### ASA 124th Meeting New Orleans 1992 October

## 1aPA9. Reciprocity and representation theorems for one-way wave fields in
fluids and solids.

**C. P. A. Wapenaar
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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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An acoustical reflection experiment is intuitively based on (i) downward
wave propagation from the acquisition surface into the medium, (ii) reflection
by inhomogeneities inside the medium, and (iii) upward propagation of the
reflected waves to the acquisition surface. The acoustic and elastodynamic wave
equations do not explicitly account for this intuitive distinction between
downward and upward propagation. These wave equations govern the total wave
field, which may be seen as a superposition of downward propagating and upward
propagating wave fields. For this reason these equations are referred to as the
two-way wave equations and their solutions are called two-way wave fields.
Analogously, the equations that explicitly govern downward and upward
propagation are referred to as the one-way wave equations and their solutions
are called one-way wave fields. In this paper reciprocity and representation
theorems are developed for one-way wave fields. These theorems are the basis
for a systematic discussion of acoustic reflection imaging in inhomogeneous
fluids and in inhomogeneous anisotropic solids.