The part is main body of Back-projection.

After preprocessing in a low frequency band, waveforms have been aligned preliminarily. Next we start to cross correlate with a higher frequency band and stack waveforms for all grid points.

set cl            = 2        # upper bound of low frequency band
set ch            = 0.5      # lower bound of low frequency band

$ csh back-projection_2.csh

# open back-projection_2.csh to look over all commands

Duplicate

Duplicate results from preprocessing in low frequency band. We repeat some steps in last chapter, and read station correction information by lower frequency saved in file cc30_raw.out.

# open stack_Tshift_raw-EU.f to look over full commands

open (11, file='cc30_raw.out')
  n_temp=0
  do
     read(11,'(i8,a3,a4)',iostat=iostat) cc_time_shift(n_temp+1),
   &net,stanm_cc(n_temp+1);if (iostat.ne.0) exit
     write(*,*)cc_time_shift(n_temp+1),
   &stanm_cc(n_temp+1)
 n_temp=n_temp+1     
  end do  
close(11)

Cross correlate 1st

Cross correlate with model station’s waveform with high frequency band. Usually, we cross correlate using a long window and remove data with low cross-correlation, then cross correlate using a shorter window.

Here are parameters:

# open back-projection_2.csh to look over all commands

set window_length_L = 40       # length of long window for cross correlation
set lag_lenth_L     = 5        # lenth of time shift
set cc_min_L        = 0.02     # minimum of cross-correlation to eliminate bad data

set window_length = 10       # length of window for cross correlation
set lag_lenth     = 10       # lenth of time shift
set cc_min        = 0.4      # minimum of cross-correlation to eliminate bad dat

Form model seismogram

Sum waveforms to form the model seismogram. Heretofore, model seismogram we talked about is from model staion. But from now, we get model waveform by average all good-quality waveforms.

Seismogram from model station (above), and synthetic model seismgram (below).

# Open stack_Tshift_raw-EU.f to view details

Cross correlate 2nd

Cross correlate with model seismogram following before steps three times.

# Open stack_Tshift_raw-EU.f to view details

Stack seismogram

We have eliminated heterogeneous effect beneath stations by shifting waveforms depend on the first grid (epicenter). For other grid points, we need to cancel out influnce of various epicentral distances, and stack seismograms for a time window.

Here are some parameters for stacking:

# open back-projection_2.csh to look over all commands

set wlen          = 10       # length of window for stacking windows
set wdif          = 2.0      # interval of stacking windows
set nwin          = 100      # number of stacking windows 

# Open stack_Tshift_raw-EU.f to view details