Faulting in vertically inhomogeneous media and its geophysical implications

Seismic data processing in vertically inhomogeneous Tl media

The first and most important step in processing data in transversely isotropic (TI) media for which velocities vary with depth is parameter estimation. The multilayer normal-moveout (NMO) equation for a dipping reflector provides the basis for extending the TI velocity analysis of Alkhalifah and Tsvankin to vertically inhomogeneous media. This NMO equation is based on a root-mean-square (rms) a...

Suspension rheology under oscillatory shear and its geophysical implications

Branching diffusion in inhomogeneous media

We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the super-critical regime, we describe the asymptotics of the number of particles in a given domain. In the sub-critical and critical regimes, we describe the distribut...

Lévy flights in inhomogeneous media.

We investigate the impact of external periodic potentials on superdiffusive random walks known as Lévy flights and show that even strongly superdiffusive transport is substantially affected by the external field. Unlike ordinary random walks, Lévy flights are surprisingly sensitive to the shape of the potential while their asymptotic behavior ceases to depend on the Lévy index mu. Our analysis ...

Localized waves in inhomogeneous media

This review examines the localization of one-dimensional nonlinear waves in an inhomogeneous multiphase medium. Particular attention is devoted to the localization of two types of waves, namely, solitary waves (domains) and switching waves that are the separation boundaries between the corresponding phases (domain walls). The localized state of such waves on both point and slowly-varying (in sp...