Zoeppritz Equations and their Approximations
When an incident P-wave strikes the boundary (or interface) between two media obliquely, the wave is split into reflected and refracted P-wave components and reflected and refracted S-wave components. The reflection and transmission coefficients vary as a function of the angle of incidence (hence, of source-receiver offset) and of the media’s elastic properties, which comprise densities and bulk and shear moduli. The Zoeppritz equations (Chapter 1) give the reflection and transmission coefficients for plane waves, as a function of the angle of incidence and as a function of the three independent elastic parameters on each side of the reflecting interface. If the reflection amplitude is observed as a function of the angle of incidence, the variation of that parameter can be used to make inferences about the elastic parameters.
Figures & Tables
We begin this book with a brief discussion on the basics of seismic-wave propagation as it relates to AVO, and we follow that with the rock-physics foundation for AVO analysis — including the use of Gassmann’s equations and fluid substitution. Then, as food for the inquisitive mind, we present briefly the early seismic observations and how they led to the birth of AVO analysis. Next, we examine the various approximations for the Zoeppritz equations and identify clearly the assumptions and limitations of each approximation. We follow that with a section on the factors that affect seismic amplitudes and a discussion of the processing considerations that are important for AVO analysis. A subsequent section explores the various techniques used in AVO interpretation. Finally, we discuss topics such as the influence of anisotropy in AVO analysis, the use of AVO inversion, estimation of uncertainty in AVO analysis, converted-wave AVO, and the future of the AVO method.