Location

SLU Location

Location ANSS

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2021/04/07 16:51:49:0 35.06 -96.32 28.6 3.6 Oklahoma Stations used: GS.OK048 N4.TUL3 O2.ARC2 O2.CHAN O2.CRES O2.DRIP O2.DRUM O2.DUST O2.ERNS O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 O2.PW18 O2.SC13 O2.SMNL O2.STIG OK.CHOK OK.DEOK OK.QUOK Filtering commands used: cut o DIST/3.5 -10 o DIST/3.5 +10 rtr taper w 0.1 hp c 0.5 n 3 lp c 0.50 n 3 Best Fitting Double Couple Mo = 8.81e+20 dyne-cm Mw = 3.23 Z = 29 km Plane Strike Dip Rake NP1 237 86 -150 NP2 145 60 -5 Principal Axes: Axis Value Plunge Azimuth T 8.81e+20 17 7 N 0.00e+00 60 245 P -8.81e+20 24 105 Moment Tensor: (dyne-cm) Component Value Mxx 7.36e+20 Mxy 2.91e+20 Mxz 3.37e+20 Myy -6.70e+20 Myz -2.83e+20 Mzz -6.65e+19 ######## ### ############ T ####### --############# ########## ---########################### -----############################# ------###########################--- -------########################------- ---------####################----------- ---------################--------------- -----------############------------------- ------------########---------------------- -------------#####------------------------ --------------#-------------------- ---- -----------###-------------------- P --- --------#######------------------- --- -----###########---------------------- --###############------------------- ##################---------------- ##################------------ #####################------- ###################### ############## Global CMT Convention Moment Tensor: R T P -6.65e+19 3.37e+20 2.83e+20 3.37e+20 7.36e+20 -2.91e+20 2.83e+20 -2.91e+20 -6.70e+20 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210407165149/index.html

Preferred Solution

      STK = 145
      DIP = 60
     RAKE = -5
       MW = 3.23
       HS = 29.0

The NDK file is 20210407165149.ndk

This was prompted by an email from Jake Walter, Ph.D. State Seismologist Oklahoma Geological Survey, who asked the following: Yesterday, we posted a fairly deep earthquake in east Oklahoma and from our body wave picks, we locate it fairly deep (28 km). I was wondering whether you had a moment tensor.

This is the result of trying such an inversion. This event is anomolous not only in the depth, but because the ML(H) is so large compared to the ML(Z), mLG and Mw.

The fist motions for a 29km depth agree very well with the RMT solution.

Moment Tensor Comparison

The following compares this source inversion to others

SLU

SLUFM

USGS/SLU Moment Tensor Solution ENS 2021/04/07 16:51:49:0 35.06 -96.32 28.6 3.6 Oklahoma Stations used: GS.OK048 N4.TUL3 O2.ARC2 O2.CHAN O2.CRES O2.DRIP O2.DRUM O2.DUST O2.ERNS O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 O2.PW18 O2.SC13 O2.SMNL O2.STIG OK.CHOK OK.DEOK OK.QUOK Filtering commands used: cut o DIST/3.5 -10 o DIST/3.5 +10 rtr taper w 0.1 hp c 0.5 n 3 lp c 0.50 n 3 Best Fitting Double Couple Mo = 8.81e+20 dyne-cm Mw = 3.23 Z = 29 km Plane Strike Dip Rake NP1 237 86 -150 NP2 145 60 -5 Principal Axes: Axis Value Plunge Azimuth T 8.81e+20 17 7 N 0.00e+00 60 245 P -8.81e+20 24 105 Moment Tensor: (dyne-cm) Component Value Mxx 7.36e+20 Mxy 2.91e+20 Mxz 3.37e+20 Myy -6.70e+20 Myz -2.83e+20 Mzz -6.65e+19 ######## ### ############ T ####### --############# ########## ---########################### -----############################# ------###########################--- -------########################------- ---------####################----------- ---------################--------------- -----------############------------------- ------------########---------------------- -------------#####------------------------ --------------#-------------------- ---- -----------###-------------------- P --- --------#######------------------- --- -----###########---------------------- --###############------------------- ##################---------------- ##################------------ #####################------- ###################### ############## Global CMT Convention Moment Tensor: R T P -6.65e+19 3.37e+20 2.83e+20 3.37e+20 7.36e+20 -2.91e+20 2.83e+20 -2.91e+20 -6.70e+20 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210407165149/index.html

First motions and takeoff angles from an elocate run.

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/3.5 -10 o DIST/3.5 +10
rtr
taper w 0.1
hp c 0.5 n 3 
lp c 0.50 n 3 

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0   120    90   -95   2.66 0.1430
WVFGRD96    2.0    55    55   -25   2.83 0.1297
WVFGRD96    3.0   170    60    55   2.94 0.1884
WVFGRD96    4.0   175    55    65   2.97 0.2374
WVFGRD96    5.0   175    50    60   2.98 0.2607
WVFGRD96    6.0   170    55    50   3.00 0.2716
WVFGRD96    7.0   165    50    35   2.99 0.2731
WVFGRD96    8.0   170    45    40   3.07 0.2830
WVFGRD96    9.0   165    55    40   3.12 0.3142
WVFGRD96   10.0   165    55    40   3.15 0.3259
WVFGRD96   11.0   160    55    35   3.18 0.3433
WVFGRD96   12.0   160    55    30   3.20 0.3553
WVFGRD96   13.0   155    55    25   3.21 0.3618
WVFGRD96   14.0   155    55    20   3.22 0.3815
WVFGRD96   15.0   155    55    25   3.23 0.3777
WVFGRD96   16.0   155    55    20   3.24 0.4026
WVFGRD96   17.0   155    55    20   3.24 0.4015
WVFGRD96   18.0   150    55    15   3.24 0.3989
WVFGRD96   19.0   150    55    15   3.24 0.4109
WVFGRD96   20.0   150    55    15   3.23 0.3949
WVFGRD96   21.0   150    50    15   3.23 0.3878
WVFGRD96   22.0   150    55    10   3.21 0.3659
WVFGRD96   23.0   150    55    10   3.20 0.3502
WVFGRD96   24.0   145    60    -5   3.19 0.3263
WVFGRD96   25.0   140    65   -20   3.21 0.3564
WVFGRD96   26.0   140    60   -15   3.21 0.3623
WVFGRD96   27.0   140    60   -10   3.22 0.3933
WVFGRD96   28.0   140    60   -10   3.23 0.4092
WVFGRD96   29.0   145    60    -5   3.23 0.4159
WVFGRD96   30.0   145    60    -5   3.23 0.4008
WVFGRD96   31.0   145    60    -5   3.22 0.3955
WVFGRD96   32.0   140    65   -20   3.20 0.3752
WVFGRD96   33.0   140    65   -20   3.20 0.3957
WVFGRD96   34.0   140    65   -20   3.19 0.3929
WVFGRD96   35.0   140    65   -25   3.19 0.3958
WVFGRD96   36.0   140    60   -20   3.18 0.4043
WVFGRD96   37.0   140    60   -20   3.18 0.3999
WVFGRD96   38.0   140    60   -20   3.18 0.3982
WVFGRD96   39.0   135    60   -20   3.21 0.3821
WVFGRD96   40.0   330    60    -5   3.26 0.3389
WVFGRD96   41.0   140    60   -25   3.31 0.2990
WVFGRD96   42.0   150    70     5   3.32 0.2795
WVFGRD96   43.0   150    70    10   3.34 0.2573
WVFGRD96   44.0   330    70    -5   3.35 0.2726
WVFGRD96   45.0   330    70    -5   3.36 0.2671
WVFGRD96   46.0   335    70     5   3.37 0.2670
WVFGRD96   47.0   150    65    10   3.37 0.2338
WVFGRD96   48.0   155    55    30   3.39 0.2143
WVFGRD96   49.0   155    55    30   3.40 0.2214

The best solution is

WVFGRD96   29.0   145    60    -5   3.23 0.4159

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/3.5 -10 o DIST/3.5 +10
rtr
taper w 0.1
hp c 0.5 n 3 
lp c 0.50 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: