INTRODUCTION

Two primary goals of seismic reflection processing are: (1) to image geologic structure and (2) to provide information about lithology for interpretation. The process used to achieve the second goal is made complex by the fact that the same seismic velocity may result from several different combinations/mixtures of materials in the earth, i.e., the possible causes of the observed behavior are often nonunique. It is therefore necessary to explore the possible range of seismic velocities that can occur within the set of circumstances deemed most likely to occur in the earth at the site of interest.

Fine horizontal layering (i.e., layers with thickness small compared to the wavelength of the seismic wave) is known to result in vertical transverse isotropy (VTI) - wherein wave speeds vary with propagation angle in such media, but are uniquely determined by the angle from the vertical. There has continued to be some doubt about the range of anisotropy parameters possible in such media. Here we will correct some common errors found in the literature. We show that Thomsen's parameter $\epsilon$ can be negative and actually has a greater negative range than indicated in previous published work. We also show that Thomsen's parameter $\delta$ can be positive in finely layered media (contrary to some erroneous claims that have appeared in the literature), and furthermore that regions having both positive $\delta$ and negative (or small) $\epsilon$ are likely to be regions of rapid spatial variation in fluid content. We use Monte Carlo simulations to establish the existence of both positive $\delta$ and negative $\epsilon$, and analysis of Backus averaging formulas to clarify when such behavior occurs.