Impulse response of density contrast wedge using normal coordinates

The exact impulse response of a point source to a rigid wedge was first derived by Biot and Tolstoy in normal coordinates [I. Tolstoy and C. S. Clay, Ocean Acoustics—Theory and Experiment in Underwater Sound (American Institute of Physics, New York, 1987), Appendix 5]. The solution is compact and includes both reflected and diffracted waves explicitly. Kinney et al. [J. Acoust. Soc. Am. 73, 183–194 (1983)] introduced the solution of free wedge (pressure release), which is similar to the rigid case except sign changes for certain terms. The solutions have been verified in laboratory experiments. However, neither model can be applied directly to many actual cases such as ocean floor, where the ratio of density of the base sediment to that of the water is neither infinite (ridge) nor zero (pressure release). The normal coordinate solution presented here is the impulse response to an isovelocity (c=c′) and density contrast (ρ≠ρ′) wedge. It is an extension to the solution given by Biot and Tolstoy. The eigenvalues νn are functions of the wedge angle and the ratio of the density of two media. For either ρ→0,∞ or ρ′→0,∞, the solution reduces to known exact solutions for ideal wedge. The diffracted part of the solution is not the solution for the ideal wedge (ρ′=0 or ρ′=∞) multiplied by an impedance factor.