Synthesis of an inhomogeneous medium from its acoustic transmission response

In 1968 Claerbout showed that the reflection response of a horizontally layered medium can be synthesized from the autocorrelation of its transmission response. During a workshop on passive imaging methods at the 2002 SEG conference, Claerbout showed that this result can be obtained straightforwardly from the principle of conservation of acoustic power. In this paper I briefly review this derivation and show that the 3D generalization can be obtained along the same lines using a power reciprocity theorem. The resulting expression confirms Claerbout's conjecture that “by crosscorrelating noise traces recorded at two locations on the surface, we can construct the wave field that would be recorded at one of the locations if there was a source at the other.”