Mark E. Everett

Finite‐element analysis of controlled‐source electromagnetic induction using Coulomb‐gauged potentials

A 3-D finite‐element solution has been used to solve controlled‐source electromagnetic (EM) induction problems in heterogeneous electrically conducting media. The solution is based on a weak formulation of the governing Maxwell equations using Coulomb‐gauged EM potentials. The resulting sparse system of linear algebraic equations is solved efficiently using the quasi‐minimal residual method with simple Jacobi scaling as a preconditioner. The main aspects of this work include the implementation of a 3-D cylindrical mesh generator with high‐quality local mesh refinement and a formulation in terms of secondary EM potentials that eliminates singularities introduced by the source. These new aspects provide quantitative induction‐log interpretation for petroleum exploration applications. Examples are given for 1-D, 2-D, and 3-D problems, and favorable comparisons are presented against other, previously published multidimensional EM induction codes. The method is general and can also be adapted for controlled‐so...

Cyclic fluid flow through a regionally extensive fracture network within the Kodiak accretionary prism

Two types of periodic textures observed in veins from the Kodiak accretionary prism attest to cyclic fluid flow through a regionally extensive fracture network buried at 8-12 km depth : (1) crack-seal microstructures with bands of mica inclusions and (2) collapse microstructures with jagged bands of residue embedded within euhedral crystals of quartz. The difference in texture reflects the closure of cracks : crack-seal microstructures record the complete chemical sealing of the crack after each fracture event, whereas the collapse features record longer fluid-filled periods followed by more rapid draining of fractures. Collapse features consist of pressure solution selvages trapped within veins and in the wall rock adjacent to euhedral growth terminations ; the high concentrations of immobile elements in these selvages indicate that these fractures closed by collapse and penetration of quartz crystals into wall rock. Analysis of chemical composition on either side of four large euhedral growth veins and whole rock analysis of slates across the Kodiak Formation reveal local depletion of silica adjacent to veins but no evidence for long-distance silica transport within the system. Both crack-seal and collapse textures are observed in a regionally extensive vein system that displays a regular geometry, with thin, closely spaced (0.5-3 cm), near-vertical crack-seal veins that connect vertically and laterally with thicker euhedral growth veins arranged in widely spaced (-500 mm) southeast dipping en echelon sets. The mesoscopic distribution and textural variability of the vein network suggests that the development of the vein system involved early nucleation and growth of vertical hydrofractures. As the fracture density increased, arrays of fractures locally provided zones of weakness and southeast dipping brittle-ductile shear zones nucleated. These en echelon cracks remained open and provided small reservoirs of fluid. Textures show that en echelon fractures remain open but periodically grow by upward and downward propagation. Crack tips are then sealed with locally derived silica, and fluid drains back into en echelon fracture arrays. This local fluid movement is punctuated by less frequent events where the system links up over a greater distance, fractured reservoirs become interconnected, and the fluid within reservoirs is drained upward or laterally. Periodic inflation and deflation of en echelon arrays may reflect periodic slip on crosscutting faults and rupture of the seals that separate reservoirs.

Geomagnetic induction in a heterogenous sphere: Azimuthally symmetric test computations and the response of an undulating 660‐km discontinuity

A finite element numerical method is presented for computing electromagnetic induction in a heterogeneous conducting sphere by external source current excitation. The numerical model has applicability in the problem of determining the three-dimensional electrical conductivity structure of Earths mantle. The formulation is in terms of vector and scalar potentials. Boundary value problems are derived for fully three-dimensional (3-D) and azimuthally symmetric geometries. To validate the code, we check against a quasi-analytic solution for an azimuthally symmetric configuration of eccentrically nested spheres and against an integral equation solution for an azimuthally symmetric, buried thin spherical shell model. To illustrate the capability of the code for modeling the electromagnetic response of realistic mantle structural variations, we compute solutions for an azimuthally symmetric electrical model whose lateral heterogeneity corresponds to zonal averages of the topographic relief on the 660-km seismic discontinuity. The latter is derived from differential shear wave travel times. The anomalous responses are small but either spatially correlated or anticorrelated with the relief, depending on the period. The behavior can be reproduced by simple one-dimensional (1-D) modeling. The volumetric heterogeneity associated with recent seismic tomographic models should yield a greater surface anomaly, since electromagnetic data are inherently more sensitive to bulk electrical properties than sharp internal interfaces. The finite element method presented here is general and can account for galvanic, oceanic, and non-P10 source effects. The present implementation does not include these complications, but the code is designed so that they can be added easily. The major obstacle to their inclusion at present is the scarcity of other 3-D solutions to validate our calculated results.

Theoretical Developments in Electromagnetic Induction Geophysics with Selected Applications in the Near Surface

Near-surface applied electromagnetic geophysics is experiencing an explosive period of growth with many innovative techniques and applications presently emergent and others certain to be forthcoming. An attempt is made here to bring together and describe some of the most notable advances. This is a difficult task since papers describing electromagnetic induction methods are widely dispersed throughout the scientific literature. The traditional topics discussed herein include modeling, inversion, heterogeneity, anisotropy, target recognition, logging, and airborne electromagnetics (EM). Several new or emerging techniques are introduced including landmine detection, biogeophysics, interferometry, shallow-water electromagnetics, radiomagnetotellurics, and airborne unexploded ordnance (UXO) discrimination. Representative case histories that illustrate the range of exciting new geoscience that has been enabled by the developing techniques are presented from important application areas such as hydrogeology, contamination, UXO and landmines, soils and agriculture, archeology, and hazards and climate.

3D controlled-source electromagnetic edge-based finite element modeling of conductive and permeable heterogeneities

A new 3D controlled-source electromagnetic finite element (FE) modeling algorithm is presented which is capable of handling local inhomogeneities in the magnetic permeability and electrical conductivity distribution of buried geologic and anthropogenic structures. An ungauged, coupled-potential formulation of the governing electromagnetic vector diffusion and scalar continuity equations is used. The formulation introduces magnetic reluctivity, the inverse of magnetic permeability, to facilitate a separation of secondary and primary potentials. The governing equations are solved using a tetrahedral edge-based FE method. The postprocessing steps to obtain electromagnetic fields are outlined. The code is validated for non-magnetic and permeable conductive structures by comparisons against analytic and previously published numerical solutions. Some limitations of the implementation are explored and directions are proposed for its further development.

3D polarimetric GPR coherency attributes and full-waveform inversion of transmission data for characterizing fractured rock

Ground-penetrating radar (GPR) can detect and describe fractures to help us characterize fractured rock formations. A fracture alters the incident waveform, or wave shape, of a GPR signal through constructive and destructive interference, depending on the aperture, fill, and orientation of the fracture. Because the electromagnetic (EM) waves of GPR are vectorial, features exhibiting strong directionality can change the state of polarization of the incident field. GPR methods that focus on changes in waveform or polarization can improve detection and discrimination of fractures within rock bodies. An algorithm based on coherency, a seismic attribute that delineates discontinuities in wavelet shape, is developed for polarimetric GPR. It uses the largest eigenvalue of the time-domain scattering matrix when calculating coherence. This algorithm is sensitive to wave shape and is unbiased by the polarization of GPR antennas. Polarimetric coherency works better than scalar coherency in removing the effects of polarization on field data collected from a fractured limestone plot used for hydrologic experimentation. Another method, for time-domain full-waveform inversion of transmission data, quantitatively determines fracture aperture and EM properties of fill, based on a thin-layer model. Inversion results from field data show consistency with the location of fractures from reflection data. These two methods offer better fracture-detection capability and quantitative information on fracture aperture, dielectric permittivity, and electrical conductivity of the fill than traditional GPR imaging and scalar-coherency attributes.

3-D finite element analysis of induction logging in a dipping formation mark

Electromagnetic induction (EMI) by a magnetic dipole located above a dipping interface is of relevance to the petroleum well-logging industry. The problem is fully three-dimensional (3-D) when formulated as above, but reduces to an analytically tractable one-dimensional (1-D) problem when cast as a small tilted coil above a horizontal interface. The two problems are related lay a simple coordinate rotation. An examination of the induced eddy currents and the electric charge accumulation at the interface help to explain the inductive and polarization effects commonly observed in induction logs from dipping geological formations. The equivalence between the 1-D and 3-D formulations of the problem enables the validation of a previously published finite element solver for 3-D controlled-source EMI.

Using homotopy to invert geophysical data

Homotopy is a powerful tool for solving nonlinear equations. It is used here to solve small‐dimensional geophysical inverse problems by locating the solutions of the governing normal equations. An Euler‐Newton numerical continuation scheme is used to map trajectories in model space that start from a prescribed solution to a trivial set of equations and terminate at a solution to the inverse problem. The trajectories often map out a continuum of equivalent solutions that are caused by model equivalences or overparameterization. This allows exploration of the solution space topology. The homotopy method, in this application, is relatively insensitive to the choice of starting model. Several examples based on synthetic controlled‐source electromagnetic (CSEM) responses are shown to illustrate the method. An inversion of actual CSEM data from the Canadian Shield is also provided.

Near-Surface Controlled-Source Electromagnetic Induction

The controlled-source electromagnetic (CSEM) induction method is emerging as a leading geophysical technique in hydrogeological studies. However, the technique is quite often misunderstood compared to other common techniques of applied geophysics: namely, seismic reflection and refraction, magnetics, gravity, and ground-penetrating radar (GPR). In this chapter we review the fundamental physical principles behind the CSEM prospecting technique, with emphasis on near-surface applications, and present some recent advances in this field that have been made by the authors. CSEM methods are defined here to be those in which the experimenter has knowledge of and control over the electromagnetic field transmitted into the ground and hence excludes magnetotellurics, related natural-source methods, and the various uncontrolled-source methods involving, for example, radio transmissions.

Geomagnetic induction in eccentrically nested spheres

Abstract We present an analytic solution for a class of multidimensional forward problems of electromagnetic induction in a heterogeneous sphere. A variety of numerical methods for 3-D global electromagnetic modeling have been introduced recently, including this sheet, perturbation expansion, and finite element/finite difference schemes. The present analytic approach provides a model response against which the accuracy of more general numerical algorithms can be tested. We solve the electromagnetic induction problem in an azimuthally symmetric system of two eccentrically nested spheres and compute the surface magnetic vector potential A Φ and polar magnetic field B θ as functions of several of the model parameters.