Propagation and Attenuation of Elastic Waves in a Double Porosity Medium

This study solves the mathematical model for the propagation of harmonic plane waves in a dissipative double porosity solid saturated by a viscous fluid. The existence of three dilatational waves is explained through three scalar potentials satisfying wave equations. Velocities of these waves are obtained from the roots of a cubic equation. Lone shear wave is identified through a vector potential satisfying a wave equation. The displacements of solid particles are expressed through these four potentials. The displacements of fluid particles in pores and fractures can also be expressed in terms of these potentials. A numerical example is solved to calculate the complex velocities of four waves in a dissipative double porosity solid. Each of the complex velocities is resolved to define the phase velocity and quality factor of attenuation for the corresponding wave. Effects of medium properties and wave frequency are analyzed numerically on the propagation characteristics of four attenuated waves. It seems that and S waves are not very sensitive to the pore/fluids characteristics, except the fracture porosity. Hence, the recovery and analysis of slower ( , ) waves become more desired to understand the fluid-rock dynamism in crustal rocks. 1. Introduction Pores are pervasive in most of the igneous, metamorphic, and sedimentary rocks in the earth’s crust. Traditional approaches to seismic exploration often make use of Biot’s theory of poroelasticity. This theory has always been limited by an explicit assumption that the porosity itself is homogeneous. For acoustic analysis of many rock samples in a laboratory setting, this assumption is known to be adequate. But, in the modeling of real heterogeneous reservoirs, it may not be a realistic assumption. In fact, porosity found in the earth may have many shapes and sizes, but two types of porosity are more important. One is matrix (or storage) porosity that occupies a finite and substantial fraction of the volume of a porous rock. Other is fracture or crack porosity that may occupy very little volume, but fluid flow occurs primarily through the fracture network. However, fluid storage occurs mostly in the porous matrix. This model identified as double porosity model [1, 2] considers a fracture network that divides the porous matrix into different blocks and the fluid in fractures surrounds the disaggregated matrix blocks supported entirely by fluid pressure. In fact, most of the near-surface rock masses are fractured to some degree. It demands to examine the coupled fluid-rock deformation through the double