR

USGS/SLU Moment Tensor Solution ENS 2021/02/05 17:48:43:0 36.31 -97.48 5.0 4.1 Oklahoma Stations used: GS.KS28 GS.OK029 GS.OK038 GS.OK048 GS.OK052 N4.R32B N4.T35B N4.TUL3 N4.U38B O2.ALVA O2.ARC2 O2.CALT O2.CHAN O2.CRES O2.DOVR O2.DRIP O2.DRUM O2.DUST O2.ERNS O2.FREE O2.FW03 O2.FW06 O2.GORE O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 O2.PW18 O2.SC07 O2.SC11 O2.SC13 O2.SC15 O2.SC16 O2.SC19 O2.SC20 O2.SMNL O2.STIG OK.AMES OK.CHOK OK.CROK OK.CSTR OK.DEOK OK.FNO OK.HTCH OK.MOOR OK.NOKA OK.W35A TX.DRZT US.CBKS US.KSU1 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 Best Fitting Double Couple Mo = 1.78e+22 dyne-cm Mw = 4.10 Z = 5 km Plane Strike Dip Rake NP1 45 85 -175 NP2 315 85 -5 Principal Axes: Axis Value Plunge Azimuth T 1.78e+22 0 180 N 0.00e+00 83 90 P -1.78e+22 7 270 Moment Tensor: (dyne-cm) Component Value Mxx 1.78e+22 Mxy 1.35e+20 Mxz -1.25e+19 Myy -1.75e+22 Myz 2.17e+21 Mzz -2.69e+20 ############## ###################### ############################ -############################- ------########################---- ---------####################------- ------------#################--------- ---------------#############------------ -----------------#########-------------- -----------------######---------------- P -------------------##------------------ -------------------##------------------ --------------------######---------------- -----------------#########-------------- ---------------#############------------ ------------#################--------- ---------####################------- ------########################---- -############################- ############################ ######### ########## ##### T ###### Global CMT Convention Moment Tensor: R T P -2.69e+20 -1.25e+19 -2.17e+21 -1.25e+19 1.78e+22 -1.35e+20 -2.17e+21 -1.35e+20 -1.75e+22 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210205174843/index.html

Regional Moment Tensor (Mwr) Moment 2.587e+15 N-m Magnitude 4.21 Mwr Depth 3.0 km Percent DC 64% Half Duration - Catalog US Data Source US 2 Contributor US 2 Nodal Planes Plane Strike Dip Rake NP1 314 89 8 NP2 224 82 179 Principal Axes Axis Value Plunge Azimuth T 2.802e+15 N-m 7 179 N -0.504e+15 N-m 82 322 P -2.298e+15 N-m 5 89

Magnitudes

mLg Magnitude

(a) mLg computed using the IASPEI formula; (b) mLg residuals ; the values used for the trimmed mean are indicated.

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

Waveform Inversion using wvfgrd96

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:

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 

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0   315    75   -10   3.83 0.4423
WVFGRD96    2.0   140    85    20   3.97 0.5500
WVFGRD96    3.0   140    90    10   4.02 0.6007
WVFGRD96    4.0   315    80   -10   4.07 0.6247
WVFGRD96    5.0   315    85    -5   4.10 0.6282
WVFGRD96    6.0   315    85    -5   4.13 0.6219
WVFGRD96    7.0   315    85    -5   4.16 0.6108
WVFGRD96    8.0   315    80    -5   4.20 0.5967
WVFGRD96    9.0   315    80    -5   4.21 0.5714
WVFGRD96   10.0   315    80    -5   4.23 0.5455
WVFGRD96   11.0   315    85    -5   4.24 0.5207
WVFGRD96   12.0   315    85    -5   4.25 0.4972
WVFGRD96   13.0   315    85    -5   4.26 0.4748
WVFGRD96   14.0   135    85   -10   4.27 0.4562
WVFGRD96   15.0   135    85   -10   4.28 0.4389
WVFGRD96   16.0   135    85   -10   4.29 0.4222
WVFGRD96   17.0   135    85   -10   4.29 0.4061
WVFGRD96   18.0   315    90    10   4.30 0.3891
WVFGRD96   19.0   135    85   -10   4.31 0.3771
WVFGRD96   20.0   315    90    10   4.31 0.3625
WVFGRD96   21.0   315    90    10   4.32 0.3522
WVFGRD96   22.0   135    85   -10   4.32 0.3449
WVFGRD96   23.0   135    85   -10   4.33 0.3375
WVFGRD96   24.0   135    80   -10   4.33 0.3309
WVFGRD96   25.0   135    85   -10   4.34 0.3259
WVFGRD96   26.0   135    85   -10   4.34 0.3214
WVFGRD96   27.0   225    80     5   4.34 0.3192
WVFGRD96   28.0   225    80     0   4.35 0.3258
WVFGRD96   29.0   225    85     5   4.36 0.3328

The best solution is

WVFGRD96    5.0   315    85    -5   4.10 0.6282

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

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 

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.

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)

 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 Bureau of Mines, UC Berkely, Caltech, UC San Diego, Saint Louis University, University of Memphis, Lamont Doherty Earth Observatory, the Oklahoma Geological Survey, TexNet, the Iris stations, the Transportable Array of EarthScope and other networks.

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: