A FAST ALGORITHM FOR THE RECONSTRUCTION OF A LAYERED ACOUSTIC MEDIUM FROM ITS TRANSMISSION RESPONSE

We derive a layer-recursive algorithm for reconstructing an equal-travel-time layered acoustic medium from its transmission response to an impulsive plane wave incident from below. The medium is bounded below by an infinite half-space from which it is probed, and it is bounded above by a free surface at which its transmission response is measured. This problem arises in the nondestructive evaluation of layered composite materials, in which the transmission response is measured. The algorithm is similar in form to the Levinson algorithm, which reconstructs a layered medium from its reflection response; it is closely related to the lattice algorithm for computing the QR factorization of a matrix. We relate the new algorithm to the Levinson, fast Cholesky, and lattice algorithms, all of which are well-known fast algorithms for signal processing.