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Unformatted text preview: Mathematical Geology, Vol. 34, No. 2, February 2002 ( C 2002) Modeling Conditional Distributions of Facies From Seismic Using Neural Nets 1 Jef Caers 2 and Xianlin Ma 2 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 geostatisti- cal 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 chan- nels, 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 sin- gle colocated seismic datum. The variation of seismic data from one window to another is ac- counted for. Several examples demonstrate that using such a window improves the predictive power of seismic data. KEY WORDS: seismic inversion, neural networks, pattern recognition. INTRODUCTION Imaging of the subsurface and 3D modeling of reservoir properties represent a major challenge, given the sparsity of hard information. Wells provide quality information on the vertical variation, but do not provide much insight on how that vertical variation varies laterally. The most prevalent source of lateral variation is seismic data. In geostatistics seismic data is typically viewed as a soft, indirect, or secondary information. To make proper use of such information, many alternative methods 1 Received 10 July 2000; accepted 12 January 2001. 2 Department of Petroleum Engineering, Stanford University, Stanford, California 94305-2220; e-mail: [email protected] 143 0882-8121/02/0200-0143/1 C 2002 International Association for Mathematical Geology 144 Caers and Ma have been proposed: • Use seismic data as a locally varying mean (Deutsch and Journel, 1998) informing the average porosity at any colocated location or as a prior probability for a certain facies to occur. • A Bayesian approach where one models the likelihood of seismic data given hard facies or porosity data. The likelihood is used in either sequen- tial simulation (Doyen and others, 1997) or Markov chain Monte Carlo simulation (Eide, Omre, and Ursin, 1996)....
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