UC Berkeley

The present work analyzes seismic attenuation due to wave-induced flow in complex poroelastic materials containing an arbitrary amount of

heterogeneity and fully or partially saturated with a mixture of fluids.

In the first part, two distinct finite-difference (FDTD) numerical schemes for solving Biot's poroelastic set of equations are introduced. The first

algorithm is designed to be used in the seismic band of frequencies; i.e., when the permeability of the medium doesn't depend on frequency. The

second algorithm accounts for viscous boundary layers that appear in the pores at high frequencies (in this case, the permeability depends on

frequency) and can be used across the entire band of frequencies.

An innovative numerical method is presented in the second part allowing computation of seismic attenuation due to wave-induced flow for any

poroelastic material. This method is applied to study the attenuation associated with different classes of materials saturated with a single

fluid (water). For a material having a self-affine (fractal) distribution of elastic properties, it is demonstrated that frequency

dependence in the attenuation is controlled by a single parameter that is directly related to the fractal dimension of the material. For

anisotropic materials, a relation is established between the attenuation levels associated with waves propagating in different directions and

the geometrical aspect ratio of the heterogeneities present within the material.

The third part concerns the study of attenuation associated with materials having a homogeneous solid skeleton

saturated with a mixture of immiscible fluids. The special case where the distribution of fluids is the result of an invasion-percolation process is

treated in detail.

Finally, the last part presents a novel experimental setup designed to measure fluctuations of the elastic properties in

real rock samples. This device performs automated micro-indentation tests at the surface of rock samples and produces maps of the spatial

distribution of Young's modulus. These maps are then used in combination with the aforementioned numerical methods to compute accurately the

attenuation as a function of frequency associated with real rock samples.