One of the primary goals of amplitude interpretation is to determine whether a water-saturated rock or a hydrocarbon-saturated rock generated the reflection of interest. In order to accomplish this task, an estimate of the difference in rock properties between the water-saturated and hydrocarbon-saturated states is required. Thus, a few basic relationships of rock physics are necessary. There are both empirical and theoretical relationships between seismic rock properties and elastic constants that will be called upon, as well as wave-propagation models.
The work presented in these notes has drawn heavily from two excellent references. The first is a tutorial article by Castagna et al. (1993): “Rock Physics—The Link Between Rock Properties and AVO Response.” The second is a book for those who want detailed solutions to various rock-property transforms but don’t want to wade through the messy math. The book is written by Mavko et al. (1998): The Rock Physics Handbook—Tools for Seismic Analysis in Porous Media. In addition, the two SEG reprint volumes, Seismic Acoustic Velocities in Reservoir Rocks, compiled by Wang and Nur (1992), provide easy access to classic articles on petrophysics.
Before a theory can be formulated for wave motion in a medium, a relationship between stress and strain is needed. For waves of infinitesimal amplitude, Hooke’s empirical law supplies this relationship. The three most commonly used elastic constants to quantitatively describe the strength of a body are the shear (μ), bulk (K), and Young’s (E) moduli. The cartoon in Fig. 2.A.1 illustrates the hypothetical experiments that measure these elastic constants.