Neural networks and AVO

Abstract

In this tutorial we will discuss how a neural network can solve a simple AVO problem. In doing so, we will shed light on two important questions: Why are some neural networks only able to solve linear problems (but others can solve nonlinear problems) and how can neural networks be trained to do these tasks? The type of neural network that we will use is the multilayer perceptron (MLP), sometimes called the multilayer feed-forward network (MLFN). The AVO problem that we will train the network to address is the recognition of a class 3 anomaly on an AVO attribute plot. As we shall see, training a computer to perform tasks that are simple for a human being (that is, an interpreter) can often be quite difficult. However, if we can train a computer to systematically and objectively interpret an AVO plot, it will be worth the effort. The basic AVO interpretation problem that we will study is differentiating the AVO responses of the two reservoirs in Figure 1. Figure 1a shows a wet sand between two shale layers and Figure 1b a gas sand between the same two shales. The P -wave velocity ( V P ), S -wave velocity ( V S ), and density (ρ) for each layer are shown. We assume that the far angle of incidence is small enough (i.e., approximately 30°) that we can ignore the third term in the Aki-Richards equation and write the reflectivity as a function of angle of incidence (𝛉): \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[ R({\theta}) = {+} B\mathrm{sin}^{2}{\theta}\] \end{document}(1) where A is the AVO intercept and B the AVO gradient. Appendix 1 gives the full expressions for A and B functions of V P , V S , ρ, and angle. Figure 1. Simple geologic models of (a) wet sand between two shale layers and (b) gas sand between the same two shales. Using …