Seismic modeling in macroscopic and microscopic domains

In principle, realistic 3D simulations of seismic waves should be feasible by directly modeling the macroscopic equations of physics or alternatively, the underlying microscopic physical processes. Modeling in the macroscopic domain consists of directly solving the assumed differential equation of physics, namely the full wave-equation for general elastic and anelastic rheologies with heterogeneity, anisotropy and attenuation. Its goal is to precisely simulate phenomena such as seismic wave propagation given the rheology of the earth thereby providing the core to interpretive modeling studies and inversion algorithms. Modeling in the microscopic domain is a new field based on simulating the underlying physical processes (e.g. molecular motions or propagation and interaction of small wave-packets). The aim is to simulate the behavior of a rock with complexity at the microscopic scale such as pore fluids, fractures and geometrically complex gain boundaries. Such simulations may provide a better understanding of how the macroscopic rheology relates to the microscopic geological features of interest.