Location

Location ANSS

The ANSS event ID is usb000ldeh and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/usb000ldeh/executive.

2013/12/07 18:10:24 35.607 -97.386 8.4 4.5 Oklahoma

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2013/12/07 18:10:24:0 35.61 -97.39 8.4 4.5 Oklahoma Stations used: AG.CCAR AG.FCAR AG.LCAR AG.WHAR AG.WLAR IU.CCM NM.MGMO NM.PBMO NM.UALR OK.U32A OK.X37A TA.435B TA.ABTX TA.KSCO TA.MSTX TA.T25A TA.TUL1 TA.U40A TA.W39A TA.W41B TA.WHTX TA.X40A TA.X43A TA.Z41A US.AMTX US.CBKS US.KSU1 US.MIAR US.WMOK Filtering commands used: cut a -30 a 210 rtr taper w 0.1 hp c 0.02 n 3 lp c 0.06 n 3 Best Fitting Double Couple Mo = 6.61e+22 dyne-cm Mw = 4.48 Z = 8 km Plane Strike Dip Rake NP1 203 81 -160 NP2 110 70 -10 Principal Axes: Axis Value Plunge Azimuth T 6.61e+22 7 335 N 0.00e+00 68 227 P -6.61e+22 21 68 Moment Tensor: (dyne-cm) Component Value Mxx 4.58e+22 Mxy -4.45e+22 Mxz -6.47e+20 Myy -3.84e+22 Myz -2.39e+22 Mzz -7.37e+21 ############## # T ##############---- #### #############-------- ###################----------- ####################-------------- ####################---------------- ####################------------- -- -###################-------------- P --- ---################--------------- --- ------##############---------------------- --------###########----------------------- -----------#######------------------------ --------------###------------------------- ----------------##---------------------- ---------------#########---------------- -------------######################### ------------######################## ----------######################## --------###################### ------###################### ---################### ############## Global CMT Convention Moment Tensor: R T P -7.37e+21 -6.47e+20 2.39e+22 -6.47e+20 4.58e+22 4.45e+22 2.39e+22 4.45e+22 -3.84e+22 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20131207181024/index.html

Preferred Solution

      STK = 110
      DIP = 70
     RAKE = -10
       MW = 4.48
       HS = 8.0

The NDK file is 20131207181024.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 2013/12/07 18:10:24:0 35.61 -97.39 8.4 4.5 Oklahoma Stations used: AG.CCAR AG.FCAR AG.LCAR AG.WHAR AG.WLAR IU.CCM NM.MGMO NM.PBMO NM.UALR OK.U32A OK.X37A TA.435B TA.ABTX TA.KSCO TA.MSTX TA.T25A TA.TUL1 TA.U40A TA.W39A TA.W41B TA.WHTX TA.X40A TA.X43A TA.Z41A US.AMTX US.CBKS US.KSU1 US.MIAR US.WMOK Filtering commands used: cut a -30 a 210 rtr taper w 0.1 hp c 0.02 n 3 lp c 0.06 n 3 Best Fitting Double Couple Mo = 6.61e+22 dyne-cm Mw = 4.48 Z = 8 km Plane Strike Dip Rake NP1 203 81 -160 NP2 110 70 -10 Principal Axes: Axis Value Plunge Azimuth T 6.61e+22 7 335 N 0.00e+00 68 227 P -6.61e+22 21 68 Moment Tensor: (dyne-cm) Component Value Mxx 4.58e+22 Mxy -4.45e+22 Mxz -6.47e+20 Myy -3.84e+22 Myz -2.39e+22 Mzz -7.37e+21 ############## # T ##############---- #### #############-------- ###################----------- ####################-------------- ####################---------------- ####################------------- -- -###################-------------- P --- ---################--------------- --- ------##############---------------------- --------###########----------------------- -----------#######------------------------ --------------###------------------------- ----------------##---------------------- ---------------#########---------------- -------------######################### ------------######################## ----------######################## --------###################### ------###################### ---################### ############## Global CMT Convention Moment Tensor: R T P -7.37e+21 -6.47e+20 2.39e+22 -6.47e+20 4.58e+22 4.45e+22 2.39e+22 4.45e+22 -3.84e+22 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20131207181024/index.html

Regional Moment Tensor (Mwr) Moment magnitude derived from a moment tensor inversion of complete waveforms at regional distances (less than ~8 degrees), generally used for the analysis of small to moderate size earthquakes (typically Mw 3.5-6.0) crust or upper mantle earthquakes. Moment 7.36e+15 N-m Magnitude 4.5 Percent DC 86% Depth 8.0 km Updated 2013-12-07 18:23:36 UTC Author us Catalog us Contributor us Code us_b000ldeh_mwr Principal Axes Axis Value Plunge Azimuth T 7.613 0 159 N -0.526 81 69 P -7.087 9 249 Nodal Planes Plane Strike Dip Rake NP1 24 84 -174 NP2 294 84 -6

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 a -30 a 210
rtr
taper w 0.1
hp c 0.02 n 3 
lp c 0.06 n 3 

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    0.5   105    65   -30   4.27 0.4698
WVFGRD96    1.0   110    70   -20   4.26 0.4951
WVFGRD96    2.0   110    70   -20   4.35 0.5928
WVFGRD96    3.0   110    75   -15   4.37 0.6302
WVFGRD96    4.0   110    80   -10   4.39 0.6513
WVFGRD96    5.0   110    75   -10   4.41 0.6617
WVFGRD96    6.0   110    75    -5   4.43 0.6667
WVFGRD96    7.0   110    75    -5   4.45 0.6701
WVFGRD96    8.0   110    70   -10   4.48 0.6748
WVFGRD96    9.0   110    70   -10   4.49 0.6694
WVFGRD96   10.0   110    75   -15   4.51 0.6634
WVFGRD96   11.0   110    75   -15   4.52 0.6571
WVFGRD96   12.0   110    75   -15   4.53 0.6490
WVFGRD96   13.0   110    75   -15   4.54 0.6390
WVFGRD96   14.0   110    75   -15   4.54 0.6275
WVFGRD96   15.0   110    75   -15   4.55 0.6144
WVFGRD96   16.0   110    75   -15   4.56 0.6001
WVFGRD96   17.0   110    75   -15   4.56 0.5850
WVFGRD96   18.0   110    75   -15   4.57 0.5690
WVFGRD96   19.0   110    75   -15   4.57 0.5527
WVFGRD96   20.0   110    75   -15   4.58 0.5366
WVFGRD96   21.0   110    75   -15   4.59 0.5224
WVFGRD96   22.0   110    75   -15   4.59 0.5067
WVFGRD96   23.0   110    75   -15   4.60 0.4904
WVFGRD96   24.0   110    75   -15   4.60 0.4749
WVFGRD96   25.0   110    75   -15   4.61 0.4591
WVFGRD96   26.0   110    80   -20   4.62 0.4435
WVFGRD96   27.0   110    80   -20   4.62 0.4285
WVFGRD96   28.0   110    80   -20   4.63 0.4134
WVFGRD96   29.0   110    80   -20   4.63 0.3980

The best solution is

WVFGRD96    8.0   110    70   -10   4.48 0.6748

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 a -30 a 210
rtr
taper w 0.1
hp c 0.02 n 3 
lp c 0.06 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