Location

SLU Location

To check the ANSS location or to compare the observed P-wave first motions to the moment tensor solution, P- and S-wave first arrival times were manually read together with the P-wave first motions. The subsequent output of the program elocate is given in the file elocate.txt. The first motion plot is shown below.

Location ANSS

The ANSS event ID is ok2020assg and the event page is at https://earthquake.usgs.gov/earthquakes/eventpage/ok2020assg/executive.

2020/01/11 05:40:18 36.292 -98.172 4.0 3.44 Oklahoma

Focal Mechanism

USGS/SLU Moment Tensor Solution ENS 2020/01/11 05:40:18:0 36.29 -98.17 4.0 3.4 Oklahoma Stations used: O2.DOVR O2.FREE O2.FW03 OK.CROK OK.FNO Filtering commands used: cut o DIST/3.3 -30 o DIST/3.3 +40 rtr taper w 0.1 hp c 0.03 n 3 lp c 0.10 n 3 Best Fitting Double Couple Mo = 1.38e+21 dyne-cm Mw = 3.36 Z = 5 km Plane Strike Dip Rake NP1 325 55 -50 NP2 89 51 -133 Principal Axes: Axis Value Plunge Azimuth T 1.38e+21 2 28 N 0.00e+00 32 119 P -1.38e+21 58 294 Moment Tensor: (dyne-cm) Component Value Mxx 1.01e+21 Mxy 7.15e+20 Mxz -2.09e+20 Myy -1.62e+19 Myz 5.88e+20 Mzz -9.94e+20 ############## ################### T --------############## ### -------------################# ------------------################ ---------------------############### ------------------------############## --------------------------############## ----------- --------------############ ------------ P ---------------############ ------------ ----------------########### #-------------------------------#########- ##------------------------------#######--- ###-----------------------------####---- ######--------------------------#------- #########-------------------####------ ###############################----- ##############################---- ############################-- ##########################-- ###################### ############## Global CMT Convention Moment Tensor: R T P -9.94e+20 -2.09e+20 -5.88e+20 -2.09e+20 1.01e+21 -7.15e+20 -5.88e+20 -7.15e+20 -1.62e+19 Details of the solution is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20200111054018/index.html

Preferred Solution

The preferred solution from an analysis of the surface-wave spectral amplitude radiation pattern, waveform inversion or first motion observations is

      STK = 325
      DIP = 55
     RAKE = -50
       MW = 3.36
       HS = 5.0

The NDK file is 20200111054018.ndk The waveform inversion is preferred.

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

The left panel of the next figure presents the focal mechanism for this earthquake (red) in the context of other nearby events (blue) in the SLU Moment Tensor Catalog. The right panel shows the inferred direction of maximum compressive stress and the type of faulting (green is strike-slip, red is normal, blue is thrust; oblique is shown by a combination of colors). Thus context plot is useful for assessing the appropriateness of the moment tensor of this event.

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 +40
rtr
taper w 0.1
hp c 0.03 n 3 
lp c 0.10 n 3

The results of this grid search are as follow:

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0    35    35   -45   3.12 0.3450
WVFGRD96    2.0    25    25   -40   3.34 0.3848
WVFGRD96    3.0   320    35   -35   3.32 0.4336
WVFGRD96    4.0   310    55   -50   3.34 0.4664
WVFGRD96    5.0   325    55   -50   3.36 0.4876
WVFGRD96    6.0   330    55   -45   3.37 0.4787
WVFGRD96    7.0   340    65   -25   3.37 0.4598
WVFGRD96    8.0   325    50   -50   3.46 0.4506
WVFGRD96    9.0   350    70   -20   3.45 0.4204
WVFGRD96   10.0   260    60     5   3.46 0.4148
WVFGRD96   11.0   260    60     5   3.48 0.4128
WVFGRD96   12.0   255    60     5   3.49 0.4093
WVFGRD96   13.0   250    60    10   3.50 0.4050
WVFGRD96   14.0   250    60    10   3.52 0.3994
WVFGRD96   15.0   245    60    10   3.54 0.3926
WVFGRD96   16.0   245    60    10   3.55 0.3847
WVFGRD96   17.0   235    65    10   3.59 0.3761
WVFGRD96   18.0   235    65    10   3.60 0.3683
WVFGRD96   19.0   230    70     5   3.63 0.3606
WVFGRD96   20.0    60    70    20   3.54 0.3619
WVFGRD96   21.0    60    65    20   3.56 0.3682
WVFGRD96   22.0    55    65    20   3.59 0.3718
WVFGRD96   23.0    55    65    20   3.59 0.3728
WVFGRD96   24.0    65    55    15   3.56 0.3777
WVFGRD96   25.0    70    50    15   3.56 0.3791
WVFGRD96   26.0    70    50    15   3.56 0.3797
WVFGRD96   27.0    75    45    15   3.57 0.3818
WVFGRD96   28.0    75    50    15   3.57 0.3804
WVFGRD96   29.0    75    50    15   3.57 0.3833

The best solution is

WVFGRD96    5.0   325    55   -50   3.36 0.4876

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 +40
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)

Assuming only a mislocation, the time shifts are fit to a functional form:

 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

Last Changed Thu Apr 25 08:28:37 AM CDT 2024