PP-wave reflection coefficient for vertically cracked media: Single set of aligned cracks

TL;DR

This paper analyzes how vertical cracks affect azimuthal amplitude variations of PP-wave reflection coefficients in different media, providing analytical and numerical insights into gas detection in rocks.

Contribution

It introduces a detailed analytical and numerical framework for understanding azimuthal amplitude variations caused by vertical cracks in various media, including gas-bearing rocks.

Findings

Azimuthal variations depend on background stiffness, incidence angle, and crack density.

Characteristic amplitude patterns can indicate gas presence in rocks.

Maximum reflection coefficients occur in specific directions depending on saturation and background properties.

Abstract

The main goal of this paper is to analyse the influence of cracks on the azimuthal variations of amplitude. We restrict our investigation to a single set of vertical, circular, and flat cavities aligned along a horizontal axis. Such cracks are embedded in either isotropic surroundings or transversely isotropic background with a vertical symmetry axis. We employ the effective medium theory to obtain either transversely-isotropic material with a horizontal symmetry axis or an orthotropic medium, respectively. To consider the amplitudes, we focus on a Vavrycuk-Psencik approximation of the PP-wave reflection coefficient. We assume that cracks are situated in one of the halfspaces being in welded contact. Azimuthal variations depend on the background stiffnesses, incidence angle, and crack density parameter. Upon analytical analysis, we indicate which factors (such as background's saturation) cause the reflection coefficient to have maximum absolute value in the direction parallel or perpendicular to cracks. We discuss the irregular cases, where such extreme values appear in the other than the aforementioned directions. Due to the support of numerical simulations, we propose graphic patterns of two-dimensional amplitude variations with azimuth. The patterns consist of a series of shapes that change with the increasing value of the crack density parameter. Schemes appear to differ depending on the incidence angle and the saturation. Finally, we extract these shapes that are characteristic of gas-bearing rocks. They may be treated as gas indicators. We support the findings and verify our patterns using real values of stiffnesses extracted from the sedimentary rocks' samples.