# Experimental and theoretical investigations into the streaming potential phenomenon with special reference to applications in glaciated terrain

Sammanfattning: The occurrence of an electrical potential difference between the ends of a capillary tube when a fluid flows through is known as the streaming potential phenomenon. It was reported by Quincke in 1859 and was studied by Helmholtz, among others, in the nineteenth century. Its geophysical manifestation is the development of electrical potential differences in the ground when groundwater flows through porous rocks or soils. The phenomenon has been comparatively little studied in a geophysical context. The present thesis is the outcome of the author's experimental and theoretical research in the phenomenon. Natural streaming potentials, along with other electrical potentials in the ground that are present even in the absence of an artificially injected current, are also known as self-potentials (SP) or self-potential anomalies. Small-scale field measurements in the present work have demonstrated that SP observations within areas of size 0.5 m by 0.5 m appear to be approximately normally distributed. Hence a mean of such observations can be accepted as a representative value of the potential of the "point". The experimental work in the thesis was undertaken to simulate the natural phenomenon in the laboratory. An equipment to measure the streaming potentials developed across soil samples as a function of the applied pressure was designed. The total applied pressure could be varied between approximately 15 and 400 kPa. Pressure differences and electrical potential differences could be measured with an accuracy of about 0.1 kPa and 1 mV, respectively. The streaming potential developed across a sample is generally observed to be proportional to the pressure difference and the constant of proportionality is called the streaming potential coefficient C. This was determined for a number of sand and moraine samples. Two methods to estimate C from field observations of SP have been developed. The first can be regarded as a correction to observations of potentials due to water flow in slopes ("topographic SP") and the second is an active method where pumping from a well is used as a controlled source of streaming potentials. A comparison of values of C obtained from laboratory measurements and from estimates based on field observations showed that laboratory data can give reasonable estimates of the in situ value of C. Field observations of SP at several different sites have been used to illustrate the stability of the potentials over extended periods of time as long as conditions in the ground stay the same. When the appearance of an SP-anomaly changes this generally reflects significant changes in the conditions in the ground. It appears that anomalies with an amplitude exceeding about 10 mV, and probably even smaller ones, are significant. A case history illustrates the occurrence of streaming potentials in a practical field situation. It is shown that the removal of a topographic trend enhances the appearance of any local anomaly patterns present in the data. In the case under consideration these patterns reflect both variations in the electrical resistivity and presence of self-potentials not of a streaming origin. The apparent streaming potential coefficient can be obtained from a plot of SP versus elevation but it was found to vary with time due to variation in the near-surface resistivity. The streaming potential phenomenon can be described by means of the theory of coupled flows which expresses the flow (of, e.g., charge, matter or heat) as a linear combination of driving forces (gradients of , e.g., electric potential, pressure or temperature). The formulation is well suited to numerical modelling, and a detailed examination of the generation of sources of conduction current in the streaming potential problem has been made. A numerical study illustrates the calculation of conduction current source terms in a practical example. A qualitative discussion of the generation of sources of conduction current, by flow of ground water, for some simple geological models has been made to further illustrate the physical mechanisms behind the streaming potential phenomenon. Although not strictly a modelling tool, a method to estimate the limiting depth to a streaming potential source region has also been devised using the formal analogy between streaming potentials and magnetostatics and following Smith's analysis for the determination of the maximum depth to the top of a magnetised body.

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