Homeomorphic imaging approach — theory and practice

Abstract

Abstract The homeomorphic imaging (HI) approach is a generalization of the common mid-point (CMP) stack to media of arbitrary structures with the following key properties: it collects and enhances useful waves; no knowledge about the velocity structure of the overburden is required for correlation and stacking; and neither the resolution of nor the information about the target objects is degraded by stacking the data. The so-called common reflecting element (CRE) method, which has all three properties, was proposed by Gelchinsky [Gelchinsky, B., 1988. Common reflecting element (CRE) method. Explor. Geophys. 19, 71–75]. However, the CRE method did not only provide a generalization of the CMP method with the key properties; it also has a topological feature that led to the creation of the HI approach. Today, HI can be regarded as a system of methods and schemes for the study of seismic structures that are based on asymptotic wave theory and on fundamental topological ideas. HI is based on a single supposition: it assumes that a target wave exists on the chosen central trace. The next step makes use of the ensemble of all possible wave fronts that can be formed in the vicinity of the central ray corresponding to the chosen central trace. This approach is applicable to a medium of arbitrary structure without the assumption of a seismic model or its parameters.