Wave processes in vertically-inhomogeneous media: a new strategy for a velocity inversion

The authors describe a closed cycle of mathematical modelling of wave propagation processes. The half-space z>0 is assumed to be filled with a vertically-inhomogeneous medium with the wave propagation velocity c(z). A source located on the free surface z=0 causes the wave process U(x,y,z,t), described by the initial boundary value problem for the wave equation. They consider two main problems: (1) Assuming c_*(z) is known for all z, the authors wish to calculate the wave field U(x,y,z,t); (2) If c_*(z) is unknown, they find it using the additional information U(x,y,t)=U(x,y,0,t). In order to solve problem (2) the optimization approach is proposed and verified. Uniqueness and stability of the minimum point of the data misfit functional are proved and convergence of iterative methods for its search is investigated. The search for the minimum point in the domain of space-time frequencies can essentially increase the efficiency of the whole process of finding the velocity c(z).