Kenkel, Johannes: 2-D Anisotropic Inversion of Frequency-Domain Induced Polarization Data. - Bonn, 2018. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc:
author = {{Johannes Kenkel}},
title = {2-D Anisotropic Inversion of Frequency-Domain Induced Polarization Data},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2018,
month = mar,

note = {Measured data in IP (time or frequency domain) are usually interpreted with inversion algorithms, which may be based on stochastic or iterative schemes for finding an optimal data-associated model of the subsurface. Despite the common presence of anisotropy in nature, for example due to layers and fractures, inversion algorithms in IP are usually constrained to isotropic parameters. To support the motivation for anisotropic inversion in IP, it is presented that its neglect leads to inversion artifacts.
This thesis introduces an anisotropy-extended complex conductivity inversion algorithm. In the course of deriving, the modeling of synthetic data from models with arbitrary distributions of anisotropic complex conductivities and arbitrary electrode positions is depicted. The modeling algorithm is based on the method of finite elements and supports discretized triangular and quadrilateral sub-regions and no-flow (Neumann) and Dirichlet boundaries. The sensitivities with respect to anisotropic complex conductivities - which are required by the iterative inversion algorithm - are presented with a direct application to the modeling algorithm and validated analytically with an adapted Greens function. Various sensitivity patterns are shown with a special focus on reconstructing anisotropy in an inversion algorithm. The essential anisotropic model update function for the iterative inversion is delineated and, in this process, penalty functions constraining the additional anisotropy-related degrees of freedom are presented and implemented. Finally, a synthetic study is executed, addressing and discussing the ability of the new anisotropic inversion algorithm to correctly reconstruct corresponding models from data that was recorded over isotropic and various anisotropic models. This thesis also gives a field demonstration that concludes with a comparison of inverted and in-situ anisotropic conductivities
The results of the presented work show successful and failed inversion scenarios. Unsatisfying inversions particularly appear if the underlying measurement data was recorded solely in one dimension (i.e., along one line), albeit insignificant if at the surface or in a borehole. In the presented examples, successful inversions are based on measured data from two dimensions, e.g. two parallel boreholes with cross-borehole measurements or combined surface and borehole setups with borehole-to-surface measurements and perpendicular electrode lines. The synthetic inversions further reveal that anisotropy support may lead to an improved and more consistent interpretation of measured data. Particularly, the anisotropic inversion has the ability to compute reconstructions with less misfit between measured and modeled data as well as with fewer artifacts. Open questions include the treatment of ambiguity that is added through the introduction of anisotropy in the inversion algorithm (i.e., three complex conductivity valued per model cell instead of one in the isotropic case). The also introduced anisotropy penalty function that is configured manually with potentially subjective criteria should be, in a future step, replaced with a more consistent and automatic mechanism. A further open question is if the anisotropic re-interpretation of already measured data that exhibits strong artifacts and a insufficient model-data misfit in an isotropic inversion (despite good data quality) can improve reconstructions in terms of consistency.
Die gemessene Daten des Messverfahrens Induzierte Polarisation (IP) im Zeit- oder Frequenzbereich werden üblicherweise mit Inversionsalgorithmen interpretiert, die auf stochastischen oder iterativen Ansätzen zum Finden eines optimalen, an die Daten angepassten Modells basieren können. Trotz der häufigen Präsenz von Anisotropie in der Natur, beispielsweise auf Grund von Schichtlagerungen oder Rissstrukturen, sind IP-Inversionsalgorithmen typischerweise auf isotrope Zielparameter beschränkt. Als Motivation für die Verwendung einer anisotropen Inversion in der IP werden die Inversionsartefakte präsentiert, die bei Nichtbeachtung von Anisotropie entstehen.},

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