An improved version of the transfer matrix approach is presented for ultrasonic wave interaction in multilayered media. Generalized expressions are obtained for reflection and transmission coefficients in either fluid or solid half-space and problems associated with numerical stability are solved efficiently. The formulation is applicable to longitudinal and shear input waves alike, at arbitrary incidence angles and for any sequence of solid or fluid layers. Also, allowance is made for viscoelastic behavior by means of relaxation functions in the Laplace transform domain. Finally, the response to arbitrary incident pulse shapes and beam profiles is described through application of two-dimensional numerical Laplace inversion.
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Lévesque et al. (1992) studied this question.