A 2D kernel determination problem in a visco‐elastic porous medium with a weakly horizontally inhomogeneity

Abstract

We consider a system of hyperbolic integro‐differential equations of SH waves in a visco‐elastic porous medium. In this work, it is assumed that the visco‐elastic porous medium has weakly horizontally inhomogeneity. The direct problem is the initial‐boundary problem: the initial data is equal to zero, and the Neumann‐type boundary condition is specified at the half‐plane boundary and is an impulse function. As additional information, the oscillation mode of the half‐plane line is given. It is assumed that the unknown kernel has the form K ( x , t )= K 0 ( t )+ ϵ x K 1 ( t )+…, where ϵ is a small parameter. In this work, we construct a method for finding K 0 , K 1 up to a correction of the order of O ( ϵ 2 ).

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DOI

10.1002/mma.6544

Citations and references