Relation Between Level Set and Truncated Pluri-Gaussian Methodologies for Facies Representation

Abstract

Truncated Gaussian/pluri-Gaussian representations and level set representations are two methodologies for implicit representation that can be applied to large-scale subsurface structures. Identification of facies in a petroleum reservoir from dynamic well data is a common field of application for these representation methodologies. No comparison of the methodologies has appeared in the literature to date. The paper seeks to improve on this situation by comparing selected level set and truncated Gaussian/pluri-Gaussian representations in detail. Strong similarities are found, in the sense that every truncated Gaussian/pluri-Gaussian representation considered has a level set counterpart. Furthermore, the transition from a truncated Gaussian/pluri-Gaussian representation to the corresponding level set representation is easily accessible. In addition to the comparison aspect, this paper also introduces a novel level set representation—the hierarchical level set representation—that removes a difficulty present in existing level set representations in a shape estimation setting. It is shown that the hierarchical level set representation corresponds to a well-known truncated pluri-Gaussian representation.