A unified approach to acoustical reflection imaging. II: The inverse problem

Using the forward matrix model, as derived in part I [A. J. Berkhout, J. Acoust. Soc. Am. 93, xxx(1993)], it is shown that the first and main part of numerical acoustic imaging consists of a wave field extrapolation process by double matrix inversion. Physically, the wave field extrapolation process means that the downward propagation effects and the upward propagation effects are eliminated from the measurements. Next, the reflection information is extracted from the wave field extrapolation result. Optionally, the reflection information is translated to discipline‐oriented material parameters by some data fitting process. Double focusing, i.e., focusing in emission and focusing in detection, is closely related to the above numerical imaging process. Finally, it is shown that imaging of zero‐offset or puls‐echo data can be formulated by single matrix inversion, involving phase shifts only.