In this papert we discuss the inverse problem of 1-dimensional acoustic wave equation and propose an approximate inversion method, called multi-reflection elimination method, with which the approximate reflectivity fu...
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In this papert we discuss the inverse problem of 1-dimensional acoustic wave equation and propose an approximate inversion method, called multi-reflection elimination method, with which the approximate reflectivity function can be directly obtained by applying a certain transform to the response. The computation efforts for such method is only of the order N log N, much less than that of solving the direct problem, which is O(N2). On the basis of the proposed method, we also construct an iterative algorithm, and prove that the convergent order of iteration is two.
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