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

Abstract

International audienceInduced 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

Geochemical and geophysical responses during the infiltration of fresh water into the contaminated saprolite of the Oak Ridge Integrated Field Research Challenge site, Tennessee

“…As the result, the ditch surrounding the S-3 pond was partially filled with water in its southern portion and meteoritic water infiltrated the perched aquifer (see Figure 2). In this section, we analyze the time-lapse resistivity data collected during this period using a recently developed method, the active time constrained (ATC) approach [see Karaoulis et al, 2011]. This time-lapse inversion is used to see how the infiltration event of fresh water was recorded in the resistivity time series and how the model described in section 3 and validated in section 4 above can be used to interpret these data.…”

“…[45] The inversion of the data was performed by using the code developed by Karaoulis et al [2011] using a Gauss-Newton approach. The errors in the data were estimated in the field by repeating the measurements and estimating their standard deviation.…”

Entropy-Bayesian Inversion of Time-Lapse Tomographic GPR data for Monitoring Dielectric Permittivity and Soil Moisture Variations

“…Such an approach is useful for highlighting changes to a system, but requires a reliable inversion of a background dataset. (Kim, Yi, Park, & Kim, 2009) and (Karaoulis et al, 2011) note that the subsurface can be treated as a space-time model, wherein the system is changing continuously on both space and time axes. The objective function therefore penalizes for changes in space-time.…”

Reservoir characterization based upon the onset of time-lapse amplitude changes

“…For example, there is a long history of time-lapse seismic techniques applied to detect fluid movement, in a variety of contexts from crosswell to surface seismic (Tura and Lumley, 1998;Landro, 2001;Hoversten et al, 2003;Calvert, 2005;Hatchell and Bourne, 2005;Hodgson et al, 2007). More recently, electromagnetic methods have been deployed for timelapse monitoring of fluid flow (Karaoulis et al, 2011). Geodetic methods, which typically involve repeated surveys over time, have also been used to detect fluid-induced ground motion (Rucci et al, 2010).…”