Genetic algorithm for estimating in-situ rock elastic constants by acoustic reflection records

Abstract

The elastic properties of rocks can be estimated from the density (ρ), acoustic (Vp), and shear (Vs) wave velocities, whose values establish the reflected wave amplitudes. This paper presents an indirect method to estimate rocks` elastic properties, that uses Vp, Vs, and ρ values supplied by the inversion of acoustic reflection records. Because of the non-uniqueness and non-linear nature of the inversion, the solution must be sought in a search space by minimizing a cost function that measures the error between the observed datum and the inferred one. The search may converge to a local minimum, and then the true global minima may not be reached. Genetic algorithms have proven to be more efficient in finding the optimal solution for this type of search space. A genetic algorithm coded in Matlab estimates ρ, Vp, and Vs through the inversion of the equation that relates them to the amplitudes and angles of incidence of the acoustic waves. Lamé elastic constant (λ), Poisson›s ratio (ν), and modulus of elasticity (E), compressibility (K) and rigidity (G) can bedeemed from ρ, Vp and Vs. The algorithm was tested in synthetic data to verify its robustness and stability, and then applied to seismic records showing a good perform in both cases. The presented method has a deeper scope than the refractionmethod, and is applicable to different engineering fields.