We review theoretical and numerical studies of the inverse problem of electrical impedance tomography which seeks the electrical conductivity and permittivity inside a body, given simultaneous measurements of electrical currents and potentials at the boundary.

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Electrical impedance tomography

The current state of understanding of the lunar interior is the sum of nearly four decades of work and a range of exploration programs spanning that same time period. Missions of the 1960s including the Rangers, Surveyors, and Lunar Orbiters, as well as Earth-based telescopic studies, laid the groundwork for the Apollo program and provided a basic understanding of the surface, its stratigraphy, and chronology. Through a combination of remote sensing, surface exploration, and sample return, the Apollo missions provided a general picture of the lunar interior and spawned the concept of the lunar magma ocean. In particular, the discovery of anorthite clasts in the returned samples led to the view that a large portion of the Moon was initially molten, and that crystallization of this magma ocean gave rise to mafic cumulates that make up the mantle, and plagioclase flotation cumulates that make up the crust (Smith et al. 1970; Wood et al. 1970). This model is now generally accepted and is the framework that unifies our knowledge of the structure and composition of the Moon. The intention of this chapter is to review the major advances that have been made over the past decade regarding the constitution of the Moon’s interior. Much of this new knowledge is a direct result of data acquired from the successful Clementine and Lunar Prospector missions, as well as the analysis of new lunar meteorites. As will be seen, results from these studies have led to many fundamental amendments to the magma ocean model.

Much of what we know from sample analyses has been previously summarized elsewhere, and only their most important aspects will be discussed in this chapter. The reader is referred to the relevant chapters in the books Basaltic Volcanism on the Terrestrial Planets (Basaltic Volcanism Study Project 1981), The …

The Constitution and Structure of the Lunar Interior

Least-squares inversion of seismic reflection waveform data can reconstruct remarkably detailed models of subsurface structure and take into account essentially any physics of seismic wave propagation that can be modelled. However, the waveform inversion objective has many spurious local minima, hence convergence of descent methods (mandatory because of problem size) to useful Earth models requires accurate initial estimates of long-scale velocity structure. Migration velocity analysis, on the other hand, is capable of correcting substantially erroneous initial estimates of velocity at long scales. Migration velocity analysis is based on prestack depth migration, which is in turn based on linearized acoustic modelling (Born or single-scattering approximation). Two major variants of prestack depth migration, using binning of surface data and Claerbout's survey-sinking concept respectively, are in widespread use. Each type of prestack migration produces an image volume depending on redundant parameters and supplies a condition on the image volume, which expresses consistency between data and velocity model and is hence a basis for velocity analysis. The survey-sinking (depth-oriented) approach to prestack migration is less subject to kinematic artefacts than is the binning-based (surface-oriented) approach. Because kinematic artefacts strongly violate the consistency or semblance conditions, this observation suggests that velocity analysis based on depth-oriented prestack migration may be more appropriate in kinematically complex areas. Appropriate choice of objective (differential semblance) turns either form of migration velocity analysis into an optimization problem, for which Newton-like methods exhibit little tendency to stagnate at nonglobal minima. The extended modelling concept links migration velocity analysis to the apparently unrelated waveform inversion approach to estimation of Earth structure: from this point of view, migration velocity analysis is a solution method for the linearized waveform inversion problem. Extended modelling also provides a basis for a nonlinear generalization of migration velocity analysis. Preliminary numerical evidence suggests a new approach to nonlinear waveform inversion, which may combine the global convergence of velocity analysis with the physical fidelity of model-based data fitting.

http://www.trip.caam.rice.edu/reports/2007/geoprosp0207.pdf

Migration velocity analysis and waveform inversion

Marine controlled-source electromagnetic CSEM surveying has been in commercial use for predrill reservoir appraisalandhydrocarbonexplorationfor10 years.Althougha recent decrease has occurred in the number of surveys and publications associated with this technique, the method has become firmly established as an important geophysical tool intheoffshoreenvironment.Thisisaconsequenceoftwoimportant aspects associated with the physics of the method: First, it is sensitive to high electrical resistivity, which, although not an unambiguous indicator of hydrocarbons, is an important property of economically viable reservoirs. Second, although the method lacks the resolution of seismic wave propagation, it has a much better intrinsic resolution than potential-field methods such as gravity and magnetic surveying, which until now have been the primary nonseismicdatasetsusedinoffshoreexploration.Althoughbymany measures marine CSEM is still in its infancy, the reliability and noise floors of the instrument systems have improved significantly over the last decade, and interpretation methodology has progressed from simple anomaly detection to 3D anisotropic inversion of multicomponent data using some of theworld’sfastestsupercomputers.Researchdirectionspresently include tackling the airwave problem in shallow water by applying time-domain methodology, continuous profiling tools, and the use of CSEM for reservoir monitoring during production.

Ten years of marine CSEM for hydrocarbon exploration

Early development of marine electromagnetic methods, dating back about 80 years, was driven largely by defense/military applications, and use for these purposes continues to this day. Deepwater, frequency-domain, electric dipole-dipole, controlled-source electromagnetic (CSEM) methods arose from academic studies of the oceanic lithosphere in the 1980s, and although the hydrocarbon exploration industry was aware of this work, the shallow-water environments being explored at that time were not ideally suited for its use. Low oil prices and increasingly successful results from 3D seismic methods further discouraged investment in costly alternative geophysical data streams. These circumstances changed in the late 1990s, when both Statoil and ExxonMobil began modeling studies and fieldtrials of CSEM surveying in deep water (around 1000 m or deeper), specifically for characterizing the resistivity of previously identified drilling targets. Trials offshore Angola in 2000–2002 by both these companies showed that ...

An introduction to marine controlled-source electromagnetic methods for hydrocarbon exploration

A method for surface estimation of reservoir properties, wherein location of and average earth resistivities above, below, and horizontally adjacent to the subsurface geologic formation are first determined using geological and geophysical data in the vicinity of the subsurface geologic formation. Then dimensions and probing frequency for an electromagnetic source are determined to substantially maximize transmitted vertical and horizontal electric currents at the subsurface geologic formation, using the location and the average earth resistivities. Next, the electromagnetic source is activated at or near surface, approximately centered above the subsurface geologic formation and a plurality of components of electromagnetic response is measured with a receiver array. Geometrical and electrical parameter constraints are determined, using the geological and geophysical data. Finally, the electromagnetic response is processed using the geometrical and electrical parameter constraints to produce inverted vertical and horizontal resistivity depth images. Optionally, the inverted resistivity depth images may be combined with the geological and geophysical data to estimate the reservoir fluid and shaliness properties.

Remote reservoir resistivity mapping

An improved method and apparatus for electromagnetic surveying of a subterranean earth formation beneath a body of water. An electric dipole current source is towed from a survey vessel in a body of water substantially parallel to the surface of the body of water and separated from the floor of the body of water by a distance less than approximately one-quarter of the distance between the surface and the floor. Alternating electric current, preferably including a plurality of sinusoidal components, is caused to flow in the source. An array of electric dipole detectors is towed from the survey vessel substantially collinearly with the current source. Each electric dipole detector of the array is separated from the current source by a distance substantially equal to an integral number of wavelengths of electromagnetic radiation, of frequency equal to that of a sinusoidal component of the source current, propagating in the water. A gradient detector array is also towed by the survey vessel in a position laterally separated from, or beneath, the mid-point of the current source. Additionally, an array of three-axis magnetic field sensors mounted in controllable instrument pods are towed by the seismic vessel on the flanks of the current source. Frequency-domain and time-domain measurements of magnetic and electric field data are obtained and analyzed to permit detection of hydrocarbons or other mineral deposits, or regions altered by their presence, within subfloor geologic formations covered by the body of water.

Method and apparatus for offshore electromagnetic sounding utilizing wavelength effects to determine optimum source and detector positions

Unusual swirl patterns of bright and dark material on the moon and Mercury are proposed to be remnants of collisions with gas/dust-rich regions within a cometary coma. This interpretation provides important new clues for understanding cometary fine structure, impact effects of low-density material, and the origin of certain pronounced magnetic anomalies.

Cometary collisions on the Moon and Mercury

Method for assessing hydrocarbon source rock potential of a subsurface region without well log information. The method uses surface electromagnetic (121) and seismic (122) survey data to obtain vertical profiles of resistivity and velocity (123), which are then analyzed in the same way as well log data are analyzed by the well known DeltaLogR method (124).

Leonard J. Srnka

Papers

An introduction to marine controlled-source electromagnetic methods for hydrocarbon exploration

Remote reservoir resistivity mapping

Method and apparatus for offshore electromagnetic sounding utilizing wavelength effects to determine optimum source and detector positions

Cometary collisions on the Moon and Mercury

Method for remote identification and characterization of hydrocarbon source rocks using seismic and electromagnetic geophysical data