title: A hybrid method for inversion of 3D DC resistivity logging measurements.
abstract: This paper focuses on the application ofhphierarchic genetic strategy (hp-HGS) for solution of a challenging problem, the inversion of 3D direct current (DC) resistivity logging measurements. The problem under consideration has been formulated as the global optimization one, for which the objective function (misfit between computed and reference data) exhibits multiple minima. In this paper, we consider the extension of thehp-HGS strategy, namely we couple thehp-HGS algorithm with a gradient based optimization method for a local search. Forward simulations are performed with a self-adaptivehpfinite element method,hp-FEM. The computational cost of misfit evaluation byhp-FEM depends strongly on the assumed accuracy. This accuracy is adapted to the tree of populations generated by thehp-HGS algorithm, which makes the global phase significantly cheaper. Moreover, tree structure of demes as well as branch reduction and conditional sprouting mechanism reduces the number of expensive local searches up to the number of minima to be recognized. The common (direct and inverse) accuracy control, crucial for thehp-HGS efficiency, has been motivated by precise mathematical considerations. Numerical results demonstrate the suitability of the proposed method for the inversion of 3D DC resistivity logging measurements.
authors: AGH University of Science and Technology, Krakow, Poland.
authors: Ewa
authors: E
authors: Gajda-Zagórska
authors: AGH University of Science and Technology, Krakow, Poland.
authors: Robert
authors: R
authors: Schaefer
authors: AGH University of Science and Technology, Krakow, Poland.
authors: Maciej
authors: M
authors: Smołka
authors: AGH University of Science and Technology, Krakow, Poland.
authors: Maciej
authors: M
authors: Paszyński
authors: BCAM and Ikerbasque, University of the Basque Country UPV/EHU, Bilbao, Spain.
authors: David
authors: D
authors: Pardo
keywords: Hierarchic genetic strategy; Hybrid method; Inverse problem