Prestack seismic amplitude analysis: An integrated overview

In this tutorial, I present an overview of the techniques that are in use for prestack seismic amplitude analysis, current and historical. I show that these techniques can be classified as being based on the computation and analysis of either some type of seismic reflection coefficient series or seismic impedance. Those techniques that are based on the seismic reflection coefficient series, or seismic reflectivity for short, are called amplitude variation with offset methods, and those that are based on the seismic impedance are referred to as prestack amplitude inversion methods. Seismic reflectivity methods include: near and far trace stacking, intercept versus gradient analysis, and the fluid factor analysis. Seismic impedance methods include: independent and simultaneous P and S-impedance inversion, lambda-mu-rho analysis, Poisson impedance inversion, elastic impedance, and extended elastic impedance inversion. The objective of this tutorial is thus to make sense of all of these methods and show how they are interrelated. The techniques will be illustrated using a 2D seismic example over a gas sand reservoir from Alberta. Although I will largely focus on isotropic methods, the last part of the tutorial will extend the analysis to anisotropic reservoirs. Introduction The amplitude variation with offset (AVO) and prestack inversion techniques have grown to include a multitude of subtechniques, each with their own assumptions. In this tutorial, I make the assumption that AVO techniques are based on the computation and analysis of some type of seismic reflection coefficient series, or reflectivity for short, and that prestack inversion techniques are based on the computation and analysis of some type of seismic impedance. To understand the distinction between impedance and reflectivity, refer to Figure 1, which shows the different ways in which geologists and geophysicists look at their data. As shown on the left side of Figure 1, the goal of all geoscientists is to understand the subsurface of the earth, which consists of a series of layers of variable structure, lithology, porosity, and fluid content. To do this, the geologist generally analyzes borehole well log measurements of some layer parameter P, whereas the geophysicist, when using exploration seismology, analyzes changes in this layer parameter at the interfaces between successive layers, called the reflectivity (R). The fundamental idea in this tutorial is that there is a relationship between P and R, and it can be written RPi 1⁄4 Piþ1 − Pi Piþ1 þ Pi 1⁄4 ΔPi 2P̄i ; (1) where ΔPi 1⁄4 Piþ1 − Pi; P̄i 1⁄4 Piþ1þPi 2 and subscript i refers to the ith layer. That is, the reflectivity is found by dividing the change in the parameter between two successive layers by twice its average value. The subscript P in the reflectivity RP indicates that the reflectivity is associated with parameter P. I will use this notation throughout the tutorial. This is, of course, an oversimplification, because the seismic trace also contains the source wavelet, amplitude scaling effects, noise contamination due to random noise and coherent noise such as multiples, static time shifts due to topography and near-surface weathering, spatial mispositioning due to structure and subsurface scattering at depth, and so on. A complete discussion of these effects and the techniques of seismic processing which have been developed to remove or ameliorate them is beyond the scope of this tutorial. Even if our processing is extremely good, we are always left with a band-limited reflectivity which can be modeled using the convolutional model, written in matrix form as 2 666666664 W 0 0 · · · 0 .. . W0 . . . .. .