Location

Location ANSS

The ANSS event ID is us1000604i and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/us1000604i/executive.

2016/07/05 17:21:57 36.271 -97.571 6.4 3.2 Oklahoma

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2016/07/05 17:21:57:0 36.27 -97.57 6.4 3.2 Oklahoma Stations used: GS.KAN14 GS.OK025 GS.OK029 GS.OK032 GS.OK033 OK.BCOK OK.CROK OK.HTCH Filtering commands used: cut o DIST/3.3 -20 o DIST/3.3 +40 rtr taper w 0.1 hp c 0.05 n 3 lp c 0.15 n 3 Best Fitting Double Couple Mo = 8.81e+20 dyne-cm Mw = 3.23 Z = 5 km Plane Strike Dip Rake NP1 150 85 -10 NP2 241 80 -175 Principal Axes: Axis Value Plunge Azimuth T 8.81e+20 3 196 N 0.00e+00 79 304 P -8.81e+20 11 105 Moment Tensor: (dyne-cm) Component Value Mxx 7.55e+20 Mxy 4.44e+20 Mxz -9.84e+18 Myy -7.29e+20 Myz -1.68e+20 Mzz -2.66e+19 ############## -##################### -----####################### ------######################## ---------######################### -----------######################### -------------##################------- ---------------############------------- ----------------#######----------------- ------------------###--------------------- -----------------##----------------------- --------------######---------------------- ------------#########----------------- - --------#############---------------- P ------################--------------- ---####################--------------- #######################------------- #######################----------- ######################-------- #######################----- #### ##############- T ########### Global CMT Convention Moment Tensor: R T P -2.66e+19 -9.84e+18 1.68e+20 -9.84e+18 7.55e+20 -4.44e+20 1.68e+20 -4.44e+20 -7.29e+20 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20160705172157/index.html

Preferred Solution

      STK = 150
      DIP = 85
     RAKE = -10
       MW = 3.23
       HS = 5.0

The NDK file is 20160705172157.ndk The waveform inversion is preferred.

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 -20 o DIST/3.3 +40
rtr
taper w 0.1
hp c 0.05 n 3 
lp c 0.15 n 3 

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0    65    75    10   2.88 0.4289
WVFGRD96    2.0   330    90    -5   3.04 0.5278
WVFGRD96    3.0   150    85     0   3.12 0.5775
WVFGRD96    4.0   330    90    10   3.18 0.6028
WVFGRD96    5.0   150    85   -10   3.23 0.6084
WVFGRD96    6.0   150    85    -5   3.28 0.6017
WVFGRD96    7.0   150    85    -5   3.32 0.5853
WVFGRD96    8.0   150    85    -5   3.37 0.5584
WVFGRD96    9.0   330    90   -15   3.41 0.5279
WVFGRD96   10.0   150    90    10   3.43 0.4960
WVFGRD96   11.0   330    90   -10   3.45 0.4613
WVFGRD96   12.0   155    85    20   3.47 0.4283
WVFGRD96   13.0   330    90   -20   3.49 0.3931
WVFGRD96   14.0   150    90    20   3.50 0.3583
WVFGRD96   15.0   150    85   -10   3.49 0.3265
WVFGRD96   16.0   150    85   -15   3.50 0.2973
WVFGRD96   17.0   150    85   -10   3.50 0.2704
WVFGRD96   18.0   150    90    40   3.55 0.2509
WVFGRD96   19.0   240    35     5   3.62 0.2392
WVFGRD96   20.0   240    35     5   3.63 0.2354
WVFGRD96   21.0   240    40     5   3.61 0.2319
WVFGRD96   22.0   240    40     0   3.62 0.2306
WVFGRD96   23.0   245    35    10   3.65 0.2426
WVFGRD96   24.0   240    45     0   3.62 0.2594
WVFGRD96   25.0   245    40     5   3.65 0.2772
WVFGRD96   26.0   245    50     5   3.62 0.2951
WVFGRD96   27.0   245    50     0   3.64 0.3169
WVFGRD96   28.0   240    75   -10   3.59 0.3361
WVFGRD96   29.0   240    75   -10   3.60 0.3570

The best solution is

WVFGRD96    5.0   150    85   -10   3.23 0.6084

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 -20 o DIST/3.3 +40
rtr
taper w 0.1
hp c 0.05 n 3 
lp c 0.15 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