Discussion and reply: comments on "electromagnetic geophysics: notes from the past and the road ahead"

pre-printThe direct current and electromagnetic methods have been around for almost 180 years and have been applied successfully in mining, petroleum, geotechnical, engineering, environmental, groundwater, and tectonic studies. Over such a long period of time, it is possible to lose track of who the pioneers were that developed the various techniques in current use and who wrote the seminal papers on these techniques. As such, a historical review paper is most welcome and, in the past, there were only few attempts to undertake this task (e.g., Rust, 1938; Ward, 1980; Fountain, 1998)

Induced polarization effect in reservoir rocks and its modeling based on generalized effective-medium theory

One of the major tasks of the petroleum resource-efficient technologies (pREFFIT) is the development and improvement of the methods of exploration for energy resources. This review paper summarizes the results of the research on induced polarization (IP) effect in reservoir rocks conducted by the University of Utah Consortium for Electromagnetic Modeling and Inversion (CEMI) and TechnoImaging. The electrical IP effect in hydrocarbon (HC) bearing reservoir rocks having nonmetallic minerals is usually associated with membrane polarization, which is caused by a variation in the mobility of the ions throughout the rock structure. This mobility is related to the size and shape of the pores filled with electrolyte and the double electrical layers. We have studied the IP response of multiphase porous systems by conducting complex resistivity (CR) frequency-domain IP measurements for two different groups of samples: sands and sandstones containing salt water in pores and those whose unsaturated pores were filled with synthetic oil. We have also studied selected carbonate reservoir formations, typical of some major HC deposits

Cross-well electromagnetic imaging in three dimensions

Journal ArticleIn this paper, we develop a new technique for 3D cross-well electromagnetic tomography, based on an EM borehole survey consisting of a moving vertical magnetic dipole transmitter, located in one or several boreholes, and a tri-axial induction receiver, located in the other boreholes. The method is based on the LQL approximation for forward modelling, which results in a fast inversion scheme. The method incorporates both a smooth regularized inversion, which generates a smooth image of the inverted resistivity, and a focusing regularized inversion, producing a sharp focused image of the geoelectrical target. The practical application of the method to synthetic data demonstrates its ability to recover the resistivity, location, and shape of resistive and conductive rock formations

Quasi-linear series in three-dimensional electromagnetic modeling

Journal ArticleWe have recently introduced a quasi-linear (QL) approximation for the solution of the three-dimension(a3l -D) electromagnetic modeling problem. In this paper we discuss an approach to improving its accuracy by considering the QL approximation so f the higher order. This approach can be considered the natural generalization of the Born series. We use the modified Green's operator with the norm less than I to ensure the convergence of the higher orders QL approximations to the true solution. This new approach produces the converged QL series, which makes it possible to estimate the accuracy of the original QL approximation without direct comparison with the rigorous full integral equation solution. It also opens principally new possibilities for fast and accurate 3-D EM modeling and inversion

Three-dimensional quasi linear electromagnetic inversion

Journal ArticleOne of the most challenging problems of electromagnetic (EM) geophysical methods is developing three-dimension(a3l- D) EM inversion techniques. This problem is of utmost importance in practical applications because of the 3-D nature of the geological structures.T he main difficulties in 3-D inversion are related to (1) limitation so f 3-D forward modeling codes available and (2) ill-posedness of the inversion procedures in general. The multidimensional EM inversion techniques existing today can handle only simple models and typically are very time consuming. We developed a new approach to a rapid 3-D EM inversion. The forward scattering problem is solved using a new quasi linear (QL) approximation of the existing integral equation algorithms developed for various sources of excitation. The QL approximation for forward modeling is based on the assumption that the anomalous field is linearly related to the normal field in the inhomogeneous domain by an electrical reflectivity tensor. We introduce also a modified material property tensor which is linearly proportional to the reflectivity tensor and the complex anomalous conductivity. The QL approximation generates a linear equation with respect to the modified material property tensor. The solution of this equation is called "a quasi-Born inversion". We apply the Tikhonov regularization for the stable solution of this problem. The next step of the inversion includes correction of the results of the quasi Born inversion: after determining a modified material property tensor, we use the electrical reflectivity tensor to evaluate the anomalous conductivity. Thus the developed inversion scheme reduces the original nonlinear inverse problem to a set of linear inverse problems, which is why we call this approach" a QL inversion". Synthetic examples (with and without random noise) of inversion demonstrate that the algorithm for inverting3 -D EM data is fast and stable

Large-scale 3D inversion of marine magnetotelluric data: Case study from the Gemini prospect, Gulf of Mexico

Journal ArticleThree-dimensional magnetotelluric (MT) inversion is an emerging technique for offshore hydrocarbon exploration. We have developed a new approach to the 3D inversion of MT data, based on the integral equation method. The Tikhonov regularization and physical constraint have been used to obtain a stable and reasonable solution of the inverse problem. The method is implemented in a fully parallel computer code. We have applied the developed method and software for the inversion of marine MT data collected by the Scripps Institution of Oceanography (SIO) in the Gemini prospect, Gulf of Mexico. The inversion domain was discretized into 1.6 million cells. It took nine hours to complete 51 iterations on the 832-processor cluster with a final misfit between the observed and predicted data of 6.2%. The inversion results reveal a resistive salt structure, which is confirmed by a comparison with the seismic data. These inversion results demonstrate that resistive geoelectrical structures like salt domes can be mapped with reasonable accuracy using the 3D inversion of marine MTdata

Large-scale 3D inversion of potential field data

Journal ArticleInversion of gravity and/or magnetic data attempts to recover the density and/or magnetic susceptibility distribution in a 3D earth model for subsequent geological interpretation. This is a challenging problem for a number of reasons. First, airborne gravity and magnetic surveys are characterized by very large data volumes. Second, the 3D modelling of data from large-scale surveys is a computationally challenging problem. Third, gravity and magnetic data are finite and noisy and their inversion is ill posed so regularization must be introduced for the recovery of the most geologically plausible solutions from an infinite number of mathematically equivalent solutions. These difficulties and how they can be addressed in terms of large-scale 3D potential field inversion are discussed in this paper. Since potential fields are linear, they lend themselves to full parallelization with near-linear scaling on modern parallel computers. Moreover, we exploit the fact that an instrument?s sensitivity (or footprint) is considerably smaller than the survey area. As multiple footprints superimpose themselves over the same 3D earth model, the sensitivity matrix for the entire earth model is constructed. We use the re-weighted regularized conjugate gradient method for minimizing the objective functional and incorporate a wide variety of regularization options. We demonstrate our approach with the 3D inversion of 1743 line km of FALCON gravity gradiometry and magnetic data acquired over the Timmins district in Ontario, Canada. Our results are shown to be in good agreement with independent interpretations of the same data

Contraction integral equation method in three-dimensional electromagnetic modeling

Journal ArticleThe integral equation method has been proven to be an efficient tool to model threedimensional electromagnetic problems . Owing to the full linear system to be solved, the method has been considered effective only in the case of models consisting of a strongly limited number of cells. However, recent advances in matrix storage and multiplication issues facilitate the modeling of horizontally large structures. Iterative methods are the most feasible techniques for obtaining accurate solutions for such problems. In this paper we demonstrate that the convergence of iterative methods can be improved significantly, if the original integral equation is replaced by an equation based on the modified Green's operator with the norm less or equal to one. That is why we call this technique the Contraction Integral Equation (CIE) method. We demonstrate that application of the modified Green's operator can be treated as a preconditioning of the original problem. We have performed a comparative study of the convergence of different iterative solvers applied to the original and contraction integral equations. The results show that the most effective solvers are the BIGGSTAB, QMRCGSTAB, and CGMRES algorithms, equipped with preconditioning based on the CIE method

Two-dimensional magnetotelluric inversion of blocky geoelectrical structures

Journal ArticleThis paper demonstrates that there are alternative approaches to the magnetotelluric (MT) inverse problem solution based on different types of geoelectrical models. The traditional approach uses smooth models to describe the conductivity distribution in underground formations. In this paper, we present a new approach, based on approximating the geology by models with blocky conductivity structures. We can select one or another class of inverse models by choosing between different stabilizing functionals in the regularization method. The final decision, w hose approach may be used for the specific MT data set, is made on the basis of available geological information. This paper describes a new way of stabilizing two-dimensional MT inversion using a minimum support functional and shows the improvement that it provides over traditional methods for geoelectrical models with blocky structures. The new method is applied to MT data collected for crustal imaging in the Carrizo Plain in California and to MT data collected for mining exploration by INCO Exploration

Rigorous 3D inversion of marine CSEM data based on the integral equation method

Journal ArticleMarine controlled-source electromagnetic (MCSEM) surveys have become an important part of offshore petroleum exploration. However, due to enormous computational difficulties with full 3D inversion, practical interpretation of MCSEM data is still a very challenging problem. We present a new approach to 3D inversion of MCSEM data based on rigorous integral-equation (IE) forward modeling and a new IE representation of the sensitivity (Fréchet derivative matrix) of observed data to variations in sea-bottom conductivity. We develop a new form of the quasi-analytical approximation for models with variable background conductivity (QAVB) and apply this form for more efficient Fréchet derivative calculations. This approach requires just one forward modeling on every iteration of the regularized gradient-type inversion algorithm, which speeds up the computations significantly. We also use a regularized focusing inversion method, which provides a sharp boundary image of the petroleum reservoir. The methodology is tested on a 3D inversion of the synthetic EM data representing a typical MCSEM survey conducted for offshore petroleum exploration