Finding the shape of a local heterogeneity by means of a structural inversion with constraints

Abstract

Various aspects of structural inversion are considered. The aim of the inversion is limited to finding the shape of an isolated 2D homogeneous body, although the technique may be generalized to the case of interfaces with steep fragments, faults or overhangs. The unknown parameters are shifts of border points. The shift directions can be normal to the initial heterogeneity configuration or to another contour. Medium properties (seismic velocities, densities, etc.) within the heterogeneity are assumed to be known. The optimal shape is determined iteratively, a quadratic objective function being minimized at each iteration with the conjugate‐gradient method. Special attention is paid to preventing self‐intersections, for which purpose each unknown parameter is forced to lie within a certain predetermined interval. In order to achieve this, the classical conjugate‐gradient method has been modified accordingly. Three numerical examples are considered. These illustrate how the developed technique can be applied to different practical problems. The first example is devoted to monitoring an oil/steam interface by gravity gradiometry measurements. In the second example, a cross‐hole seismic experiment is simulated. It is shown that a structural inversion can restore the configuration of a local body much more accurately than traditional seismic tomography. In the third example, the shape of a salt dome is reconstructed by joint inversion of refracted traveltimes and gravity measurements. This example demonstrates how different kinds of data, used simultaneously in a structural inversion, can complement each other.

Structure‐coupled multiphysics imaging in geophysical sciences

“…An appropriate measure of data misfit is minimized subject to the conditions of structural similarity enforced on the sought physical models (Figure 2). Simultaneous multidimensional inverse modeling or “joint inversion” of multiphysics data with structural constraints (Figure 2) has been shown to lead to models that are in better accord and closer to the true system property distribution [ Haber and Oldenburg , 1997; Zhang and Morgan , 1997; Berge et al , 2000; Ditmar , 2002; Musil et al , 2003; Gallardo and Meju , 2003, 2004, 2007; Meju , 2005; Chen et al , 2006; Linde et al , 2006, 2008; Bedrosian , 2007; Bedrosian et al , 2007; Gallardo 2007a; Hu et al , 2007; Infante et al , 2010]. However, not all physical property distributions in the subsurface will be structurally coincident and some flexibility in model reconstruction may be necessary in some geological environments.…”

Joint two-dimensional cross-gradient imaging of magnetotelluric and seismic traveltime data for structural and lithological classification

“…Berge et al 2000; Tillmann & Stocker 2000; Roecker et al 2004) or predefined structures with exactly coincident borders (e.g. Lines et al 1988; Afnimar et al 2002; Ditmar 2002; Gallardo et al 2005b); however, their usefulness is limited in heterogeneous models. Other approaches have shown that the field of the physical property gradients (or curvature) can characterize the geometrical features of an image and might be used as a linkage for two disparate data sets (Haber & Oldenburg 1997; Droske & Rumpf 2003; Gallardo & Meju 2003; Saunders et al 2005).…”

Lithotype discrimination within a gridded model by inverting gravity data

“…Another example of explicit structural inversion is the study by Ditmar (2002), with the aim of finding the shape of an isolated 2-D body of (known) anomalous density. In this case, the outline of the body is described by connected nodes.…”