Reflection characteristics of thin-beds with aligned fractures

Abstract

Fractures are ubiquitous in rock and therefore considerably affect the overall mechanical properties of rock. In this study, effective medium theory is used to analyze the reflection characteristics of elastic waves in thin-beds containing aligned fractures. First, elastic parameters are obtained for a single thin bed containing discrete vertical fractures. Then, an exact solution is derived for the reflection coefficient of elastic waves in horizontally transverse isotropic (HTI) thin-beds using the propagation matrix method. Next, the effects of the fracture density and fillings on the reflection pattern are analyzed. Thin-beds without fractures are equivalent to a vertically transverse isotropic (VTI) medium in the long-wavelength limit. The introduction of vertical fractures makes thin-beds equivalent to a single thin bed in an orthorhombic anisotropic (ORT) medium (where the thickness of ORT thin bed is the total thickness of the original thin-beds). The ORT model of fractured thin-beds is presented by the equivalent medium theory. The results obtained using the HTI thin-beds and ORT models are compared, and the influences of the ORT model accuracy and formation parameters (such as thickness-to-wavelength ratio of a single thin bed, total thickness of thin-beds, etc.) on the ORT approximation results are analyzed. The response characteristics of elastic waves in complex thin-beds with fractures determined in this study can give an important guidance to real applications in geophysics and rock mechanics.