FINITE ELEMENT MODELLING OF BOREHOLE SEISMIC RESPONSES IN LAYERED ANISOTROPIC FORMATIONS AND ITS USE FOR ELASTIC INVERSION

摘要

A method of simulating a borehole acoustic response in an anisotropic formation of the crust of the earth, the method comprising formulating a geometric model of the formation, the geometric model comprising a plurality of layers definable in a cylindrical coordinate system defined by an axial direction normal to each of the layers, a radial direction relative to the axial direction, and a circumferential direction relative to the axial direction; formulating a computational model of wave propagation in the formation, the computational model comprising one or more field variables and a wave equation describing a behaviour of the one or more field variables, wherein the one or more field variables are represented as respective Fourier series expansions of p-periodic harmonics in the circumferential direction, and numerically solving the computational model.