Location

Location ANSS

The ANSS event ID is us10004a85 and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/us10004a85/executive.

2015/12/29 11:39:19 35.665 -97.405 6.5 4.3 Oklahoma

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2015/12/29 11:39:19:0 35.67 -97.40 6.5 4.3 Oklahoma Stations used: AG.FCAR AG.HHAR AG.WHAR AG.WLAR GS.KAN01 GS.KAN05 GS.KAN06 GS.KAN08 GS.KAN10 GS.KAN11 GS.KAN12 GS.KAN13 GS.KAN14 GS.KAN16 GS.OK031 GS.OK035 N4.237B N4.R32B N4.R40B N4.S39B N4.T35B N4.U38B N4.Z35B N4.Z38B NM.MGMO OK.BCOK OK.BLOK OK.CCOK OK.CHOK OK.CROK OK.FNO OK.OKCFA OK.U32A OK.W35A OK.X34A OK.X37A TA.ABTX TA.MSTX TA.TUL1 TA.U40A TA.W39A TA.WHTX TA.X40A US.CBKS US.KSU1 US.MIAR US.NATX Filtering commands used: cut o DIST/3.3 -30 o DIST/3.3 +70 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.07 n 3 Best Fitting Double Couple Mo = 3.09e+22 dyne-cm Mw = 4.26 Z = 5 km Plane Strike Dip Rake NP1 35 85 175 NP2 125 85 5 Principal Axes: Axis Value Plunge Azimuth T 3.09e+22 7 350 N 0.00e+00 83 170 P -3.09e+22 0 80 Moment Tensor: (dyne-cm) Component Value Mxx 2.85e+22 Mxy -1.07e+22 Mxz 3.71e+21 Myy -2.90e+22 Myz -6.77e+20 Mzz 4.68e+20 ## T ######### ###### ############# #########################--- #########################----- ##########################-------- ---#######################---------- ------####################------------ ---------#################-------------- ------------#############-------------- ---------------#########---------------- P -----------------######----------------- --------------------##-------------------- ---------------------##------------------- ------------------#######--------------- -----------------##########------------- ---------------##############--------- ------------####################---- ----------######################## ------######################## ----######################## ###################### ############## Global CMT Convention Moment Tensor: R T P 4.68e+20 3.71e+21 6.77e+20 3.71e+21 2.85e+22 1.07e+22 6.77e+20 1.07e+22 -2.90e+22 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20151229113919/index.html

Preferred Solution

      STK = 125
      DIP = 85
     RAKE = 5
       MW = 4.26
       HS = 5.0

The NDK file is 20151229113919.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

USGSMT

USGS/SLU Moment Tensor Solution ENS 2015/12/29 11:39:19:0 35.67 -97.40 6.5 4.3 Oklahoma Stations used: AG.FCAR AG.HHAR AG.WHAR AG.WLAR GS.KAN01 GS.KAN05 GS.KAN06 GS.KAN08 GS.KAN10 GS.KAN11 GS.KAN12 GS.KAN13 GS.KAN14 GS.KAN16 GS.OK031 GS.OK035 N4.237B N4.R32B N4.R40B N4.S39B N4.T35B N4.U38B N4.Z35B N4.Z38B NM.MGMO OK.BCOK OK.BLOK OK.CCOK OK.CHOK OK.CROK OK.FNO OK.OKCFA OK.U32A OK.W35A OK.X34A OK.X37A TA.ABTX TA.MSTX TA.TUL1 TA.U40A TA.W39A TA.WHTX TA.X40A US.CBKS US.KSU1 US.MIAR US.NATX Filtering commands used: cut o DIST/3.3 -30 o DIST/3.3 +70 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.07 n 3 Best Fitting Double Couple Mo = 3.09e+22 dyne-cm Mw = 4.26 Z = 5 km Plane Strike Dip Rake NP1 35 85 175 NP2 125 85 5 Principal Axes: Axis Value Plunge Azimuth T 3.09e+22 7 350 N 0.00e+00 83 170 P -3.09e+22 0 80 Moment Tensor: (dyne-cm) Component Value Mxx 2.85e+22 Mxy -1.07e+22 Mxz 3.71e+21 Myy -2.90e+22 Myz -6.77e+20 Mzz 4.68e+20 ## T ######### ###### ############# #########################--- #########################----- ##########################-------- ---#######################---------- ------####################------------ ---------#################-------------- ------------#############-------------- ---------------#########---------------- P -----------------######----------------- --------------------##-------------------- ---------------------##------------------- ------------------#######--------------- -----------------##########------------- ---------------##############--------- ------------####################---- ----------######################## ------######################## ----######################## ###################### ############## Global CMT Convention Moment Tensor: R T P 4.68e+20 3.71e+21 6.77e+20 3.71e+21 2.85e+22 1.07e+22 6.77e+20 1.07e+22 -2.90e+22 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20151229113919/index.html

Regional Moment Tensor (Mwr) Moment 3.044e+15 N-m Magnitude 4.26 Depth 4.0 km Percent DC 82% Half Duration – Catalog US (us10004a85) Data Source US1 Contributor US1 Nodal Planes Plane Strike Dip Rake NP1 36 89 174 NP2 126 84 1 Principal Axes Axis Value Plunge Azimuth T 3.178 5 351 N -0.289 84 201 P -2.889 3 81

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 -30 o DIST/3.3 +70
rtr
taper w 0.1
hp c 0.03 n 3 
lp c 0.07 n 3 

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0   125    85     5   4.02 0.4229
WVFGRD96    2.0   125    85     5   4.14 0.5389
WVFGRD96    3.0   125    85     5   4.19 0.5855
WVFGRD96    4.0   125    85     5   4.23 0.6025
WVFGRD96    5.0   125    85     5   4.26 0.6025
WVFGRD96    6.0   125    80     5   4.29 0.5948
WVFGRD96    7.0   125    80    10   4.32 0.5868
WVFGRD96    8.0   125    80    10   4.34 0.5794
WVFGRD96    9.0   125    80    15   4.36 0.5623
WVFGRD96   10.0   125    80    15   4.37 0.5457
WVFGRD96   11.0   125    80    15   4.38 0.5298
WVFGRD96   12.0   305    80    20   4.39 0.5139
WVFGRD96   13.0   305    80    15   4.40 0.5008
WVFGRD96   14.0   305    80    15   4.41 0.4880
WVFGRD96   15.0   305    80    15   4.42 0.4754
WVFGRD96   16.0   305    80    15   4.42 0.4632
WVFGRD96   17.0   305    80    15   4.43 0.4507
WVFGRD96   18.0   305    80    15   4.43 0.4385
WVFGRD96   19.0   305    80    15   4.44 0.4275
WVFGRD96   20.0   305    80    15   4.44 0.4167
WVFGRD96   21.0   305    80    15   4.45 0.4068
WVFGRD96   22.0   305    80    15   4.46 0.3979
WVFGRD96   23.0   305    80    15   4.46 0.3895
WVFGRD96   24.0   305    80    15   4.47 0.3827
WVFGRD96   25.0   305    80    15   4.47 0.3773
WVFGRD96   26.0   305    80    15   4.48 0.3723
WVFGRD96   27.0   305    80    15   4.49 0.3689
WVFGRD96   28.0   215    90    10   4.48 0.3726
WVFGRD96   29.0   215    90    10   4.49 0.3763

The best solution is

WVFGRD96    5.0   125    85     5   4.26 0.6025

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 -30 o DIST/3.3 +70
rtr
taper w 0.1
hp c 0.03 n 3 
lp c 0.07 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