Location

Location ANSS

The ANSS event ID is ok2021kemx and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/ok2021kemx/executive.

2021/05/25 18:24:57 36.286 -99.915 7.7 4.05 Oklahoma

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2021/05/25 18:24:57:0 36.29 -99.92 7.7 4.1 Oklahoma Stations used: C0.LAMA C0.T25A GS.KS28 GS.OK029 GS.OK038 GS.OK051 GS.OK052 N4.KSCO N4.MSTX N4.R32B N4.T35B N4.TUL3 O2.ALVA O2.ARC2 O2.CALT O2.CHAN O2.CRES O2.DOVR O2.DRUM O2.ERNS O2.FREE O2.FW03 O2.FW06 O2.GORE O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 O2.PW18 O2.SC11 O2.SC15 O2.SC16 O2.SC19 O2.SC20 O2.SMNL OK.AMES OK.CROK OK.CSTR OK.ELIS OK.FNO OK.HTCH OK.W35A TX.DKNS TX.DRZT TX.PH02 TX.POST TX.RTBA TX.SMWD US.AMTX US.CBKS US.KSU1 YX.UNM5 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 = 1.60e+22 dyne-cm Mw = 4.07 Z = 12 km Plane Strike Dip Rake NP1 285 50 -65 NP2 69 46 -117 Principal Axes: Axis Value Plunge Azimuth T 1.60e+22 2 358 N 0.00e+00 19 88 P -1.60e+22 71 262 Moment Tensor: (dyne-cm) Component Value Mxx 1.59e+22 Mxy -9.18e+20 Mxz 1.31e+21 Myy -1.64e+21 Myz 4.86e+21 Mzz -1.43e+22 ##### T ###### ######### ########## ############################ ############################## ################################## #######------------################# ###-----------------------############ #-----------------------------#########- ---------------------------------######- ------------------------------------###--- -------------- ------------------------- -------------- P --------------------##--- -------------- -------------------####-- ---------------------------------####### -------------------------------######### #--------------------------########### ###-------------------############## #########----##################### ############################## ############################ ###################### ############## Global CMT Convention Moment Tensor: R T P -1.43e+22 1.31e+21 -4.86e+21 1.31e+21 1.59e+22 9.18e+20 -4.86e+21 9.18e+20 -1.64e+21 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210525182457/index.html

Preferred Solution

      STK = 285
      DIP = 50
     RAKE = -65
       MW = 4.07
       HS = 12.0

The NDK file is 20210525182457.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to those provided by others. The purpose is to look for major differences and also to note slight differences that might be inherent to the processing procedure. For completeness the USGS/SLU solution is repeated from above.

SLU

USGSMWR

USGS/SLU Moment Tensor Solution ENS 2021/05/25 18:24:57:0 36.29 -99.92 7.7 4.1 Oklahoma Stations used: C0.LAMA C0.T25A GS.KS28 GS.OK029 GS.OK038 GS.OK051 GS.OK052 N4.KSCO N4.MSTX N4.R32B N4.T35B N4.TUL3 O2.ALVA O2.ARC2 O2.CALT O2.CHAN O2.CRES O2.DOVR O2.DRUM O2.ERNS O2.FREE O2.FW03 O2.FW06 O2.GORE O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 O2.PW18 O2.SC11 O2.SC15 O2.SC16 O2.SC19 O2.SC20 O2.SMNL OK.AMES OK.CROK OK.CSTR OK.ELIS OK.FNO OK.HTCH OK.W35A TX.DKNS TX.DRZT TX.PH02 TX.POST TX.RTBA TX.SMWD US.AMTX US.CBKS US.KSU1 YX.UNM5 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 = 1.60e+22 dyne-cm Mw = 4.07 Z = 12 km Plane Strike Dip Rake NP1 285 50 -65 NP2 69 46 -117 Principal Axes: Axis Value Plunge Azimuth T 1.60e+22 2 358 N 0.00e+00 19 88 P -1.60e+22 71 262 Moment Tensor: (dyne-cm) Component Value Mxx 1.59e+22 Mxy -9.18e+20 Mxz 1.31e+21 Myy -1.64e+21 Myz 4.86e+21 Mzz -1.43e+22 ##### T ###### ######### ########## ############################ ############################## ################################## #######------------################# ###-----------------------############ #-----------------------------#########- ---------------------------------######- ------------------------------------###--- -------------- ------------------------- -------------- P --------------------##--- -------------- -------------------####-- ---------------------------------####### -------------------------------######### #--------------------------########### ###-------------------############## #########----##################### ############################## ############################ ###################### ############## Global CMT Convention Moment Tensor: R T P -1.43e+22 1.31e+21 -4.86e+21 1.31e+21 1.59e+22 9.18e+20 -4.86e+21 9.18e+20 -1.64e+21 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20210525182457/index.html

Regional Moment Tensor (Mwr) Moment 1.517e+15 N-m Magnitude 4.05 Mwr Depth 9.0 km Percent DC 80% Half Duration - Catalog US Data Source US 3 Contributor US 3 Nodal Planes Plane Strike Dip Rake NP1 73 41 -101 NP2 267 50 -81 Principal Axes Axis Value Plunge Azimuth T 1.591e+15 N-m 5 350 N -0.160e+15 N-m 7 81 P -1.431e+15 N-m 81 228

Magnitudes

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 M_L by application of the respective IASPEI formulae. As a research study, the linear distance term of the IASPEI formula for M_L is adjusted to remove a linear distance trend in residuals to give a regionally defined M_L. The defined M_L 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.

mLg Magnitude

Left: mLg computed using the IASPEI formula. Center: mLg residuals versus epicentral distance ; the values used for the trimmed mean magnitude estimate are indicated. Right: residuals as a function of distance and azimuth.

ML Magnitude

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.

Context

Waveform Inversion using wvfgrd96

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.

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'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 0.10 n 3 

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0     5    50    95   3.58 0.1839
WVFGRD96    2.0     5    50    95   3.73 0.2391
WVFGRD96    3.0   145    40    25   3.76 0.2435
WVFGRD96    4.0   135    40     0   3.79 0.2787
WVFGRD96    5.0   300    40   -30   3.84 0.3228
WVFGRD96    6.0   290    55   -60   3.89 0.3688
WVFGRD96    7.0   290    55   -60   3.92 0.4106
WVFGRD96    8.0   280    55   -75   4.01 0.4440
WVFGRD96    9.0   275    50   -80   4.04 0.4735
WVFGRD96   10.0   280    50   -70   4.05 0.4915
WVFGRD96   11.0   280    50   -70   4.06 0.4998
WVFGRD96   12.0   285    50   -65   4.07 0.5008
WVFGRD96   13.0   290    55   -60   4.08 0.4967
WVFGRD96   14.0   290    55   -55   4.08 0.4886
WVFGRD96   15.0   290    55   -55   4.09 0.4777
WVFGRD96   16.0   290    55   -55   4.11 0.4645
WVFGRD96   17.0   290    55   -55   4.11 0.4495
WVFGRD96   18.0   290    55   -55   4.12 0.4326
WVFGRD96   19.0   295    60   -50   4.13 0.4152
WVFGRD96   20.0   295    60   -50   4.13 0.3975
WVFGRD96   21.0   295    60   -50   4.15 0.3809
WVFGRD96   22.0   300    60   -40   4.15 0.3618
WVFGRD96   23.0   300    60   -40   4.15 0.3435
WVFGRD96   24.0   300    65   -40   4.15 0.3257
WVFGRD96   25.0   300    65   -40   4.15 0.3086
WVFGRD96   26.0   300    65   -40   4.16 0.2926
WVFGRD96   27.0   235    55    35   4.14 0.2792
WVFGRD96   28.0   235    55    35   4.14 0.2701
WVFGRD96   29.0   235    60    35   4.14 0.2609

The best solution is

WVFGRD96   12.0   285    50   -65   4.07 0.5008

The mechanism corresponding 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, 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 0.10 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. The time scale is relative to the first trace sample.

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:

• 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.

Velocity Model

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