Amr Adel Geophysics.docx

Natural potentials and currents Electrical investigations of natural electrical properties arebased on the measurement of the voltage between a pair of electrodes implanted in the ground. Natural differences in potential occur in relation to subsurface bodies that create their own electric fields. The bodies act like simple voltaic cells; their potential arises from electrochemical action. Natural currents (called telluric currents) flow in the crust and mantle of the Earth. They are induced electromagnetically by electric currents in the ionosphere .In studying natural potentials and currents the scientist has no control over the source of the signal. This restricts the interpretation, which is mostly only qualitative. The natural methods are not as useful as controlled induction methods, such as resistivity and electromagnetic techniques, but they are inexpensive and fast. 1 Self-potential (spontaneous potential) A potential that originates spontaneously in the ground is called a self-potential (or spontaneous potential). Some self-potentials are due to man-made disturbances of the environment, such as buried electrical cables, drainage pipes or waste disposal sites. They are important in the study of environmental problems. Other self-potentials are natural effects due to mechanical or electrochemical action. In every case the groundwater plays a key role by acting as an electrolyte. Some self-potentials have a mechanical origin. When an electrolyte is forced to flow through a narrow pipe, a potential difference (voltage) may arise between the ends of the pipe. Its amplitude depends on the electrical resistivity and viscosity of the electrolyte, and on the pressure difference that causes the flow. The voltage is due to differences in the electrokinetic or streaming potential, which in turn is influenced by the interaction between the liquid and the surface of the solid (an effect called the zeta-potential). The voltage can be positive or negative and may amount to some hundreds of millivolts. This type of self-potential can be observed in conjunction with seepage of water from dams, or the flow of groundwater through different lithological units. Most self-potentials have an electrochemical origin. For example, if the ionic concentration in an electrolyte varies with location, the ions tend to diffuse through the electrolyte so as to equalize the concentration. The diffusion is driven by an electric diffusion potential, which depends on the temperature as well as the difference in ionic concentration.When a metallic electrode is inserted in the ground, the metal reacts electrochemically with the electrolyte (i.e., groundwater), causing a contact potential. If two identical electrodes are inserted in the ground, variations in concentration of the electrolyte cause different electrochemical reactions at each electrode. A potential difference arises, called the Nernst potential. The combined diffusion and Nernst potentials are called the electrochemical self-potential. It is temperature sensitive and may be either positive or negative, amounting to at most a few tens of millivolts.

The self-potentials that originate by the above mechanisms are attracting increased attention in environmental and engineering situations. However, in the exploration for subsurface regions of mineralization they are often smaller than the potentials associated with orebodies and are classified accordingly as “background potentials.”The self-potential associated with an orebody is called its “mineralization potential.” Self-potential (SP) anomalies across orebodies are invariably negative, amounting usually to a few hundred millivolts. They are most commonly associated with sulfide ores, such as pyrite, pyrrhotite, and chalcopyrite, but also with graphite and some metallic oxides. The origin of the mineralization type of self-potential is still obscure, despite decades of applied investigations. At one time it was thought that the effect arose from galvanic action. This occurs when dissimilar metal electrodes are placed in an electrolyte. Unequal contact potentials are formed between the metals and the electrolyte, giving rise to a potential difference between the electrodes. According to this model an orebody behaves like a simple voltaic cell, with groundwater acting as the electrolyte. It was believed that oxidation of the part of the orebody above the water table produced a potential difference between the upper and lower parts, causing a spontaneous electric polarization of the body. Oxidation involves the addition of electrons, so the top of the orebody becomes negatively charged, explaining the observed negative anomalies. Unfortunately, this simple model does not explain many of the observed features of selfpotential anomalies and has proved to be untenable. Another mechanism for self-potential depends on variations in oxidation (redox) potential with depth (Fig. 4.42). The ground above the water table is more accessible to oxygen than the submersed part, so moisture above the water table contains more oxidized ions than that below it. An electrochemical reaction takes place at the surface between the orebody and the host rock above the water table. It results in reduction of the oxidized ions in theadjacent solution. An excess of negative ions appears above the water table. A simultaneous reaction between the submersed part of the orebody and the groundwater causes oxidation of the reduced ions present in the groundwater. This produces excess positive ions in the solution and liberates electrons at the surface of the orebody, which acts as a conductor connecting the two half-cells. Electrons flow from the deep part to the shallow part of the orebody. Outside the orebody, positive ions move from bottom to top along the electric field lines. The equipotential surfaces are normal to the field lines. The self-potential is measured where they intersect the ground surface . The redox model is inadequate for the same reason as the galvanic model; it fails to account for many of the observed features of self-potential anomalies. In particular, the association of selfpotential models with the water table has been cast in doubt. Moreover, sulfide orebodies appear to persist for geological lengths of time, so that a mechanism involving permanent flow of charge appears unlikely. Self-potential is a feature of a stable system that

is perturbed by making an electrical connection between the host rock and the sulfide conductor through the inserted electrodes and their connecting wire. The observed potential difference appears to be due to the difference in oxidation potential between the locations of the measurement electrodes, one inside and the other outside the zone of mineralization. 2 SP surveying The equipment needed for an SP survey is very simple. It consists of a sensitive high-impedance digital voltmeter to measure the natural potential difference between two electrodes implanted in the ground. Simple metal stakes are inadequate as electrodes. Electrochemical reactions take place between the metal and moisture in the ground, causing the build-up of spurious charges on the electrodes, which can falsify or obscure the small natural self-potentials. To avoid or minimize this effect non-polarizable electrodes are used. Each electrode consists of a metal rod submersed in a saturated solution of its own msalt; a common arrangement is a copper rod in copper msulfate solution. The combination is contained in a mceramic pot which allows the electrolyte to leak slowly through its porous walls, thereby making electrical mcontact with the ground. Two field methods are in common use .The gradient method employs a fixed separation between the electrodes, of the order of 10 m. The potential difference is measured between the electrodes, then the pair is moved forward along the survey line until the trailing electrode occupies the location previously occupied by the leading electrode. The total potential at a measurement station relative to a starting point outside the study area is found by summing the incremental potential differences. Some electrode polarization is unavoidable, even with nonpolarizable electrodes. This gives rise to a small error ineach measurement; these add up to a cumulative error in the total potential. The polarization effects can sometimes be reduced by interchanging the leading and trailing electrodes. In this “leapfrog” technique the leading electrode for one measurement is kept in place and becomes the trailing electrode for the next measurement; meanwhile the previous trailing electrode is moved ahead to become the leading electrode. Cumulative error is the most serious disadvantage of the fixed electrode configuration. A practical advantage of the technique is that only a short length of nconnecting wire must be moved along with the electrodes. The total field method utilizes a fixed electrode at a base station outside the area of exploration and a mobile measuring electrode. With this method the total potential is measured directly at each station. The wire connecting the electrodes has to be long enough to allow good coverage

of the area of interest. This necessitates a long wire that must be wound or unwound on a reel for each measurement station. However, the total field method results in smaller cumulative error than the gradient method. It allows more flexibility in placing the mobile electrode and usually gives data of better quality. Hence, the total field method is usually preferred except in difficult terrain. The surveying procedure with each technique consists of measuring potential at discrete stations along a profile. As in gravity and magnetic surveys, the data are mapped and interpretations of anomalies are based on their geometry. Methods used to interpret self-potential anomalies are often qualitative or are based on simple geometric models. Visual inspection of mapped anomalies may reveal trends related to elongation of the orebody; crowding of contour lines can indicate its orientation. Profiles plotted in known directions across the anomaly can be compared with curves generated from simple models of the source. For example, a polarized sphere may be used to model the source of approximately circular anomalies, while a horizontal line source (or polarized cylinder) may be used to model an elongate anomaly. A common and effective method is to model SP anomalies with point sources; complex anomalies are modelled with combinations of sources and sinks.

Hypothetical contour lines of a negative selfpotentialanomaly over an orebody; the asymmetry of the anomaly along the profile AB suggests that the orebody dips toward A.

4.3.4.3 Telluric currents

Ultraviolet radiation from the Sun ionizes molecules of air in the thin upper atmosphere of the Earth. The ions accumulate in several layers, forming the ionosphere at altitudes between about 80 km and 1500 km above the Earth’s surface. Electric currents in the ionosphere arise from systematic motions of the ions, which are affected by various factors such as the daily and monthly tides, seasonal variations in insolation and the periodic fluctuation in ionization related to the 11-yr sunspot cycle. The currents produce varying magnetic fields with the same frequencies, which are observed at the surface of the Earth and can be analyzed from long-term continuous records of the geomagnetic field. The ionospheric effects show up in the energy spectrum of the geomagnetic field as distinct peaks representing periods that range from fractions of a second (geomagnetic pulsations) to several years .The magnetic fields inducefluctuating electric currents, called telluric currents, that flow in horizontal layers in the crust and mantle. The current pattern consists of several huge whorls, thousands of kilometers across, which remain fixed with respect to the Sun and thus move around the Earth as it rotates. The distribution of telluric current density depends on the variation of resistivity in the horizontal conducting layers. At shallow crustal depths the lines of current flow are disturbed by subsurface structures which cause contrasts in resistivity. These could arise from geological structures or the presence of mineralized zones. Consider, for example, a buried anticline which has a highly resistive rock (such as granite) as its core and is overlain by a conducting layer of porous sedimentary rocks saturated with groundwater. The horizontal flow of telluric current across the anticline chooses the less-resistive path through the conducting sediments. The current lines bunch together over the axis of the anticline, increasing the horizontal current density. The equipotential surfaces mnormal to the current lines intersect the ground surface, where potential differences can be measured with a high-impedance voltmeter. The field equipment for measuring telluric current density is simple. The sensors are a pair of non-polarizable electrodes with a fixed separation L of the order of 10–100 m. The potential difference V between the electrodes is measured with a high-impedance voltmeter. The electric field E at a point mid-way between the electrodes mcan be assumed to be V/L. Using Ohm’s law, and assuming that the telluric current flows in conducting rock layer with resistivity r1, the telluric current density J at each measurement station along a profile . The direction of the telluric current is not known, so two pairs of electrodes oriented perpendicular to each other are used. One pair is aligned north–south, the other east–west. Telluric currents vary unpredictably with time, but they change only slowly within a

homogeneous region. To keep track of the temporal changes an orthogonal pair of electrodes is set up at a fixed base station outside the area to be explored. Another orthogonal pair is moved across the survey area. The potential differences across each electrode pair in the mobile and base arrays are recorded simultaneously for several minutes at each measurement station. Correlation of the records allows removal of the temporal changes in direction and intensity of the telluric currents. The deflection of telluric current by a resistive subsurface structure is greatly idealized. It assumes an infinite resistivity r2 in the core of the anticline. In practice, the current is not completely diverted through the better-conducting layer; part flows through the more resistive layer as well. Thus we cannot assume that the resistivity r1 corresponds to the good conductor. Rather, it represents some undefined mixture of the values r1 and r2. It is not the true resistivity of either layer, but the apparent resistivity of the measurement.

Telluric current lines are deflected by changes in thickness ofa conducting layer over a more resistive structure (bottom). The telluriccurrent density (top) is obtained from the voltagemeasured between apair of fixedseparation electrodes at the surface (afterRobinson andÇoruh, 1988).

5 Resistivity surveying

The large contrast in resistivity between orebodies and their host rocks is exploited in electrical resistivity prospecting, especially for minerals that occur as good conductors. Representative examples are the sulfide ores of iron, copper and nickel. Electrical resistivity surveying is also an important geophysical technique in environmental applications. For example, due to the good electrical conductivity of groundwater the resistivity of a sedimentary rock is much lower when it is waterlogged than in the dry state. Instead of relying on natural currents, two electrodes are used to supply a controlled electrical current to the ground. As in the telluric method, the lines of current flow adapt to the subsurface resistivity pattern so that the potential difference between equipotential surfaces can be measured where they intersect the ground surface, using a second pair of electrodes. A simple direct current can cause charges to accumulate on the potential electrodes, which results in spurious signals. A common practice is to commutate the direct current so that its direction is reversed every few seconds; alternatively a low-frequency alternating current may be used. In multi-electrode investigations the current electrode-pair and potential electrode-pair are usually interchangeable 1 Potential of a single electrode Consider the flow of current around an electrode that introduces a current I at the surface of a uniform halfspace . The point of contact acts as a current source, from which the current disperses outward. The electric field lines are parallel to the current flow and normal to the equipotential surfaces, which are hemispherical in shape. The current density J is equal to I divided by the surface area, which is 2_r2 for a hemisphere of radius r. The electric field E at distance r from the input electrode is obtained from Ohm’s law. Putting this expression in Eq. (4.74) yields the electric potential U at distance r from the input electrode: If the ground is a uniform half-space, the electric field lines around a source electrode, which supplies current to the ground, are directed radially outward (Fig. 4.47b). Around a sink electrode, where current flows out of the ground, the field lines are directed radially inward .The equipotential surfaces around a source or sink electrode are hemispheres, if we regard the electrodein isolation. The potential around a source is positive and diminishes as 1/r with increasing distance. The sign of I is negative at a sink, where the current flows out of the ground. Thus, around a sink the potential is negative and increases (becomes less negative) as 1/r with increasing distance from the sink. We can use these observations to calculate the potential difference between a second pair of electrodes at known distances from the source and sink.

Electric field lines and equipotential surfaces around a single electrode at the surface of a uniform half-space: (a) hemispherical equipotential surfaces, (b) radially outward field lines around a source, and (c) radially inward field lines around a sink.

2 The general four-electrode method Consider an arrangement consisting of a pair of current electrodes and a pair of potential electrodes (Fig. 4.48). The current electrodes A and B act as source and sink, respectively. At the detection electrode C the potential due to the source A is _rI/(2_rAC), while the potential due to the sink .The combined potential at C is Similarly, the resultant potential at D is The potential difference measured by a voltmeter connected between C and D is All quantities in this equation can be measured at theground surface except the resistivity

General four-electrode configuration for resistivity measurement, consisting of a pair of current electrodes (A, B) and a pair of potential electrodes (C, D).

3 Special electrode configurations The general formula for the resistivity measured by a four electrode method is simpler for some special geometries of the current and potential electrodes. The most commonly used configurations are the Wenner, Schlumberger and double-dipole arrangements. In each configuration the four electrodes are collinear but their geometries and spacings are different. In the Wenner configuration the current and potential electrode pairs have a common midpoint and the distances between adjacent electrodes are equal, so that rAC_rDB_a, andInserting these values in gives In the Schlumberger configuration the current and potential pairs of electrodes often also have a common mid-point, but the distances between adjacent electrodes differ. Let the separations of the current and potential electrodes be L and a, respectively. Then rAC_ rDB_(L – a)/2 and rAD_rCB_(L_a)/2. Substituting in the general formula, we get In this configuration the separation of the current electrodes is kept much larger than that of the potential electrodes (L_a). Under these conditions, Eq. (4.92) simplifies to In the double-dipole configuration (Fig. 4.49c) the spacing of the electrodes in each pair is a, while the distance between their mid-points is L, which is generally much larger than a. Note that detection electrode D is defined as the potential electrode closer to current sink B. In this case rAD_rBC_L, rAC_L_a, and rBD_L – a. The measured resistivity

Two modes of investigation can be used with each electrode configuration. The Wenner configuration is best adapted to lateral profiling. The assemblage of four electrodes is displaced stepwise along a profile while maintaining constant values of the inter-electrode distances corresponding to the configuration employed. The separation of the current electrodes is chosen so that the current flow is maximized in depths where lateral resistivity contrasts are expected. Results from a number of profiles may be compiled in a resistivity map of the region of interest. The regional survey reveals the horizontal variations in resistivity within an area at a particular depth. It is best suited to locating steeply dipping contacts between rocks with a strong

resistivity contrast and good conducr tors such as mineralized dikes, which may be potential orebodies. In vertical electrical sounding (VES) the goal is to observe the variation of resistivity with depth. The technique is best adapted to determining depth and resistivity for flat-lying layered rock structures, such as sedimentary beds, or the depth to the water table. The Schlumberger configuration is most commonly used for VES investigations. The mid-point of the array is kept fixed while the distance between the current electrodes is progressively increased. This causes the current lines to penetrate to ever greater depths, depending on the vertical distribution of conductivity.

4 Current distribution The current pattern in a uniform half-space extends laterally on either side of the profile line. Viewed from above, the current lines bulge outward between source and sink with a geometry similar to that shown in Fig. In a vertical section the current lines resemble half of a dipole geometry. In three dimensions the current can be visualized as flowing through tubes that fatten as they leave the source and narrow as they converge towards the sink. Figure 4.50 shows the flow pattern of the current in a verticalsection through the “tubes” in a uniform half-space. In order to evaluate the depth penetration of current in a uniform half-space we define orthogonal Cartesian coordinates with the x-axis parallel to the profile and the z-axis vertical (Fig. 4.51a). Let the spacing of the current electrodes be L and the resistivity of the half-space be r. The horizontal electric field Ex at (x, y, z) is (4.96) where r1_(x2_y2_z2)1/2 and r2_((L – x)2_y2_z2)1/2. Differentiating and using Ohm’s law (Eq. (4.80)) gives the horizontal current density Jx at (x, y, z):

(a) Parameters of the four-electrode arrangement, (b) distribution of current lines in a two-layer ground with resistivities r1 and r2 (r1_r2) and (c) the variation of apparent resistivity as the current electrode spacing is varied for the two cases of r1_r2 and r1_r2.

5 Apparent resistivity In the idealized case of a perfectly uniform conducting half-space the current flow lines resemble a dipole pattern (Fig. 4.50), and the resistivity determined with a four-electrode configuration is the true resistivity of the half-space. But in real situations the resistivity is determined by different lithologies and geological structures and so may be very inhomogeneous. This complexity is not taken into account when measuring resistivity with a four-electrode method, which assumes that the ground is uniform. The result of such a measurement is the apparent resistivity of an equivalent uniform half-space and generally does not represent the true resistivity of any part of the ground.

Consider a horizontally layered structure in which a layer of thickness d and resistivity r1 overlies a conducting half-space with a lower resistivity r2 (Fig. 4.52). If the current electrodes are close together, so that L_d, all or most of the current flows in the more resistive upper layer, so that the measured resistivity is close to the true value of the upper layer, r1. With increasing separation of the current electrodes the depth reached by the current lines increases. Proportionally more current flows in the less resistive layer, so the measured resistivity decreases. Conversely, if the upper layer is a better conductor than the lower layer, the apparent resistivity increases with increasing electrode spacing. When the electrode separation is much larger than the thickness of the upper layer (L _d) the measured resistivity is close to the value r2 of the bottom layer. Between the extreme situations the apparent resistivity determined from the measured current and voltage is not related simply to the true resistivity of either layer. 4.3.5.6 Vertical electrical sounding A two-layer situation is encountered often in electrical prospecting, for example when a conducting overburden overlies a resistive basement. It is also common in environmental applications, when the conducting water table lies under drier, more resistive soil or rocks. Before the advent of portable computers, two-layer cases were interpreted with the aid of characteristic curves. These theoretical curves, calculated for a particular four-electrode array, take into account the change in depth penetration when current lines cross the boundary to a layer with different resistivity. The electrical boundary conditions require continuity of the component of current density J normal to the interface and of the component of electric field E tangential to the interface. At a boundary the current lines behave like optical or seismic rays, and are guided by similar laws of reflection and refraction. For example, if u is the angle between a current line and the normal to the interface, the electrical “law of refraction” is (4.102) In a set of characteristic curves the apparent resistivity ra is normalized by the resistivity r1 of the upper layer and

the electrode spacing is expressed as a multiple of the layer thickness. The shape of the curve of apparent resistivity versus electrode spacing depends on the resistivity contrast between the two layers, and a family of characteristic curves is calculated for different ratios of r2/r1 (Fig. 4.53). The resistivity contrast is conveniently expressed by a kfactor defined as (4.103) The k-factor ranges between _1 and _1 as the resistivity ratio r2/r1 varies between 0 and #. The characteristic curves, drawn as full logarithmic plots on a transparent overlay, are compared graphically with the field data to find the best-fitting characteristic curve. The comparison yields the resistivities r1 and r2 of the upper and lower layers, respectively, and the layer thickness, d. Although characteristic curves can also be computed for the interpretation of structures with multiple horizontal layers, modern VES analyses take advantage of the flexibility offered by small computers with graphic outputs on which the apparent resistivity curves can be assessed visually. The first step in the analysis consists of classifying the shape of the vertical sounding profile.

The apparent resistivity curve for a three-layer structure generally has one of four typical shapes, determined by the vertical sequence of resistivities in the layers (Fig. 4.54). The type K curve rises to a maximum then decreases, indicating that the intermediate layer has higher resistivity than the top and bottom layers. The type H curve shows the opposite effect; it falls to a minimum then increases again due to an intermediate layer that is a better conductor than the top and bottom layers. The type A curve may show some changes in gradient but the apparent resistivity generally increases continuously with increasing electrode separation, indicating that the true resistivities increase with depth from layer to layer. The type Q curve exhibits the opposite effect; it decreases continuously along with a progressive decrease of resistivity with depth. Once the observed resistivity profile has been identified as of K, H, A or Q type, the next step is equivalent to one-dimensional inversion of the field data. The technique involves iterative procedures that would be very time-consuming without a fast computer. The method assumes the equations for the theoretical response of a multi-layered ground. Each layer is characterized by its thickness and resistivity, each of which must be determined. A first estimate of these parameters is made for each layer and the predicted curve of apparent resistivity versus electrode spacing is computed. The discrepancies between the observed and theoretical curves are then determined point by point. The layer parameters used in the governing equations are next adjusted, and the calculation is repeated with the corrected values, giving a new predicted curve to compare with the field data. Using modern computers the procedure can be reiterated rapidly until the discrepancies are smaller than a pre-determined value. The inversion method is equivalent to matching automatically the observed and theoretical curves. A onedimensional analysis accommodates only the variations of resistivity and layer thickness with depth. The response of a vertically layered structure has an analytical solution, so efficient inversion algorithms can be established. In recent years, procedures have been proposed that also take into account lateral heterogeneities. The response of two- or three-dimensional structures must be approximated by a numerical solution, based on the finitedifference

or finite-element techniques. The number of unknown quantities increases, as do the computational difficulties of the inversion. 4.3.5.7 Induced polarization If commutated direct current is used in a four-electrode resistivity survey, the sequence of positive and negative flow may be interspersed with periods when the current is off. The inducing current then has a box-like appearance (Fig. 4.55a). When the current is interrupted, the voltage across the potential electrodes does not drop immediately to zero. After an initial abrupt drop to a fraction of its steady-state value it decays slowly for several seconds (Fig. 4.55b). Conversely, when the current is switched on, the potential rises suddenly at first and then gradually approaches the steady-state value. The slow decay and growth of part ofthe signal are due to induced polarization, which results from two similar effects related to the rock structure: membrane polarization and electrode polarization.