Multi-Channel Inversion: (A Draft for Thesis Chapter 3)
, by Shuki Ronen
Pre stack partial migration and interpolation of missing data
can be combined into one process,
multi-channel inversion,
based on the wave equation and Fourier analysis of aliasing.
The process has two functions:
(1) Interpolation: finding the model which best fits the aliased data.
(2) Offset extrapolation:
the model is the ideal zero offset section, the data are collected
with finite offset between shot and receiver.
I review the formulation and present results
of multi-channel inversion applied to field data,
using samples from 2-D data to simulate the cross-line direction in 3-D.
A specific design of a 3-D experiment, suitable to multi-channel inversion,
is proposed.
The inversion is done with conjugate-gradient,
an iterative method which in this case converges in few iterations.
The first iteration is equivalent to
DMO-stacking with zero data in place of missing data.
STANFORD