Time-lapse three-dimensional inversion of complex conductivity data using an active time constrained (ATC) approach - Archive ouverte HAL Access content directly
Journal Articles Geophysical Journal International Year : 2011

Time-lapse three-dimensional inversion of complex conductivity data using an active time constrained (ATC) approach

(1) , (2) , (3) , (4) , (1) , (5)
1
2
3
4
5

Abstract

Induced polarization (more precisely the magnitude and phase of impedance of the subsurface) is measured using a network of electrodes located at the ground surface or in boreholes. This method yields important information related to the distribution of permeability and contaminants in the shallow subsurface. We propose a new time-lapse 3-D modelling and inversion algorithm to image the evolution of complex conductivity over time. We discretize the subsurface using hexahedron cells. Each cell is assigned a complex resistivity or conductivity value. Using the finite-element approach, we model the in-phase and out-of-phase (quadrature) electrical potentials on the 3-D grid, which are then transformed into apparent complex resistivity. Inhomogeneous Dirichlet boundary conditions are used at the boundary of the domain. The calculation of the Jacobian matrix is based on the principles of reciprocity. The goal of time-lapse inversion is to determine the change in the complex resistivity of each cell of the spatial grid as a function of time. Each model along the time axis is called a 'reference space model'. This approach can be simplified into an inverse problem looking for the optimum of several reference space models using the approximation that the material properties vary linearly in time between two subsequent reference models. Regularizations in both space domain and time domain reduce inversion artefacts and improve the stability of the inversion problem. In addition, the use of the time-lapse equations allows the simultaneous inversion of data obtained at different times in just one inversion step (4-D inversion). The advantages of this new inversion algorithm are demonstrated on synthetic time-lapse data resulting from the simulation of a salt tracer test in a heterogeneous random material described by an anisotropic semi-variogram.
Fichier principal
Vignette du fichier
187-1-237.pdf (2.17 Mo) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

insu-00680765 , version 1 (02-03-2021)

Identifiers

Cite

M. Karaoulis, André Revil, D.D. Werkema, B.J. Minsley, W. F. Woodruff, et al.. Time-lapse three-dimensional inversion of complex conductivity data using an active time constrained (ATC) approach. Geophysical Journal International, 2011, 187 (1), pp.237-251. ⟨10.1111/j.1365-246X.2011.05156.x⟩. ⟨insu-00680765⟩
79 View
21 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More