Estimation of Thomsen Anisotropy Parameters Using the P-wave Velocities on a Cylindrical Shale Sample

Abstract

In this paper we present a new approach to the estimation of Thomsen anisotropy parameters from laboratory data on cylindrical rock samples. Using tomography-style transducers array, ultrasonic P-wave ray velocities are measured on a transversely isotropic shale sample. This approach is applied to core samples cut along and normal to the bedding plane. Synthetic and actual laboratory data from an anisotropic shale specimen are used as examples. The fast simulated re-annealing method is used to search for the anisotropy parameters.

Estimation of anisotropy parameters using the P‐wave velocities on a cylindrical shale sample

“…The derivatives of the ray velocity with respect to the model parameters and the ray parameter can be derived from the equations 1-3. In contrary to our previous approach to compute the dp dm (Nadri et al, 2011), where we used the derivatives of source-receiver offset with respect to either model parameters in a constant ray parameter or ray parameter which requires z Δ ˗the difference in source-receiver locations along the z axis and will be zero if they are in the same level˗, here we take the derivatives with respect to cosine of azimuth ( ϕ ) which can be easily derived from equation 4. The connection of azimuth ( ϕ ) with both model parameters and ray parameter come through the ray angle ( ψ ) in equation 5.…”