Interpreting seismic waveforms: forward and inverse problems for heterogeneous media

Much of seismology still relies heavily on ray theory or on phase integral (WKBJ) methods to interpret observed seismograms. These approximations have limited validity in the real Earth. Using a one-way approximation to the Helmholtz equation, I show that the inverse problem for both body waves and surface waves becomes ill-posed at some distance from the source, since phase and group delays satisfy a diffusion equation. This defines theoretical limits for the resolution.