New parallel stochastic global integral and local differential equation modeling and inversion

In this paper, a new parallel modeling and inversion algorithm using a Stoc hastic Global Integral and Local Differential equation (SGILD) decompositio n is presented. We derived new acoustic integral equations and differential equations for statistical moments of the parameters and field. The:new sta tistical moment integral equations on the boundary and local differential e quations in domain will be used together to obtain mean wave field and its moments in the modeling. The new moment global Jacobian volume integral equ ations and the local Jacobian differential equations in domain will be used together to update the mean parameters and their moments in the inversion. A new parallel multiple hierarchy substructure direct algorithm or direct- iteration hybrid algorithm will be used to solve the sparse matrices and on e smaller full matrix from domain to the boundary, in parallel. The SGILD m odeling and imaging algorithm has many advantages over the conventional ima ging approaches. The SGILD algorithm can be used for the stochastic acousti c, electromagnetic, and flow modeling and inversion. (C) 1999 Elsevier Scie nce B.V. All rights reserved.