Structurally coupled joint inversion on irregular meshes
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Date
2020
Publication Type
Doctoral Thesis
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Abstract
Geophysical data, measured at the Earth’s surface or in boreholes, are used to image the distribution of geophysical properties in the subsurface of the Earth. The resulting property models are essential to gain information about the Earth’s interior, for example, when exploring for natural resources. In order to transform the measured data into a property model, inversion techniques are deployed. Deterministic inversion problems suffer from non-uniqueness and often produce models with limited resolution. Joint inversion of complementary geophysical data can mitigate non-uniqueness and improve model resolution. Jointly inverting different data sets for different property models requires these models to be linked, which is achieved either through a petrophysical relationship or structural coupling.
The subsurface model is commonly discretized into regularly spaced, rectangular cells and almost all joint inversion algorithms are designed for such regular grids. In this thesis I exclusively work with models that are discretized on irregular triangular and tetrahedral meshes. I develop a new structural joint inversion algorithm suitable for joint inversions on irregular meshes that combines geostatistical regularization and a novel correlation-based approach for calculating cross-gradient coupling operators.
In deterministic inversion approaches, regularization constraints are imposed to find a solution to the non-unique inverse problem. Geostatistical regularization operators, based on a spatial correlation model, are an alternative to standard regularization (damping and smoothing). I show how geostatistical regularization operators are calculated for irregular meshes and how inclusion of prior geological information through these operators can improve inversion results compared to standard smoothing constraints.
In structural joint inversion, cross-gradient operators couple the different property models by promoting structural similarity between them. I present a novel approach for defining these operators on the basis of a correlation model, allowing to impose structural similarity on an actual physical length scale. The developed joint inversion framework is successfully applied to 2D and 3D synthetic data examples as well as 2D field data.
Furthermore, I study cross-gradient fields calculated with differently sized cross-gradient operators and asses their performance in joint inversion. I also demonstrate how these novel operators can be used to jointly invert data from geophysical methods that provide different resolution power.
I conclude that imposing regularization and cross-gradient operators that are based on spatial correlation can improve joint inversion on irregular meshes. These operators provide an elegant way to include prior information into joint inversion. The synthetic studies performed in this thesis reveal that property distributions recovered with the presented joint inversion are close to their true distribution and are an improvement over results obtained from individual inversions of the same data. Joint inversion of field data yielded property models that are in agreement with known geological features. The developments and topics addressed in this thesis shall advance joint inversion, specifically for applications on irregular meshes.
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Examiner : Robertsson, Johan O.A.
Examiner : Doetsch, Joseph
Examiner : Schmelzbach, Cédric
Examiner : Dahlin, Torleif
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ETH Zurich
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Subject
joint inversion; Geophysical inversion; Electrical resistivity tomography (ERT); Geophysics
Organisational unit
03953 - Robertsson, Johan / Robertsson, Johan