Modeling Conditional Distributions of Facies from Seismic Using Neural Nets

We present a general, flexible, and fast neural network approach to the modeling of a conditional distribution of a discrete random variable, given a continuous or discrete random vector. Although many more applications of the neural net technique could be envisioned, the aim is to apply the developed methodology to the integration of seismic data into reservoir models. Many geostatistical methods for integrating seismic data rely on a screening assumption of further away seismic events by the colocated seismic datum. Such assumption makes the task of modeling cross-covariances and local conditional distributions much easier. In many cases, however, the seismic data exhibit distinct and locally varying spatial patterns of continuity related to geological events such as channels, shale bodies, or fractures. The previous screening assumption prevents recognizing and hence utilizing these patterns of seismic data. In this paper we propose to relate seismic data to facies or petrophysical properties through a colocated window of seismic information instead of the single colocated seismic datum. The variation of seismic data from one window to another is accounted for. Several examples demonstrate that using such a window improves the predictive power of seismic data.