algorithm.txt

Basic (single window) algorithm.

- Read in input traces
- window input traces
- generate Hilbert transform of traces (using FFT and IFFT)
- loop over fast-direction -90 -> 90
      - rotate real traces to fast-slow reference frame
      - rotate Hilbert traces to fast-slow reference frame
      - loop over time-lags
            - time-lag real and Hilbert traces 1/2 dt
            - if required, apply ScS correction
                  - calculate the reflection matrix in the F-S ref. frame
                  - corrected traces are the sum of the real traces
                      multiplied by the real part of the R' matrix and  
                      the Hilbert traces multiplied by the imaginary part
                      part of the R' matrix 
            - time-lag corrected traces by remaining dt
            - calculate either second eigenvalue of the covariance matrix or                     transverse energy (requires source polarisation) for current 
                dt, phi
      - end time-lag loop
- end fast-direction loop
- interpolate error grid in the time-lag direction
- normalise interpolated error grid, use 95% confidence interval to determine
    error estimate in phi and delta-t
- determine dt and phi corresponding to minimum L2 or TE
- resample traces to be equal to error grid interpolation
- generate Hilbert transform of interpolated traces
- rotate real and Hilbert interpolated traces to best phi
- time-lag real and Hilbert interpolated traces 1/2 best dt
- if required, apply ScS correction as before
- time-lag corrected traces second 1/2 best dt
- generate covariance matrix of corrected traces, use to determine source            polarisation