Electromagnetic induction in a fully 3‐D anisotropic earth

Abstract

The bulk electrical anisotropy of sedimentary formations is a macroscopic phenomenon which can result from the presence of porosity variations, laminated shaly sands, and water saturation. Accounting for its effect on induction log responses is an ongoing research problem for the well‐logging community since these types of sedimentary structures have long been correlated with productive hydrocarbon reservoirs such as the Jurassic Norphlet Sandstone and Permian Rotliegendes Sandstone. Presented here is a staggered‐grid finite‐difference method for simulating electromagnetic (EM) induction in a fully 3‐D anisotropic medium. The electrical conductivity of the formation is represented as a full 3 × 3 tensor whose elements can vary arbitrarily with position throughout the formation. To demonstrate the validity of this approach, finite‐difference results are compared against analytic and quasi‐analytic solutions for tractable 1‐D and 3‐D model geometries. As a final example, we simulate 2C–40 induction tool responses in a crossbedded aeolian sandstone to illustrate the magnitude of the challenge faced by interpreters when electrical anisotropy is neglected.