Through the multiresolution decomposition and compression of operator matrix and seismic wave field matrix, we proposed a new method of seismic modeling in wavelet domain.

In this paper, several existence and uniqueness theorems of solutions are proved for the system of nonlinear random operator equations with stochastic domain by using general random contraction.

The dielectric property of dispersive media is written as rational polynomial function, the relation between D and E is derived in time domain. It is named shift operator FDTD (SO-FDTD) method.