R. Jeffrey Lytle

Analysis of electrical conductivity imaging

We investigate the feasibility of imaging the electrical conductivity in a cross‐section of an object (such as a core sample) by numerical inversion of low‐frequency, electromagnetic (EM) boundary data. Current flow is assumed to be confined to the cross‐section, which is modeled as a network of resistors. The network serves as a discrete approximation of the distributed‐parameter system that is described mathematically by Maxwell’s equations for steady current flow in a nonhomogeneous medium. A complete set of linearly independent voltage vectors is applied to the peripheral nodes, and the resulting node currents serve as the measured data for estimating the internal conductivity pattern (image). We generate estimates of this conductivity image by using an iterative process on network equations that are linearized in the unknown conductance variables. The mathematical feasibility of this approach is demonstrated by computer simulation studies using data generated from the network model. Reconstructed ima...

Iterative Ray Tracing between Boreholes for Underground Image Reconstruction

A computerized method is described for calculating an image of the refractive index distribution in a plane bounded by two underground boreholes. The scanning geometry is assumed to be limited to probing from borehole to borehole, with rays at numerous depths and angles to effectively cover the cross section between holes. A geometrical optics model is assumed for the transmission data. We stress situations where significant bending of electromagnetic or seismic rays occurs. Image reconstruction involves an iterated sequence of numerical ray tracing and linear system inversion. A similar approach, discussed in the literature, sometimes fails to converge. We report here our refinements of this method, including use of a smoothness constraint.

Measurement of Earth Medium Electrical Characteristics: Techniques, Results, and Applications

An overview of measurement techniques, measurement results, and factors influencing the conductivity and dielectric constant of earth medium is given. Application of these measurement techniques to geophysical investigations is also discussed.

Design of a Miniature Directional Antenna for Geophysical Probing from Boreholes

In this report we describe a design for a miniaturized directional antenna for use in geophysical exploration from boreholes. Mathematical results are given which indicate the antenna characteristics. The concept we use involves an antenna eccentrically located within a high dielectric constant or high permeability sheath.

Subsurface Probing by High-Frequency Measurements of the Wave Tilt of Electromagnetic Surface Waves

An overview of the tilt of an electromagnetic surface wave propagating along the surface of the earth is given. High-frequency wave-tilt measurements can have important applications in low conductivity regions such as desert and permafrost areas. A specific application includes determining the depth of permafrost. Past applications of wave-tilt measurements were primarily with lower frequencies in regions with high ground conductivities. Thus low frequencies (<1 MHz) were needed to probe to significant depths. Wave-tilt calculations show that for low surface conductivities, it may be feasible to probe to significant depths using high frequencies (>1 MHz). This enables resolution of thicknesses of layers, a result that has not been possible at low frequencies in the higher conductivity media. It is noted that differences in wave tilt occur for vertically and horizontally polarized surface waves. These wave-tilt differences are useful because they indicate profile characteristics that are sensitive in different ways to the two polarizations.

Detecting High-Contrast Seismic Anomalies Using Cross-Borehole Probing

Seismic probing between boreholes is useful for locating high-contrast geophysical anomalies such as an abandoned tunnel. Theoretical studies of continuous wave (CW) seismic wave interaction with a tunnel show that both the signal minima and the phase structure of the received signal can be used for locating the anomaly. The theoretical studies show that as the source and receiver are lowered in separate boreholes straddling the anomaly, the signal minima and the phase structure can be interpreted to yield both the lateral and vertical positions of the anomaly. Plane waves of compressional, horizontally polarized shear, and vertically polarized shear wave types incident on a cylindrical horizontal anomaly have been considered. The total seismic field has been calculated using an exact formulation. The variation of the response is studied as a function of the ratio of anomaly diameter to wavelength. The resulting fields in the receiver borehole are an effective diagnostic when a wavelength in the surrounding medium is less than or equal to the diameter of the anomaly. These results are analogous to the corresponding electromagnetic case which has been studied previously.

A Computer Program for Four Probe Resistivity Measurements in a Horizontally Layered Earth

A computer code to plot the response of a dipole-dipole resistivity array over a many-layered earth is described.

Resistivity And Induced-Polarization Probing in the Vicinity of a Spherical Anomaly

The mathematical formulae governing the interaction of a low-frequency source of electric current with a spherical anomaly are given. These formulae are used to determine the apparent resistivity and induced-polarization response between electrodes located within boreholes in the medium. Numerical results are given illustrating the spatial variation of these parameters.

The Potential Field around Subsurface Electrically Excited Conductors

A simple mathematical model has been developed for determining the depth and radius of an excited electrical conductor (e.g., a grout ball) located underground. The method uses voltage profiles, measured on the ground surface or in boreholes, and it is expected to be more accurate than conventional four-probe resistivity surveys.