Forward and Inverse NMO

The algorithm for both forward and inverse NMO with the non-stationary all-pass filtering approach is the following:

1.

Compute the maximum and minimum NMO correction required in the data according to the offsets, reflection times and velocities.

2.

Use the previous information to precompute all the NMO time shifts in the frequency domain by application of an all-pass non-stationary linear phase filter.

3.

Take the inverse Fourier transform to get the precomputed impulse responses in time domain.

4.

For each trace, form the impulse response matrix selecting from the precomputed ones those required according to the NMO shifts appropriate to that trace.

5.

Carry out the filtering by multiplying the trace by the the impulse response matrix.