WAVE PROCESSES IN VERTICALLY-INHOMOGENEOUS MEDIA - A NEW STRATEGY FORA VELOCITY INVERSION

This paper describes a closed cycle of mathematical modelling of wave propagation processes. The half-space z > 0 is assumed to be filled wi th a vertically-inhomogeneous medium with the wave propagation velocit y c(z). A source located on the free surface z = 0 causes the wave pro cess U(x, y, z, t), described by the initial boundary value problem fo r the wave equation. We consider two main problems: (1) Assuming c(z) is known for all z, we wish to calculate the wave field U(x , y, z, t ); (2) If c(z) is unknown, we find it using the additional informatio n U(x, y, t) = U(x, y, 0, t). In order to solve problem (2) the optimi zation approach is proposed and verified. Uniqueness and stability of the minimum point of the data misfit functional are proved and converg ence of iterative methods for its search is investigated. The search f or the minimum point in the domain of space-time frequencies can essen tially increase the efficiency of the whole process of finding the vel ocity c(z).