2D data modelling by electrical resistivity tomography for complex subsurface geology

Abstract

A B S T R A C TA new tool for two-dimensional apparent-resistivity data modelling and inversion is presented. The study is developed according to the idea that the best way to deal with ill-posedness of geoelectrical inverse problems lies in constructing algorithms which allow a flexible control of the physical and mathematical elements involved in the resolution.The forward problem is solved through a finite-difference algorithm, whose main features are a versatile user-defined discretization of the domain and a new approach to the solution of the inverse Fourier transform.The inversion procedure is based on an iterative smoothness-constrained leastsquares algorithm. As mentioned, the code is constructed to ensure flexibility in resolution. This is first achieved by starting the inversion from an arbitrarily defined model. In our approach, a Jacobian matrix is calculated at each iteration, using a generalization of Cohn's network sensitivity theorem. Another versatile feature is the issue of introducing a priori information about the solution. Regions of the domain can be constrained to vary between two limits (the lower and upper bounds) by using inequality constraints. A second possibility is to include the starting model in the objective function used to determine an improved estimate of the unknown parameters and to constrain the solution to the above model. Furthermore, the possibility either of defining a discretization of the domain that exactly fits the underground structures or of refining the mesh of the grid certainly leads to more accurate solutions. Control on the mathematical elements in the inversion algorithm is also allowed. The smoothness matrix can be modified in order to penalize roughness in any one direction. An empirical way of assigning the regularization parameter (damping) is defined, but the user can also decide to assign it manually at each iteration.An appropriate tool was constructed with the purpose of handling the inversion results, for example to correct reconstructed models and to check the effects of such changes on the calculated apparent resistivity.Tests on synthetic and real data, in particular in handling indeterminate cases, show that the flexible approach is a good way to build a detailed picture of the prospected area. *

Estimation of glacier thicknesses and basal properties using the horizontal-to-vertical component spectral ratio (HVSR) technique from passive seismic data

“…The adopted ERT algorithm uses a smoothness-constrained approach under the Occam assumptions (e.g. Cardarelli and Fischanger, 2006) with a careful reweighting of the inversion parameters (Morelli and LaBrecque, 1996). The resulting inversion misfit was <5% for the majority of the data points, providing fully-interpretable results.…”

Evaluation of the layering of rock strata and basement rock depth of a university teaching hospital premises in northern Nigeria

“…In cases where resistivity contrast is gradual, smooth inversion is more suitable, while when there is a sharp variation in resistivity contrast, block inversion is preferable (Cardarelli and Fischanger, 2006). Interpreting the resistivity data consists of two steps: a physical interpretation of the measured data, resulting in a physical model, and a geological interpretation of the resulting physical parameters (Barker, 2001;Batayneh, 2006;Dahlin, 1996;Griffiths and Barker, 1993;Hassan, et al, 1991;Loke andBarker, 1996 andGriffiths et al, 1990).…”

The use of reference models from a priori data to guide 2D inversion of electrical resistivity tomography data

“…The initial models are simple layered models, with boundaries derived from borehole logs and ground penetrating radar data, and resistivities from preliminary inversions of the ERT data using the apparent resistivity pseudosections as initial models. Cardarelli and Fischanger (2006) demonstrate that for an ERT survey over a tomb, inversion using structured reference models based on a priori data produces a good solution model. In this case, the reference model is based on prior knowledge of the typical shape of the type of tomb being surveyed.…”