Numerical Simulations for Acoustic Reflection Imaging with FDM and FEM

Abstract

Acoustic reflection imaging can be applied to detect fractures or interfaces away from the borehole. Although acoustic reflection imaging tools have been available for nearly a decade, some problems still remain. The most difficult are those involved in extracting reflection waves from dominant borehole mode waves, and imaging a complex geologic body exactly. Numerical forward modeling can help us to understand the wave field for acoustic reflection logging, and to verifying the data processing algorithms. In this paper, we report developments in the finite difference method (FDM) and finite element method (FEM) programs to acoustic reflection imaging cases. In particular, the FEM program is employed first to simulate a formation interface and then a fluid-filled fracture outside the fluid-filled borehole model. The FDM is applied in conjunction with an equivalent medium method to simulate the response of fractures outside a borehole. Our results demonstrate that the equivalent medium method can be utilized with the FDM to simulate a fractured formation model effectively. Although the FEM can simulate the reflection logging more accurately, the associated increased computational costs must be justified. For simple models such as linear fractures and interfaces, the FDM may produce a sufficiently accurate result.