Aj. Berkhout et Cpa. Wapenaar, A UNIFIED APPROACH TO ACOUSTICAL REFLECTION IMAGING .2. THE INVERSE PROBLEM, The Journal of the Acoustical Society of America, 93(4), 1993, pp. 2017-2023
Using the forward matrix model, as derived in part I [A. J. Berkhout,
J. Acoust. Soc. Am. 93, 2005-2016(1993) ], it is shown that the first
and main part of numerical acoustic imaging consists of a wave field e
xtrapolation process by double matrix inversion. Physically, the wave
field extrapolation process means that the downward propagation effect
s and the upward propagation effects are eliminated from the measureme
nts. Next, the reflection information is extracted from the wave field
extrapolation result. Optionally, the reflection information is trans
lated to discipline-oriented material parameters by some data fitting
process. Double focusing, i.e., focusing in emission and focusing in d
etection, is closely related to the above numerical imaging process. F
inally, it is shown that imaging of zero-offset or puls-echo data can
be formulated by single matrix inversion, involving phase shifts only.