### ASA 124th Meeting New Orleans 1992 October

## 4pUW5. A unified approach to acoustical reflection imaging.

**A. J. Berkhout
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*Lab. of Seismics and Acoust., Delft Univ. of Technol., P.O. Box 5046, 2600
GA Delft, The Netherlands
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A discrete theory is proposed that represents acoustical reflection
measurements in terms of a so-called data matrix. One column of the data matrix
is related to one source position; one row is related to one detector position.
In the proposed theory, the data matrix is expressed in a sequence of matrix
operators. Those operators quantify the physical processes of emission,
downward propagation, reflection, upward propagation, and detection in
inhomogeneous media. The concept of optimum ``illumination'' is introduced.
Using the matrix formulation, it is shown how to design an experiment that is
optimum for a specific target area. The imaging process is formulated in terms
of double inversion: one inversion for the downward propagation operator and
one inversion for the upward propagation operator. It is shown that double
focusing (in emission and in detection) represents an economic version of the
double inversion process. The proposed theory is pre-eminently suited to
discuss imaging technology on a conceptual level.