Ray tracing methods for inverse problems

We discuss the origin, use and implementation of ray tracing methods for no nlinear inverse modelling problems associated with wave propagation phenome na. These methods have a long tradition in acoustic and elastodynamic wave propagation problems for Various important applications, and they can surel y be helpful in other realms, including electromagnetic wave propagation an d diffusion dominated phenomena. The subjacent models used for forward simulation have increased in complexi ty and dimension as computer power has enabled us to solve such problems in an acceptable amount of time. Thus, we will devote part of this paper to d iscuss modelling issues and the parallel implementation of algorithms for a pplications in earth sciences.