Frank Dale Morgan

Dielectric spectroscopy of sedimentary rocks

A physiochemical model for the complex dielectric response of sedimentary rocks is used to invert broadband dielectric spectra for effective grain size distributions. The complex dielectric response of each grain within the “water-wet” granular matrix is obtained by superimposing the polarization of the electrochemical double layer, which is assumed to surround each grain, with the complex dielectric response of the dry mineral grain. The effective complex dielectric response of the water-wet matrix (grains and surface phase) is obtained by volume averaging over the entire distribution of particle sizes. The complex dielectric response of the total mixture (water-wet matrix and bulk pore solution) is obtained using the Bruggeman-Hanai-Sen effective medium theory. Studies of Berea sandstone show that the grain size distribution, obtained by inverting the real part of the complex dielectric spectra, is similar to the grain size distribution obtained from optical images of the sample in thin section. The current model, however, does not account for surface roughness effects or the polarization of counterions over multiple grain lengths; therefore the grain size distribution obtained by dielectric spectroscopy is broader than the image-derived distribution. The dielectric-derived grain size distribution can be fit with two separate power laws that crossover at R ≅ 1 μm, which corresponds to a relaxation frequency of 2 kHz. The low-frequency dielectric response (f 2 kHz) is primarily controlled by the clay size grains and surface roughness, which has a fractal dimension of d = 2.48±0.07. At very low frequencies (f < 0.1 Hz) the dielectric response appears to be controlled by the electrochemical polarization of counterions over multiple grain lengths. A more general model should account for the effects of surface roughness and grain interactions on the dielectric response. It would also be useful to develop a simplified version of this model, perhaps similar in form to the empirically derived Cole-Cole response, which could be more easily used to model and interpret electrical geophysical field surveys (e.g., induced-polarization, ground-penetrating radar, and time domain reflectometery measurements).

Three-dimensional source inversion of self-potential data

[1] The self-potential (SP) method has long been used for a variety of geophysical applications because of its ease of acquisition, but has suffered from difficulty in interpretation of the data. Self-potential signals result from a source term that is coupled with the earth resistivity and appropriate boundary conditions. This work describes an inversion methodology for determining the self-potential sources from measured SP and resistivity data. The SP source inversion is a linear problem, though it is complicated by nonuniqueness that is common to potential-field problems. The linear operator is also poorly conditioned because of the limited set of measurements, which are often constrained to the earths surface. Our approach utilizes model regularization that selects a class of solutions which fit the data with sources that are spatially compact. Large variations in sensitivity due to distance and resistivity structure throughout the model are addressed through the use of a scaling term derived from the Greens functions that define the linear operator. A significant benefit of these methods is the resolution of targets at depth from surface measurements alone. This inversion technique is first illustrated with a simple synthetic data set. In a second example we apply this approach to a field data set taken from previously published literature and investigate the effects of different resistivity structure assumptions on the inversion results. The spatial distribution of sources provides useful information that can subsequently be interpreted in terms of physical processes that generate the SP data.

Self potentials in cave detection

The major application of the self potential (SP) method has been in mineral exploration and in recent years increasingly in environmental and engineering investigations. The SP method simply measures a naturally occurring potential between electrodes on the surface or in boreholes. There are three mechanisms that generate self potentials: streaming potentials due to fluid flow, electrochemical potentials generated by concentration differences of electrolytes, and thermoelectric potentials from temperature gradients.

Temperature‐dependent streaming potentials: 1. Theory

[1]xa0The variation of streaming potentials (voltage/pressure cross-coupling coefficient) with temperature is examined with particular emphasis on the effect of temperature on zeta potentials. The variation of streaming potential with temperature cannot be explained solely by the known temperature dependence of water viscosity, permittivity, and conductivity; the change of zeta potential with temperature must also be included. Many previous experimental studies show that the magnitude of the zeta potential increases with temperature. It was found in this study that the increase is controlled primarily by the surface charge density. These changes are influenced by the absorption properties of the surface and thus the surface charge, which in turn affects the Stern layer charge and properties of the electrical double layer. It is found that the slope of the temperature versus zeta potential curve is controlled by the change in enthalpy of the surface reactions. It was also found that viscosity is the most dominant term in the coupling coefficient, but changes in the conductivity model used to determine zeta potentials can also affect streaming potential coupling coefficient results. For the cases studied, the temperature-dependent zeta potential is determined by the temperature-dependent behavior of the Debye-Huckel parameter, 4%; the diffuse layer of electrical double layer (EDL), 6%; and the surface charge, 90%. The Revil and Glover model was able to account for much of the change in the surface charge density caused by changes in temperature.

Electromagnetic cave-to-surface mapping system

This paper presents the principle, design, construction, and methodology for an electromagnetic (EM) system to be used in the detection/location and mapping of underground cavities using surface measurements. The EM instrument consists of a loop-loop transmitter/receiver system with the transmitter placed inside the cavity. The transmitters position and depth are determined by analyzing the shape and distribution of the transmitted field on the surface. From the perspective of a cylindrical coordinate system, the vertical component of the through rock transmitted magnetic field peaks at the point where the transmitter and receiver are vertically collinear. On the other hand, the horizontal component reaches a minimum at this point. Based on these observations, a procedure is presented and tested that efficiently locates the position as well as the depth of the transmitter. A physical model for the system was developed and compared to the results of calibration experiments, with very good agreement. The model allows the study of different responses for EM waves/fields propagating through a homogenous Earth of different electrical characteristics and therefore enables several type-curves to be generated that aid in the development of an optimal system.

Pore Scale Modeling of Rock Properties and Comparison to Laboratory Measurements

The microstructure of a porous medium and the physical characteristics of the solid and the fluids that occupy the pore space determine the macroscopic transport properties of the medium. The computation of macroscopic properties from the rock microtomography is becoming an increasingly studied topic (Alder et al., 1990; Arns, 2001; Pal et al., 2002; Kameda et al., 2006; Toumelin et al., 2008). The purpose of this paper is to test numerical calculations of the geometrical and transport properties (electrical conductivity, permeability, specific surface area and surface conductivity) of porous, permeable rocks, given the 3D digital microtomography images.

An approach for simultaneously inverting MT data for resistivity and susceptibility

We present a technique for inverting magnetotelluric (MT) data for simultaneous estimates of resistivity and susceptibility. We demonstrate the efficacy of the method by processing a large survey collected in the Dayangshu (DYS) basin of Northeast China. MT is one of the most important geophysical exploration techniques, and has been widely applied to both resource exploration and the determination of deep crustal structure. In most conventional MT inversion algorithms, the subsurface is assumed to be nonmagnetic and only resistivity is estimated. Most normal sedimentary rocks, granite, and a few weakly metamorphic rocks are effectively non-magnetic. However, there are a class of rocks with high levels of magnetism such as Basalt. It has been previously shown that the magnetic properties of rocks significantly effects MT response. If an MT investigation is carried out in a region underlain by highly magnetic materials, conventional inversion techniques generate estimates with anomalous resistivity values. We develop a simultaneous inversion method to deal with this case. Our method considers both electrical and magnetic effects and simultaneously inverts MT measurements for subsurface resistivity and susceptibility. This paper presents the basic theory of the method and a case study taken from Chinas DYS basin. The case study demonstrates that simultaneous inversion can improve the quality of resistivity inversions, and more importantly, obtain information about rock susceptibility. Estimates of susceptibility are a valuable tool for the identification and mapping of volcanic strata with high levels of magnetism.

Reinterpretation of a vintage 4.5-km resistivity line through Sulphur Springs, St. Lucia

Saint Lucia is part of the Lesser Antilles volcanic island arc in the eastern Caribbean (Figure 1). Volcanic activity has been concentrated in the southern half of the island for the last several million years (Wohletz et al., 1986). The Sulphur Springs geothermal area lies within what has been identified as the Qualibou Caldera. Geologic studies have shown that recent volcanic activity in the area has been of a type that is likely to emplace a magma heat source for high temperature geothermal systems to naturally develop. Any evidence for a supposed intrusion beneath Sulphur Springs comes from temperature measurements of the superheated steam and wells, and from microseismic data (GENZL, 1992). Aspinall et al. (1976) suggest two fluid bodies, one near Sulphur Springs at a depth between 0.5 and 2 km and a second on the northern caldera rim at depths greater than 1 km.

Self Potentials In Cave Detection

been in mineral exploration and in recent years increasingly in environmental and engineering investigations. The SP method simply measures a naturally occurring potential between electrodes on the surface or in boreholes. There are three mechanisms that generate self potentials: streaming potentials due to fluid flow, electrochemical potentials generated by concentration differences of electrolytes, and thermoelectric potentials from temperature gradients. Self potential, SP, and streaming potentials will be used interchangeably as we are only interested in potentials generated from fluid flow in this study. Deformation of groundwater flow by preferential drainage paths increases water flow velocity and intensifies streaming potentials caused by filtration. In the case we are studying, the drainage paths are defined by flow into cavities. SP anomalies can be from tens to hundreds of millivolts depending on the pressure drop, lithology, and chemical composition of the water. On the boundary of solid and liquid phases, an electrically charged electrochemical layer is formed between the mineral and pore moisture. Streaming potentials are directly proportional to the potential difference between the immobile part of the electrochemical layer and the free solution. Streaming potentials decrease as the electrolyte concentration increases. Most mineral surfaces are negatively charged, hence an excess of positive ions is drawn to the surface to form the electrochemical boundary layer. The positive ions are carried in the direction of the water flow—hence areas of water inflow are characterized by positive anomalies and those of flow sources by negative ones. In a permeable and homogeneous medium, the streaming potentials show the contours of groundwater flow. The slope from a line plot of SP data is proportional to the hydraulic gradient in the direction of the survey line. The theoretical basis of the streaming potential was first worked out by Helmholtz. He proposed that streaming potentials are present when a conduction current balances the convection current caused by the preferential transport of positive ions (Figure 1). As the fluid moves under a pressure difference, P, it drags positive charge with it producing the convection current. The conduction current is simply an Ohm’s law equilibrium balancing current. At steady state Iconv = Icond, leading to the Helmholtz-Smoluchowski equation