Patent ID: 9557442
Date: 2017-01-31
CPC Classifications: G01V

Claim:
1. A method of predicting properties of an anisotropic formation in the crust of the earth, the formation including a rock formation comprising a plurality of elastically anisotropic layers, the plurality of elastically anisotropic layers of the formation being orthotropic materials being π-periodic in the circumferential direction, the method comprising: receiving acoustic sensor measurements from a sensor system provided in a borehole, the sensor system comprising a transmitter and a receiver and being configured to emit an acoustic signal and receive an acoustic response from the surrounding formation responsive to the emitted acoustic signal; collecting the acoustic sensor measurements as a function of depth of the borehole; formulating, based on the acoustic sensor data, a model geometry of the formation, the model geometry comprising a plurality of elastically anisotropic 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, the elastic anisotropy of each layer of the formation being describable by an orthotropic material law being theta dependent and π-periodic in the circumferential direction, each layer having its own orthotropic velocity characteristics; formulating a computational model of wave propagation in the model geometry of the formation, the computational model comprising one or more field variables, the one or more field variables including a time-dependent displacement field, wherein a wave equation describing wave propagation in the plurality of elastically anisotropic layers and a behaviour of the one or more field variables is described by the time-dependent displacement field, a stiffness matrix and a mass matrix representing the orthotropic elastic properties and the mass of the formation and wherein the one or more field variables are theta dependent and represented as respective coupled Fourier series expansions of π-periodic harmonics in the circumferential direction, the resulting propagating waves or modes derived from the wave equation being likewise coupled; and numerically solving the computational model, to thereby predict one or more physical properties of the formation selected from the list of properties including: a velocity of sound propagation through the formation, a density of the formation, a permeability of the formation, a porosity of the formation, a resistivity of the formation, a permittivity of the formation, and a Young's modulus of the formation.