New 3D Parallel GILD EM Modeling and Inversion

G. Xie and J. Li, Lawrence Berkeley National Laboratory

Research Objectives

Three-dimensional electromagnetic (EM) forward modeling and inversion algorithms play an important role in geophysical exploration, oil reservoir management, and environmental site characterization. In this project, we seek to develop a new global integral and local differential (GILD) parallel modeling and nonlinear inversion algorithm, designed to overcome the limitations of conventional inversion. The algorithm and developed software are important for coupled high-resolution imaging of field data in all frequency bands and many data configurations.

Computational Approach

The new parallel GILD modeling and inversion method consists of five parts:

1. A domain decomposed into subdomain SI and subdomain SII (Figure 1).
2. A new global boundary magnetic integral equation on the boundary and local magnetic differential equations in domain, to be used together (in the modeling step) to obtain the electromagnetic field.
3. A new global magnetic Jacobian volume integral equation in SI and a local magnetic Jacobian differential equation in SII, to be used together in the inversion step to update the electric conductivity and permittivity from the magnetic field data.
4. Subdomain SII naturally decomposed into 4n smaller subcubic domains; the sparse matrix in each subcubic domain can be inverted separately, in parallel.
5. A new parallel multiple hierarchy substructure direct algorithm, a new parallel multiple hierarchy preconditioned conjugate gradient, or Markov chain Monte Carlo (MCMC) approach, to be used to solve the smaller 2 ( 2 block matrices in SI from domain to the boundary, recursively and in parallel.

Accomplishments

We have developed the new 3D parallel GILD EM modeling and inversion algorithm. A primary 3D GILD inversion code was tested on a Cray T3D and obtained high-resolution imaging from synthetic and field data. Recently we have been developing a 3D GILD EM modeling and inversion code on the NERSC T3E. The current work involves changing PGHPF to MPI, developing a large-scale GILD parallel modeling and inversion code, GILD@T3E, choosing the optimal regularizing operator and parameter, improving the parallel performance, and making 3D EM images from field data. An example of 2.5D GILD high-resolution resistivity imaging is shown in Figure 2.

Significance

We are using the new 3D GILD modeling and inversion to develop a high resolution electromagnetic, seismic, and hydrology-coupled GEO-HYDRO imaging. The new high-resolution imaging software will be an essential tool for DOE projects involving oil, gas, coal, geothermal energy, and geophysical exploration; and environmental restoration of contaminated sites and nuclear waste.

Publications

G. Xie and J. Li, "New 3D nonlinear electromagnetic inversion," in Three Dimensional Electromagnetics (Tulsa, OK: Society of Exploration Geophysicists [SEG], 1998).

G. Xie, J. Li, and E. Majer, "New 3D parallel SGILD modeling and inversion," Berkeley Lab Technical Report LBNL-42252 (1998).

G. Xie, J. Li, E. Majer, and D. Zou, "New 3D parallel GILD electromagnetic modeling and nonlinear inversion using global integral and local differential equation," Berkeley Lab Technical Report LBNL-42105 (1998).