Discussion

Special care was taken in the processing of this event because it was shallow an thus had significant short-period surface waves. Because of this an incorrect model would improperly model the surface waves to the detriment of the solution. A comparison of the observed SLU/USGS dispersion at the coordinates near the epicentral coordinates of (38N, 98W) shows (comparison ) that the local structure must be intermediate between the CUS and WUS models. On the other hand CRUST1.0 fits the dispersion well. The CRUST1.0 model was changed in that the S-velocity in the first layer was changed from 1.070 km/s to 1.250 km/s which gives a Poisson ratio more typical of rock.

Surprisingly, This improved model provides excellent fits, especially to the P wave over a wide range if diatances.

By being able to fit the short period dispersion ebtter, higher freuqencies could be used and the results believed.

Location

Location ANSS

2020/01/19 19:08:41 38.020 -97.970 4.6 4.4 Kansas

Focal Mechanism

 USGS/SLU Moment Tensor Solution
 ENS  2020/01/19 19:08:41:0  38.02  -97.97   4.6 4.4 Kansas
 
 Stations used:
   AG.HHAR C0.LAMA GS.OK029 GS.OK038 GS.OK048 GS.OK051 
   GS.OK052 N4.BGNE N4.KSCO N4.N35B N4.P38B N4.R32B N4.T35B 
   N4.TUL3 N4.U38B O2.ARC2 O2.CALT O2.CHAN O2.CRES O2.DOVR 
   O2.DRUM O2.DUST O2.ERNS O2.FREE O2.FW03 O2.FW06 O2.KS01 
   O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 O2.PW18 O2.SC04 
   O2.SC07 O2.SC11 O2.SC12 O2.SC13 O2.SC14 O2.SC15 O2.SC17 
   O2.SC19 O2.SC20 O2.SMNL OK.AMES OK.CHOK OK.CROK OK.DEOK 
   OK.ELIS OK.FNO OK.HTCH OK.MOOR OK.NOKA OK.QUOK OK.RLOK 
   OK.SWND OK.W35A OK.X34A TX.DRZT TX.SMWD US.CBKS US.KSU1 
   US.WMOK 
 
 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 = 5.96e+22 dyne-cm
  Mw = 4.45 
  Z  = 4 km
  Plane   Strike  Dip  Rake
   NP1      300    85   -10
   NP2       31    80   -175
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   5.96e+22      3     346
    N   0.00e+00     79      94
    P  -5.96e+22     11     255

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     5.20e+22
       Mxy    -2.84e+22
       Mxz     6.27e+21
       Myy    -5.02e+22
       Myz     9.52e+21
       Mzz    -1.80e+21
                                                     
                                                     
                                                     
                                                     
                      T ###########                  
                 ####   ###############              
              ########################----           
             #########################-----          
           ##########################--------        
          -#########################----------       
         ------####################------------      
        -----------###############--------------     
        --------------###########---------------     
       -------------------#######----------------    
       ----------------------##------------------    
       -----------------------##-----------------    
       -   ------------------######--------------    
         P -----------------##########----------     
           ----------------##############-------     
         -----------------#################----      
          --------------######################       
           ------------######################        
             --------######################          
              ------######################           
                 -#####################              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -1.80e+21   6.27e+21  -9.52e+21 
  6.27e+21   5.20e+22   2.84e+22 
 -9.52e+21   2.84e+22  -5.02e+22 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20200119190841/index.html
        

Preferred Solution

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

      STK = 300
      DIP = 85
     RAKE = -10
       MW = 4.45
       HS = 4.0

The NDK file is 20200119190841.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others
SLU
USGSMWR
 USGS/SLU Moment Tensor Solution
 ENS  2020/01/19 19:08:41:0  38.02  -97.97   4.6 4.4 Kansas
 
 Stations used:
   AG.HHAR C0.LAMA GS.OK029 GS.OK038 GS.OK048 GS.OK051 
   GS.OK052 N4.BGNE N4.KSCO N4.N35B N4.P38B N4.R32B N4.T35B 
   N4.TUL3 N4.U38B O2.ARC2 O2.CALT O2.CHAN O2.CRES O2.DOVR 
   O2.DRUM O2.DUST O2.ERNS O2.FREE O2.FW03 O2.FW06 O2.KS01 
   O2.MRSH O2.PERK O2.PERY O2.PW05 O2.PW09 O2.PW18 O2.SC04 
   O2.SC07 O2.SC11 O2.SC12 O2.SC13 O2.SC14 O2.SC15 O2.SC17 
   O2.SC19 O2.SC20 O2.SMNL OK.AMES OK.CHOK OK.CROK OK.DEOK 
   OK.ELIS OK.FNO OK.HTCH OK.MOOR OK.NOKA OK.QUOK OK.RLOK 
   OK.SWND OK.W35A OK.X34A TX.DRZT TX.SMWD US.CBKS US.KSU1 
   US.WMOK 
 
 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 = 5.96e+22 dyne-cm
  Mw = 4.45 
  Z  = 4 km
  Plane   Strike  Dip  Rake
   NP1      300    85   -10
   NP2       31    80   -175
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   5.96e+22      3     346
    N   0.00e+00     79      94
    P  -5.96e+22     11     255

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     5.20e+22
       Mxy    -2.84e+22
       Mxz     6.27e+21
       Myy    -5.02e+22
       Myz     9.52e+21
       Mzz    -1.80e+21
                                                     
                                                     
                                                     
                                                     
                      T ###########                  
                 ####   ###############              
              ########################----           
             #########################-----          
           ##########################--------        
          -#########################----------       
         ------####################------------      
        -----------###############--------------     
        --------------###########---------------     
       -------------------#######----------------    
       ----------------------##------------------    
       -----------------------##-----------------    
       -   ------------------######--------------    
         P -----------------##########----------     
           ----------------##############-------     
         -----------------#################----      
          --------------######################       
           ------------######################        
             --------######################          
              ------######################           
                 -#####################              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
 -1.80e+21   6.27e+21  -9.52e+21 
  6.27e+21   5.20e+22   2.84e+22 
 -9.52e+21   2.84e+22  -5.02e+22 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20200119190841/index.html
	
Regional Moment Tensor (Mwr)
Moment 7.218e+15 N-m
Magnitude 4.51 Mwr
Depth 3.0 km
Percent DC 100%
Half Duration -
Catalog US
Data Source US 1
Contributor US 1

Nodal Planes
Plane Strike Dip Rake
NP1 299 65 -19
NP2 38 73 -153

Principal Axes
Axis Value Plunge Azimuth
T 7.222e+15 N-m 5 167
N -0.008e+15 N-m 59 69
P -7.215e+15 N-m 31 260

        

Magnitudes

mLg Magnitude


(a) mLg computed using the IASPEI formula; (b) mLg residuals ; the values used for the trimmed mean are indicated.

ML Magnitude


(a) ML computed using the IASPEI formula for Horizontal components; (b) 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.


(a) ML computed using the IASPEI formula for Vertical components (research); (b) 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.

Context

The next figure presents the focal mechanism for this earthquake (red) in the context of other events (blue) in the SLU Moment Tensor Catalog which are within ± 0.5 degrees of the new event. This comparison is shown in the left panel of the figure. 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).

Waveform Inversion using wvfgrd96

The focal mechanism was determined using broadband seismic waveforms. The location of the event and the and stations used for 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 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 
The results of this grid search from 0.5 to 19 km depth are as follow:

           DEPTH  STK   DIP  RAKE   MW    FIT
WVFGRD96    1.0   305    70    15   4.31 0.4778
WVFGRD96    2.0   120    90     5   4.36 0.5666
WVFGRD96    3.0   300    85   -10   4.42 0.6068
WVFGRD96    4.0   300    85   -10   4.45 0.6084
WVFGRD96    5.0   120    85    15   4.47 0.5976
WVFGRD96    6.0   120    85    15   4.49 0.5923
WVFGRD96    7.0   305    75    15   4.50 0.5889
WVFGRD96    8.0   300    80    10   4.52 0.5840
WVFGRD96    9.0   300    80    10   4.53 0.5767
WVFGRD96   10.0   300    80    10   4.55 0.5672
WVFGRD96   11.0   300    80    10   4.56 0.5554
WVFGRD96   12.0   300    80    10   4.57 0.5408
WVFGRD96   13.0   300    80    10   4.59 0.5240

The best solution is

WVFGRD96    4.0   300    85   -10   4.45 0.6084

The mechanism correspond 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 and because the velocity model used in the predictions may not be perfect. 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.
Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to thewavefroms. 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:

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.

Discussion

Acknowledgements

Thanks also to the many seismic network operators whose dedication make this effort possible: University of Nevada Reno, University of Alaska, University of Washington, Oregon State University, University of Utah, Montana Bureau of Mines, UC Berkely, Caltech, UC San Diego, Saint Louis University, University of Memphis, Lamont Doherty Earth Observatory, the Oklahoma Geological Survey, TexNet, the Iris stations, the Transportable Array of EarthScope and other networks.

Velocity Model

The HutchKS model used for the waveform synthetic seismograms and for the surface wave eigenfunctions and dispersion is as follows:

MODEL.01
CRUST1.0 at (38.01, -98.01) with top layer adjusted
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
 0.500  2.500    1.250     2.110   225.0  100.0  0.0   0.0 1.0 1.0
 1.200  4.600    2.590     2.460   225.0  100.0  0.0   0.0 1.0 1.0
12.020  6.100    3.530     2.740   0.0  0.0  0.0   0.0 1.0 1.0
13.530  6.500    3.710     2.830   0.0  0.0  0.0   0.0 1.0 1.0
12.020  6.900    3.930     2.920   0.0  0.0  0.0   0.0 1.0 1.0
 0.000  8.160    4.530     3.360   0.0  0.0  0.0   0.0 1.0 1.0

Quality Control

Here we tabulate the reasons for not using certain digital data sets

The following stations did not have a valid response files:

Last Changed Mon Jan 20 17:04:33 CST 2020