In seismic exploration the ground is illuminated with accoustic or elastic waves in the 5-100 Hz frequency band. The scattered energy is recorded for multiple source and receiver positions. From measurements of the scattered wavefield can be deduced information about properties of the subsurface. The limited bandwidth of the illumination and the lack of low frequencies is a significant constraint on the resolution of the answers obtainable. The earth is often characterised by piecewise smooth regions separated by interfaces at which the elastic properties effectively have jump discontinuities. Knowledge of the properties (especially sound velocities) of the medium and the locations of the interfaces can be used to infer information about potential oil reservoirs in the subsurface. This Faraday Partnership project will consider deterministic models and probabilistic methods, and develop hybrid models.