The equivalent force system of a monopole source in a fluid‐filled open borehole

Abstract

One of the major contributors to the complexity of boundary‐value problems pertaining to theoretical modeling of exploration elastodynamics is the presence of both vertical and horizontal discontinuities. It has been known for a long time that it is sometimes possible to replace certain boundaries by a system of images, provided the extra stresses and displacements induced by these images could indeed mimic the discontinuities caused by the said boundaries (e.g., Ben‐Menahem and Singh, 1981). In this vein, we show that part of the field created by a monopole source acting on the axis of a fluid‐filled open borehole surrounded by a homogeneous and isotropic formation, can be reconstructed with the aid of an equivalent force system (EFS) that mimics the geometrodynamic effects of the borehole. The advantages of the EFS are twofold. In the first place, it simplifies the physical setup and brings many seemingly different problems into a common denominator in a sense that they are reduced to fields of known basic force systems. Second, and this is not less important, much computer time is saved and numerical complexities are avoided.