A numerical simulation of the acoustic and elastic wavefields radiated by a source on a fluid‐filled borehole embedded in a layered medium

Abstract

We present a method of calculation to simulate the propagation of acoustic and elastic waves generated by a borehole source embedded in a layered medium. The method is formulated as a boundary element technique where the Green’s functions are calculated by the discrete wavenumber method. The restrictive assumptions are that the borehole is cylindrical and that its axis runs normal to the layer interfaces. The physics of the method rely on Huygens’s principle that states that a diffracting boundary—the borehole wall in the present case—can be represented as a distribution of secondary sources. The borehole is discretized into small cylindrical elements and each element is represented by three sources: a volume source representing the wavefield diffracted in the fluid and two surface forces that give rise to the elastic wavefield radiated outside the borehole. The strength of each source is obtained by solving the linear system of equations that describes the boundary conditions at the borehole wall. The method is used to generate synthetic acoustic logs and to investigate the wavefield radiated into the formation. The simulations considered display the Stoneley wave reflections at the bed boundaries and show the importance of the diffraction that takes place where the borehole wall intersects the layer interfaces.