A comprehensive study of including structural orientation information in geophysical inversions

Abstract

S U M M A R YIn this paper, we investigate options for incorporating structural orientation information into under-determined inversions in a deterministic framework (i.e. minimization of an objective function). The first approach involves a rotation of an orthogonal system of smoothness operators, for which there are some important practical details in the implementation that avoid asymmetric inversion results. The second approach relies on addition of linear constraints into the optimization problem, which is solved using a logarithmic barrier method. A 2-D synthetic example is provided involving a synclinal magnetic structure and we invert two sets of real survey data in 3-D (one gravity data, the other magnetic data). Using those examples, we demonstrate how different types of orientation information can be incorporated into inversions. Incorporating orientation information can yield bodies that have expected aspect ratios and axis orientations. Physical property increase or decrease in particular directions can also be obtained.To be reliable, earth models used for mineral exploration should be consistent with all available geophysical and geological information. Due to data uncertainty and other aspects inherent to the under-determined geophysical inverse problem, there are an infinite number of models that can fit the geophysical data to the desired degree (i.e. the problem is non-unique). Further information is essential for a unique solution. Incorporating prior geological knowledge can reduce ambiguity and enhance inversion results, leading to more reliable earth models.An important form of available geological information is structural orientation. This can involve the orientation of a body (i.e. the strike, dip, and tilt of its major axes), aspect ratios (i.e. the relative lengths of a body's major axes) and physical property trends (i.e. increase, decrease, or constant in a particular direction). The ability to specify such information becomes especially important for survey methods with limited depth resolution. The lack of resolution can lead to recovery of an object with an incorrect or distorted dip and by including orientation information the results can be dramatically improved at depth.Many researchers have provided functionality for incorporating different types of geological information into their particular inversion frameworks. In this paper, we investigate how orientation information can be placed into our deterministic inversion framework in which a computationally well-behaved function is minimized subject to optional constraints. Before introducing our methods we provide an overview of some techniques used by other authors for comparison. Bosch et al. (2001) and Guillen et al. (2008) work in a stochastic inversion framework that directly recovers rock type (i.e. a lithologic inversion) from a list of those assumed present. Prior information is placed into the problem through probability density functions and topology rules (relationships between rock units). The model space (i.e. all p...

Multidomain petrophysically constrained inversion and geology differentiation using guided fuzzy c-means clustering

“…Li and Oldenburg (2000) propose an inversion algorithm that allows geologic dip and strike information to be incorporated into inversions by rotating the local orthogonal coordinate system of smoothness operators for inversion. Lelièvre and Oldenburg (2009) extend this approach so that structural orientation information can be specified pointwise for the entire model domain. Lelièvre (2009) categorizes the geologic information as either located or nonlocated and develops new algorithms for incorporating into geophysical inversions useful geologic information such as physical property values, physical property trend information, and structural orientation information.…”

2D joint inversion of geophysical data using petrophysical clustering and facies deformation

“…The idea of the image-guided inversion proposed by Ma et al (2012) and later by Zhou et al (2014) is to extract the structural information contained in the geologic cross section and to impose this structural information to the model covariance matrix in smoothing in preferential directions at different locations. This approach is, therefore, more general than the classical Tikhonov regularization in which an isotropic and spatially invariant smoothing is applied (or by applying the same smoothing in the vertical and horizontal directions for the entire tomogram; see the discussion in Lelièvre and Farquharson, 2013). We use a part-based representation approach (Lee and Seung, 1999) in which the structural information is neither completely stationary, as in Tikhonov regularization, nor completely nonstationary, as in the image-guided inversion (Zhou et al, 2014).…”

3D stochastic inversion of potential field data using structural geologic constraints

“…In a deterministic framework, Li and Oldenburg (2000) and Lelièvre and Oldenburg (2009) investigated options for incorporating structural orientation data into underdetermined inversions by minimization of an objective function. Barbosa and Silva (2006) introduced a technique in a user-friendly environment for helping forward modeling and testing geological hypotheses.…”