Location

2015/05/02 16:23:07 42.212 -85.429 5.9 4.9 Michigan

Arrival Times (from USGS)

Arrival time list

Felt Map

USGS Felt map for this earthquake

USGS Felt reports main page

Focal Mechanism

 USGS/SLU Moment Tensor Solution
 ENS  2015/05/02 16:23:07:0  42.21  -85.43   5.9 4.9 Michigan
 
 Stations used:
   CN.SADO IU.WCI LD.ALLY LD.WVNY N4.D41A N4.E43A N4.E46A 
   N4.F42A N4.G40A N4.G45A N4.H43A N4.I40B N4.I42A N4.I45A 
   N4.I49A N4.J47A N4.J54A N4.K43A N4.K50A N4.L40A N4.L42A 
   N4.L48A N4.M44A N4.M50A N4.M52A N4.N41A N4.N47A N4.N49A 
   N4.N51A N4.N53A N4.O44A N4.O49A N4.O52A N4.O54A N4.P43A 
   N4.P46A N4.P48A N4.P51A N4.P53A N4.Q44B N4.Q51A N4.Q52A 
   N4.Q54A N4.R49A N4.R50A N4.R53A N4.S44A N4.S51A N4.T47A 
   N4.T50A NM.BLO NM.SIUC NM.SLM NM.USIN NW.HQIL TA.L44A 
   TA.M53A TA.M54A TA.N54A TA.O53A TA.P49A TA.P52A TA.SFIN 
   US.AAM US.ACSO US.COWI US.ERPA US.GLMI US.HDIL US.JFWS 
   WU.MEDO 
 
 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 0.10 n 3 
 
 Best Fitting Double Couple
  Mo = 2.88e+22 dyne-cm
  Mw = 4.24 
  Z  = 5 km
  Plane   Strike  Dip  Rake
   NP1      210    90   -175
   NP2      120    85     0
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   2.88e+22      4     345
    N   0.00e+00     85     210
    P  -2.88e+22      4      75

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     2.49e+22
       Mxy    -1.44e+22
       Mxz     1.26e+21
       Myy    -2.49e+22
       Myz    -2.18e+21
       Mzz     0.00e+00
                                                     
                                                     
                                                     
                                                     
                      T ###########                  
                 ####   ##############-              
              #######################-----           
             #######################-------          
           ########################----------        
          ########################------------       
         ----####################--------------      
        -------#################--------------       
        ----------#############--------------- P     
       --------------#########----------------       
       -----------------#####--------------------    
       ------------------------------------------    
       -------------------####-------------------    
        -----------------#########--------------     
        ----------------#############-----------     
         --------------##################------      
          ------------#######################-       
           ----------########################        
             -------#######################          
              -----#######################           
                 -#####################              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  0.00e+00   1.26e+21   2.18e+21 
  1.26e+21   2.49e+22   1.44e+22 
  2.18e+21   1.44e+22  -2.49e+22 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20150502162307/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 = 120
      DIP = 85
     RAKE = 0
       MW = 4.24
       HS = 5.0

The NDK file is 20150502162307.ndk The waveform inversion is preferred.

Moment Tensor Comparison

The following compares this source inversion to others
SLU
USGSMT
 USGS/SLU Moment Tensor Solution
 ENS  2015/05/02 16:23:07:0  42.21  -85.43   5.9 4.9 Michigan
 
 Stations used:
   CN.SADO IU.WCI LD.ALLY LD.WVNY N4.D41A N4.E43A N4.E46A 
   N4.F42A N4.G40A N4.G45A N4.H43A N4.I40B N4.I42A N4.I45A 
   N4.I49A N4.J47A N4.J54A N4.K43A N4.K50A N4.L40A N4.L42A 
   N4.L48A N4.M44A N4.M50A N4.M52A N4.N41A N4.N47A N4.N49A 
   N4.N51A N4.N53A N4.O44A N4.O49A N4.O52A N4.O54A N4.P43A 
   N4.P46A N4.P48A N4.P51A N4.P53A N4.Q44B N4.Q51A N4.Q52A 
   N4.Q54A N4.R49A N4.R50A N4.R53A N4.S44A N4.S51A N4.T47A 
   N4.T50A NM.BLO NM.SIUC NM.SLM NM.USIN NW.HQIL TA.L44A 
   TA.M53A TA.M54A TA.N54A TA.O53A TA.P49A TA.P52A TA.SFIN 
   US.AAM US.ACSO US.COWI US.ERPA US.GLMI US.HDIL US.JFWS 
   WU.MEDO 
 
 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 0.10 n 3 
 
 Best Fitting Double Couple
  Mo = 2.88e+22 dyne-cm
  Mw = 4.24 
  Z  = 5 km
  Plane   Strike  Dip  Rake
   NP1      210    90   -175
   NP2      120    85     0
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   2.88e+22      4     345
    N   0.00e+00     85     210
    P  -2.88e+22      4      75

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx     2.49e+22
       Mxy    -1.44e+22
       Mxz     1.26e+21
       Myy    -2.49e+22
       Myz    -2.18e+21
       Mzz     0.00e+00
                                                     
                                                     
                                                     
                                                     
                      T ###########                  
                 ####   ##############-              
              #######################-----           
             #######################-------          
           ########################----------        
          ########################------------       
         ----####################--------------      
        -------#################--------------       
        ----------#############--------------- P     
       --------------#########----------------       
       -----------------#####--------------------    
       ------------------------------------------    
       -------------------####-------------------    
        -----------------#########--------------     
        ----------------#############-----------     
         --------------##################------      
          ------------#######################-       
           ----------########################        
             -------#######################          
              -----#######################           
                 -#####################              
                     ##############                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  0.00e+00   1.26e+21   2.18e+21 
  1.26e+21   2.49e+22   1.44e+22 
  2.18e+21   1.44e+22  -2.49e+22 


Details of the solution is found at

http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20150502162307/index.html
	
Regional Moment Tensor (Mwr)
Moment	2.139e+15 N-m
Magnitude	4.15
Depth	8.0 km
Percent DC	80%
Half Duration	–
Catalog	US (us20002avh)
Data Source	US1
Contributor	US1
Nodal Planes
Plane	Strike	Dip	Rake
NP1	213	89	-168
NP2	122	78	-1
Principal Axes
Axis	Value	Plunge	Azimuth
T	2.241	8	347
N	-0.222	78	218
P	-2.020	9	78

        

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

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 -30 o DIST/3.3 +70
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   115    80    -5   4.13 0.6195
WVFGRD96    2.0   115    85     0   4.17 0.6996
WVFGRD96    3.0   120    85     0   4.20 0.7475
WVFGRD96    4.0   120    85     0   4.23 0.7721
WVFGRD96    5.0   120    85     0   4.24 0.7813
WVFGRD96    6.0   120    85     0   4.25 0.7807
WVFGRD96    7.0   120    85     0   4.26 0.7748
WVFGRD96    8.0   120    85     5   4.27 0.7662
WVFGRD96    9.0   120    85     5   4.28 0.7583
WVFGRD96   10.0   120    85     5   4.29 0.7503
WVFGRD96   11.0   300    85     0   4.30 0.7424
WVFGRD96   12.0   300    85     5   4.31 0.7314
WVFGRD96   13.0   300    85     0   4.31 0.7191
WVFGRD96   14.0   300    85     0   4.32 0.7052
WVFGRD96   15.0   300    90     0   4.33 0.6905
WVFGRD96   16.0   120    90     0   4.33 0.6761
WVFGRD96   17.0   300    90     0   4.34 0.6613
WVFGRD96   18.0   120    90     0   4.35 0.6452
WVFGRD96   19.0   120    90     5   4.36 0.6290
WVFGRD96   20.0   120    85     5   4.36 0.6145
WVFGRD96   21.0   120    90     5   4.37 0.5997
WVFGRD96   22.0   120    85     5   4.37 0.5854
WVFGRD96   23.0   300    90     0   4.38 0.5723
WVFGRD96   24.0   300    90     0   4.38 0.5618
WVFGRD96   25.0   120    85     0   4.39 0.5535
WVFGRD96   26.0   120    85     0   4.39 0.5447
WVFGRD96   27.0   120    85    -5   4.40 0.5383
WVFGRD96   28.0   120    85    -5   4.40 0.5335
WVFGRD96   29.0   120    85    -5   4.41 0.5282

The best solution is

WVFGRD96    5.0   120    85     0   4.24 0.7813

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 -30 o DIST/3.3 +70
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.

Surface-Wave Focal Mechanism

The following figure shows the stations used in the grid search for the best focal mechanism to fit the surface-wave spectral amplitudes of the Love and Rayleigh waves.
Location of broadband stations used to obtain focal mechanism from surface-wave spectral amplitudes

The surface-wave determined focal mechanism is shown here.


  NODAL PLANES 

  
  STK=      24.56
  DIP=      85.02
 RAKE=     174.98
  
             OR
  
  STK=     114.99
  DIP=      85.00
 RAKE=       5.00
 
 
DEPTH = 7.0 km
 
Mw = 4.31
Best Fit 0.8634 - P-T axis plot gives solutions with FIT greater than FIT90

First motion data

The P-wave first motion data for focal mechanism studies are as follow:

Sta Az    Dist   First motion

Surface-wave analysis

Surface wave analysis was performed using codes from Computer Programs in Seismology, specifically the multiple filter analysis program do_mft and the surface-wave radiation pattern search program srfgrd96.

Data preparation

Digital data were collected, instrument response removed and traces converted to Z, R an T components. Multiple filter analysis was applied to the Z and T traces to obtain the Rayleigh- and Love-wave spectral amplitudes, respectively. These were input to the search program which examined all depths between 1 and 25 km and all possible mechanisms.
Best mechanism fit as a function of depth. The preferred depth is given above. Lower hemisphere projection

Pressure-tension axis trends. Since the surface-wave spectra search does not distinguish between P and T axes and since there is a 180 ambiguity in strike, all possible P and T axes are plotted. First motion data and waveforms will be used to select the preferred mechanism. The purpose of this plot is to provide an idea of the possible range of solutions. The P and T-axes for all mechanisms with goodness of fit greater than 0.9 FITMAX (above) are plotted here.


Focal mechanism sensitivity at the preferred depth. The red color indicates a very good fit to the Love and Rayleigh wave radiation patterns. 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. Because of the symmetry of the spectral amplitude rediation patterns, only strikes from 0-180 degrees are sampled.

Love-wave radiation patterns

Rayleigh-wave radiation patterns

Broadband station distribution

The distribution of broadband stations with azimuth and distance is
Listing of broadband stations used

Waveform comparison for this mechanism

Since the analysis of the surface-wave radiation patterns uses only spectral amplitudes and because the surfave-wave radiation patterns have a 180 degree symmetry, each surface-wave solution consists of four possible focal mechanisms corresponding to the interchange of the P- and T-axes and a roation of the mechanism by 180 degrees. To select one mechanism, P-wave first motion can be used. This was not possible in this case because all the P-wave first motions were emergent ( a feature of the P-wave wave takeoff angle, the station location and the mechanism). The other way to select among the mechanisms is to compute forward synthetics and compare the observed and predicted waveforms.

The fits to the waveforms with the given mechanism are show below:

This figure shows the fit to the three components of motion (Z - vertical, R-radial and T - transverse). For each station and component, the observed traces is shown in red and the model predicted trace in blue. The traces represent filtered ground velocity in units of meters/sec (the peak value is printed adjacent to each trace; each pair of traces to plotted to the same scale to emphasize the difference in levels). Both synthetic and observed traces have been filtered using the SAC 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 0.10 n 3 

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 Bureas of Mines, UC Berkely, Caltech, UC San Diego, Saint Louis University, University of Memphis, Lamont Doherty Earth Observatory, the Iris stations and the Transportable Array of EarthScope.

Appendix A


Spectra fit plots to each station

Velocity Model

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

MODEL.01
CUS Model with Q from simple gamma values
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
  1.0000  5.0000  2.8900  2.5000 0.172E-02 0.387E-02 0.00  0.00  1.00  1.00 
  9.0000  6.1000  3.5200  2.7300 0.160E-02 0.363E-02 0.00  0.00  1.00  1.00 
 10.0000  6.4000  3.7000  2.8200 0.149E-02 0.336E-02 0.00  0.00  1.00  1.00 
 20.0000  6.7000  3.8700  2.9020 0.000E-04 0.000E-04 0.00  0.00  1.00  1.00 
  0.0000  8.1500  4.7000  3.3640 0.194E-02 0.431E-02 0.00  0.00  1.00  1.00 

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 Dec 7 00:03:02 CST 2015