Use of wave modeling and inversion for the interpretation of the characteristics of rocks and geologic formations requires the understanding of the relationship between the seismic attributes and the rock properties. In particular, in the exploration of oil and gas reservoirs, it is important to predict the porosity, the presence of fluids (type and saturation), the preferential directions of fluid flow (anisotropy), the presence of abnormal pore pressures (overpressure), etc. These microstructural properties and the in-situ rock conditions can be obtained, in principle, from the seismic attributes, using realistic constitutive equations.

This lecture briefly outlines the physics and simulation of wave propagation in anisotropic, anelastic, and porous media, including the analogy between acoustic waves (in the general sense) and electromagnetic waves. Most of the numerical techniques have been recently developed; for instance, the solution of the poro-viscoelastic wave equation for reservoir seismics, and the domain-decomposition methods for wave propagation at the ocean bottom.

The applications include evaluation of methane hydrate content, upscaling techniques, detection of overpressure, propagation in permafrost, exploration of the Earth's deep crust, time-lapse sesimics for monitoring of CO2 sequestration, borehole stability, the mesoscopic loss mechanism in rocks, geo-radar applications, and low-frequency electromagnetic prospecting in the Earth. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock physics, and material science — including many branches of acoustics of fluids and solids (acoustics of materials, nondestructive testing, etc.) — may also find the presentation useful.