Cross-correlation

Cross-correlation methods

Time domain correlation

• cc_time: only calculate cross-correlation coefficient at the specific time window

Frequncy domain correlation

• cc_freq: Do cross-correlation using FFTW
• correlatec: Call the crscor function in SAC's libsac to do the cross-correlation. Please refer to Chinese SAC Documentation for more details.
• sac_wfcc: This is Lupei Zhu's code downloaded from Introduction to SAC on 2020 Aug. 18.
• PCC2: This is Martin Schimmel's code downloaded from here on 2021 Feb. 22.
• ObsPy: corss_correlation
• SAC: correlate

cc_time

Do correlation in time domain.

Usage:
  cc_time -Ttmark/ts/te [-h] sacifle1 sacfile2

Options:
  -T: tmark/begin time (sec)/end time (sec)
  -h: show usage

Examples:
  cc_time -T1/-3/4 seis1.sac seis2.sac

cc_freq

Do correlation in frequency domain.

Usage:
  cc_freq -Ttmark/ts/te [-Occf] [-Wtaper] [-Acczero]
          [-h] sacfile1 sacfile2

Options:
  -T: tmark/begin time (sec)/end time (sec)
  -O: cross-correlation function file
  -W: taper (0: NO (default); 1: hanning; 2: cos)
  -A: only output cross-correlation at zero lag time (0: YES; 1: NO (default))
  -h: show usage

Examples:
  cc_freq -T1/-3/4 seis1.sac seis2.sac
  cc_freq -T1/-3/4 -A0 seis1.sac seis2.sac
  cc_freq -T1/-3/4 -W1 seis1.sac seis2.sac
  cc_freq -T1/-3/4 -Occf12.sac seis1.sac seis2.sac

correlatec

Do correlation in frequency domain calling crscor.

Usage:
  correlatec -Ttmark/ts/te [-Occf] [-Wtaper] [-Acczero]
             [-h] sacfile1 sacfile2

Options:
  -T: tmark/begin time (sec)/end time (sec)
  -O: cross-correlation function file
  -W: taper (0: NO (default); 1: hanning; 2: cos)
  -A: only output cross-correlation at zero lag time (0: YES; 1: NO (default))
  -h: show usage

Examples:
  correlatec -T1/-3/4 seis1.sac seis2.sac
  correlatec -T1/-3/4 -A0 seis1.sac seis2.sac
  correlatec -T1/-3/4 -W1 seis1.sac seis2.sac
  correlatec -T1/-3/4 -Occf12.sac seis1.sac seis2.sac

Notes

When we do correlation, some pre-processing may have been done, e.g., rmean, rtrend, taper.

$ SAC
$ r seis.sac
$ rmean; rtrend; taper;

Some codes (e.g., cc-time) may just use the RAW data, while some codes (e.g., cc_freq and correlatec) may do some processing in the running, e.g. taper. Therefore, we have to be very careful to explain the difference between different codes if the data preprocessing is a little different. Maybe we should add those pre-processing in the code, so that we can choose whether to use it.

Be careful about reference time between different codes!!! Usually, we use the tmark (-5 -> b; -4 -> e; -3 -> 0; -2 -> a; 0-9 -> T0-9) as the reference time. But some code may add additional shift for some purpose, e.g., sac_wfcc adds tmark to the time shift.