Inversion of IP Logging with Improved Krylov Subspace Methods

Abstract

Induced polarization logging is widely used in deep mineral exploration. The data interpretation requires fast and reliable forward and inversion solutions. We have developed an efficient inversion framework in this paper. The forward problem was solved using a finite element approximation with a recycling Krylov subspace algorithm for the multiple linear systems. Considering the model complexity in 3D modeling of logging, mixed meshes were employed to model borehole geometries. The inverse implementation is based on the GaussNewton and Jacobian-free Krylov techniques. We used a coarse mesh for inversion to reduce the ill-posedness. The formulae for Jacobian-vector and Jacobian-transport-vector products were deduced to avoid the storage of derivative matrices. Model updates were calculated efficiently by an inexact preconditioned conjugate gradient algorithm.

Numerical Simulation of Temperature Field for Bedrock Fracture Groundwater at Zhangzhou Geothermal Field

“…1 clearly shows that it is at the intersection area of the F 2 and F 3 that forms the high temperature center of the field. The groundwater flow and temperature distributions are mainly controlled by F 2 and F 3 fractures and other fractures may slightly influence the water flow but the effect can be ignored [3,6,10,11].…”