Geological Objects and Physical Parameter Fields in the Subsurface: A Review

Guillaume Caumon

doi:10.1007/978-3-319-78999-6_28

Abstract

Geologists and geophysicists often approach the study of the Earth using different and complementary perspectives. To simplify, geologists like to define and study objects and make hypotheses about their origin, whereas geophysicists often see the earth as a large, mostly unknown multivariate parameter field controlling complex physical processes. This chapter discusses some strategies to combine both approaches. In particular, I review some practical and theoretical frameworks associating petrophysical heterogeneities to the geometry and the history of geological objects. These frameworks open interesting perspectives to define prior parameter space in geophysical inverse problems, which can be consequential in under-constrained cases.

Highlights

It aims at complementing the existing reviews and discussions of Linde et al (2015) and Jessell et al (2014), who address this problem with similar objectives but different perspectives
The orientation of heterogeneities within a geological object depends on the object geometry
Links exist between the random field and object-based frameworks in cases where the canonical random field theory is applicable

Summary

28.1 Introduction

The earth is three-dimensional, heterogeneous and, for its major part, inaccessible to direct observations. A recurrent challenge for geoscientists and engineers is, to predict the likely nature or behavior of the subsurface from limited data. In all fields of geophysics sensu lato, these forecasts may use physically and mathematically-based data processing (such as upward continuation of potential fields, seismic processing, classical processing of ground penetrating radar (Nobakht et al 2013), reservoir production decline curves (Davis and Annan 1989; Fetkovich 1980, Fig. 28.1a), or the resolution of an inverse problem that explicitly uses physical models computing observations from some earth parameters and physical parameters (Fig. 28.1b–d, f–h). Forecasts (e.g., about the location and volume of a specific formation or resource) and geological scenarios involve direct.

Caumon

28.2 Motivations for Explicit Geological Parameterizations

28.3 Parameterizations for Physical Models

28.4 Geological Parameterizations

28.4.1 Spatial Random Fields

28.4.2 Object Models

28.5 Conclusions and Challenges