Waveform filtering for moment tensor inversion

Introduction

The purpose of this display is to show the effect of a rejection filter on the processing. I consider events for which moment tensors have been obtained. I compare the ground velocities bandpass fitlered in the 0.02 - 0.10 Hz band on the left to those filtered with a rejection filter. Thue purpose of the filtering is to provide a simple waveform for inversion. At times the regional signal is affected by microseisms with frequency of about 0.16 Hz or by teleseismic surface waves with frequency of about 0.05 Hz. Coherent noise is typically a problem with small events. The reason that we want a simple waveform for the inversion is avoid the time shift operation of the inversion code latching onto the wrong peak.

We consider the following earthquakes:

Earthquake of 20070806055945 Example of microseism rejection that also overcomes inadequacies of velocity model
Earthquake of 20070818131630 Example of teleseism surface wave rejection
Earthquake of 20090501013358 Example of microseism rejection that isolates pulse-like signal

In this comparison I use a standard time window of 10 seconds before predicted/observed P and 150 seconds after. In the actual inversion this window was mad much shorter to degradation of the goodness of fit parameter because of the post-signal noise.

Earthquake of 20070806055945

The processing of the Nevada event is found at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20070806055945/index.html

 SLU Moment Tensor Solution
 2007/08/06 05:59:45 37.811 -114.433 5.0 4.1 Nevada
 
 Best Fitting Double Couple
    Mo = 8.04e+21 dyne-cm
    Mw = 3.87 
    Z  = 8 km
     Plane   Strike  Dip  Rake
      NP1       14    82   145
      NP2      110    55    10
 Principal Axes:
   Axis    Value   Plunge  Azimuth
     T   8.04e+21     30     326
     N   0.00e+00     54     183
     P  -8.04e+21     18      67



 Moment Tensor: (dyne-cm)
    Component  Value
       Mxx     3.01e+21
       Mxy    -5.39e+21
       Mxz     2.00e+21
       Myy    -4.32e+21
       Myz    -4.10e+21
       Mzz     1.31e+21
                                                     
                                                     
                                                     
                                                     
                     ############--                  
                 ################------              
              ###################---------           
             #####   ############----------          
           ####### T ############------------        
          ########   ###########--------------       
         #######################----------   --      
        -#######################---------- P ---     
        -######################-----------   ---     
       ---#####################------------------    
       -----##################-------------------    
       ------#################-------------------    
       --------##############--------------------    
        ----------###########-------------------     
        -------------#######--------------------     
         ----------------###-----------------##      
          -----------------######------#######       
           ----------------##################        
             -------------#################          
              -----------#################           
                 -------###############              
                     --############                  
                                                     
                                                     
                                                     

 Harvard Convention
 Moment Tensor:
      R          T          F
  1.31e+21   2.00e+21   4.10e+21 
  2.00e+21   3.01e+21   5.39e+21 
  4.10e+21   5.39e+21  -4.32e+21

Standard Filter	Microseism Rejection Filter

Filter: hp c 0.01 n 3 lp c 0.10 n 3	Filter: hp c 0.01 n 3 lp c 0.10 n 3 br c 0.12 0.25 n 4 p 2

Earthquake of 20070818131630

The processing of this earthquake is documented at http://www.eas.slu.edu/eqc/eqc_mt/MECH.NA/20070818131630/index.html

 SLU Moment Tensor Solution
 2007/08/18 13:16:30 38.07 -113.31 7.0 3.9 Utah
 
 Best Fitting Double Couple
    Mo = 3.76e+21 dyne-cm
    Mw = 3.65 
    Z  = 9 km
     Plane   Strike  Dip  Rake
      NP1       65    75   -75
      NP2      199    21   -134
 Principal Axes:
   Axis    Value   Plunge  Azimuth
     T   3.76e+21     28     143
     N   0.00e+00     14     241
     P  -3.76e+21     57     355



 Moment Tensor: (dyne-cm)
    Component  Value
       Mxx     7.71e+20
       Mxy    -1.30e+21
       Mxz    -2.96e+21
       Myy     1.04e+21
       Myz     1.10e+21
       Mzz    -1.82e+21
                                                     
                                                     
                                                     
                                                     
                     #######-------                  
                 ######----------------              
              ######----------------------           
             #####-------------------------          
           #####-----------------------------        
          #####-----------   -----------------       
         #####------------ P -----------------#      
        #####-------------   ----------------###     
        ####-------------------------------#####     
       #####----------------------------#########    
       ####---------------------------###########    
       ####------------------------##############    
       ####--------------------##################    
        ###----------------#####################     
        ####----------##########################     
         ###---################################      
          ---#######################   #######       
           ---###################### T ######        
             --#####################   ####          
              --##########################           
                 -#####################              
                     ##############                  
                                                     
                                                     
                                                     

 Harvard Convention
 Moment Tensor:
      R          T          F
 -1.82e+21  -2.96e+21  -1.10e+21 
 -2.96e+21   7.71e+20   1.30e+21 
 -1.10e+21   1.30e+21   1.04e+21

Standard Filter	Teleseismic Surface Wave Rejection

Filter: hp c 0.02 n 3 lp c 0.10 n 3	Filter: hp c 0.05 n 3 lp c 0.15 n 3 br c 0.045 0.055 n 4 p 2

Earthquake of 20090501013358

The solution for this earthquake is to be found at the link http://eqinfo.eas.slu.edu/Earthquake_Center/MECH.NA/20090501013358/index.html

 USGS/SLU Moment Tensor Solution
 ENS  2009/05/01 01:33:58:0  36.85 -104.78   5.0 3.5 New Mexico
 
 Stations used:
   IU.ANMO TA.Q25A TA.R25A TA.S25A TA.T21A TA.T22A TA.T23A 
   TA.T24A TA.T25A TA.U21A TA.U24A TA.U25A TA.U26A TA.V24A 
   TA.V25A TA.W23A TA.W24A TA.X23A TA.X24A TA.X25A TA.X26A 
 
 Filtering commands used:
   hp c 0.02 n 3
   lp c 0.10 n 3
   br c 0.12 0.25 n 4 p 2
 
 Best Fitting Double Couple
  Mo = 6.24e+20 dyne-cm
  Mw = 3.13 
  Z  = 8 km
  Plane   Strike  Dip  Rake
   NP1      185    85    20
   NP2       93    70   175
  Principal Axes:
   Axis    Value   Plunge  Azimuth
    T   6.24e+20     18      51
    N   0.00e+00     69     198
    P  -6.24e+20     10     317

 Moment Tensor: (dyne-cm)
    Component   Value
       Mxx    -1.02e+20
       Mxy     5.78e+20
       Mxz     3.26e+19
       Myy     6.46e+19
       Myz     2.14e+20
       Mzz     3.70e+19
                                                     
                                                     
                                                     
                                                     
                     --------######                  
                 ------------##########              
                 ------------#############           
             - P -----------###############          
           ---   -----------############   ##        
          ------------------############ T ###       
         -------------------############   ####      
        -------------------#####################     
        -------------------#####################     
       --------------------######################    
       #-------------------######################    
       ###-----------------######################    
       ########-----------####################---    
        ###############---############----------     
        ##################----------------------     
         #################---------------------      
          ################--------------------       
           ###############-------------------        
             #############-----------------          
              ############----------------           
                 #########-------------              
                     #####---------                  
                                                     
                                                     
                                                     
 Global CMT Convention Moment Tensor:
      R          T          P
  3.70e+19   3.26e+19  -2.14e+20 
  3.26e+19  -1.02e+20  -5.78e+20 
 -2.14e+20  -5.78e+20   6.46e+19

Standard Filter	Microseism Reject filter

Filter: hp c 0.02 n 3 lp c 0.10 n 3	Filter: hp c 0.02 n 3 lp c 0.10 n 3 br c 0.12 0.25 n 4 p 2