TABLETOP MODELS FOR ELECTRICAL AND ELECTROMAGNETIC GEOPHYSICS

Transcription

1 TABLETOP MODELS FOR ELECTRICAL AND ELECTROMAGNETIC GEOPHYSICS Charles T. Young Department of Geological Engineering and Sciences, Michigan Technological University, Houghton, MI 49931, (906) , fax (906) , ABSTRACT Tabletop models were created from common materials to demonstrate concepts in direct current electrical resistivity, self potential and electromagnetic geophysical methods. The models can be used as a laboratory exercise or as a classroom demonstration. Data profiles over the models are similar to those computed from equations and from field examples. The signals are generated with a function generator or battery and are measured with a digital multimeter. The experiment is greatly facilitated by using a multimeter that can be connected to the serial port of a computer. The tabletop models reinforce concepts learned in basic physics courses, introductory geology and geophysics courses, and in environmental engineering courses. Keywords: geophysics, DC resistivity, self-potential, electromagnetic, table top model INTRODUCTION These tabletop models demonstrate concepts in direct current electrical resistivity, self potential and electromagnetic profiling. DC resistivity is commonly used to find the depth to water table and bedrock, and to locate buried geological contacts between formations of distinctive resistivities, and zones of contaminated, conductive ground water. The self-potential method is used to search for natural occurring voltages generated from conductive ore deposits, percolating groundwater and other causes. Electromagnetic methods are used in mining exploration to locate conductive ore bodies and in environmental work to locate contaminated conductive ground water. The models use equipment which is available in a school electronics shop or may be purchased at an electronics store. DC RESISTIVITY PRINCIPLES Readers unfamiliar with geo-resistivity principles should read Boyd (2000), an online tutorial which uses minimal mathematics. More advanced discussions may be found in Berger (1992), Reynolds (1997) and Avants et al. (1999). An essential summary follows. The DC resistivity method uses four electrodes in a line on the surface, as illustrated in Figure 1. Current is circulated through the outer two electrodes, and the electrical potential is measured at the inner two electrodes. The apparent resistivity, a, of the earth, in ohm-m, is computed by a =K (V/I), where V is the potential, in volts, measured between the two inner electrodes, I is the current, in amps, circulated through the outer two electrodes, and K is the geometry factor in meters computed from the electrode spacings. The equation is derived assuming that the subsurface is homogeneous, in which case it would yield the true resistivity of the subsurface. But, since the subsurface is rarely homogeneous near the measurement station, the equation defines the apparent resistivity, a, which represents a weighted average of true resistivities of the subsurface. If the electrodes are spaced equally along a line with separation (a) the array is known as a Wenner array and K=2?a. In field settings, the metal electrodes placed in the soil develop a potential due to local variations in the chemistry of the moisture in the soil. To minimize this potential, the current commonly used is a square wave, and the polarity of the voltmeter is switched accordingly. In resistivity profiling, the electrodes are deployed at a constant separation and the array is moved as a whole along the survey line. The voltage is affected by the material from the surface to infinite depth, but shallow material has the most influence. Profiling can be used to find a buried geologic contact such as a fault between formations of differing resistivities. In environmental work, profiling is used is to search for electrically conductive leachate from a leaking landfill. The method is used in archaeological work to locate ancient buried foundations, moats, paths, roadways, etc. It is important to select an electrode spacing that is appropriate to the features of interest. The model experiment can demonstrate this by acquiring data over objects emplaced at various depths. In addition to constant separation profiling, data are also obtained by vertical electric sounding, in which case the electrode separation is increased to find the variation of resistivity with depth. In the last ten years profiling and sounding have been combined by using apparatus with 20 to 50 electrodes. The current and potential measurements are switched among the electrodes to produce a data cross section that reveals variations laterally and with depth (Berger, 1992, and agiusa.com/sections.shtml) Profiling and sounding can be carried out with table top models but only the constant separation profiling will be discussed here. DC RESISTIVITY MODEL Materials and Equipment - The measurements are scaled-down versions of the procedure used outdoors with commercial equipment. Tap water in a plastic tub provides an ideal host medium. A four-terminal array is deployed at the surface of the water. The geometric factor is constant for the array. Only the voltage at the 594 Journal of Geoscience Education, v. 50, n. 5, November, 2002, p

2 Figure 1. Conceptual diagram for measurement of earth apparent resistivity. The plane of the figure represents a cross section of a uniform earth. Current electrodes are shown at the earth s surface, and are connected to a battery and ammeter; potential electrodes are shown at the earth s surface, and are connected to a voltmeter. The arrows in the subsurface indicate the direction of subsurface current flow, each continuous line in the subsurface is the location of a constant electrical voltage. potential electrodes is measured in the experiment; the current is assumed to be constant. The current electrodes are energized by a function generator; profile data can be obtained over a underwater body such as a brick. The brick can be wrapped in plastic wrap to make it resistive and wrapped in aluminum foil to make it conductive. The electrodes are screws mounted 4 cm apart on an insulating foam plastic bar, as shown in Figure 2. The foam is useful because it floats and tends to keep the electrodes immersed in water at a constant depth. The signal source is a 1000 Hz AC signal from a function generator. The theory of electrical resistivity measurements assumes direct current, but in practice, the use of low frequency AC is equivalent to using DC. The physical model is a plastic tub (dimensions 500 x 300 by 170 mm deep) filled about two-thirds full of tap water. The subsurface body for the resistivity model is a common red brick (dimensions approximately 200 x 90 x 60 mm). The arrangement of the tub, brick and electrode array are shown in Figure 3. The finite size tank has some limitations; the ideal responses for resistivity and self potential assume that the target or source is immersed in a host medium which is an infinite half-space. If the tub is placed on a surface that is not perfectly level, the variation in the depth of water may affect the background voltages from one end of the profile to the other. Figure 2. Details of electrode array for the resistivity model. SAMPLE RESULTS FOR DC RESISTIVITY PROFILING Figure 4 presents a plot of the voltage measured for a profile across an unwrapped brick with a water depth of 15 mm to the top of the brick, with the unwrapped brick and with the brick wrapped in aluminum for with a water depth of 30 mm to the top of the brick. For the shallow brick, the data show high values over the center of the brick. In addition, there are two bumps in the data that occur when the electrode array is over the edges of the brick. If water depth over the brick were less, these bumps would be sharper. They are caused by current deflection at the edge of the brick. Examples of computed apparent resistivities for profiles over narrow resistive bodies shows similar cusps, for example Figure 7.14 page 439 in Reynolds (1997). If the profile were conducted with the electrode array parallel to the long axis of the brick, there should be no bumps. The data over the unwrapped brick at 30 mm depth show a one millivolt positive anomaly over the brick, which is too small to show in the plot. The difference in the responses of the unwrapped brick at 15 and 30 mm illustrate that the constant spacing profile is much more sensitive to shallow objects than to deeper objects. The strength of the response depends on the electrical conductivity of the buried body. For the brick at 30 mm depth wrapped in foil, the data show quite low voltages in the center of the profile. The strong negative response due to the deeper brick wrapped in foil is primarily due to the fact that the resistivity contrast between the water and the aluminum foil is enormous. The foil is approximately 10 8 Young - Tabletop Models for Electrical and Electromagnetic Geophysics 595

3 Figure 3. Arrangement of apparatus for model resistivity profiling. more conductive than the brick. By comparison, the brick without the foil is probably about 10 to 100 times more resistive than the water. SELF POTENTIAL PRINCIPLES Self potential (SP), also known as spontaneous polarization, is natural electrical potential caused by electrochemical (battery-like) reaction of buried conductors with differences in soil moisture chemistry, by seeping water, and by other causes (Reynolds 1997). An SP field survey utilizes non-polarizing electrodes, a digital voltmeter with a high input impedance, and a long reel of single-conductor stranded wire. The field survey is carried out by establishing a base location for one electrode, moving the other electrode along survey lines, and measuring the potential difference between the electrodes with the voltmeter, as illustrated in Figure 5. A common conceptual model for self potential sources is a buried vertical or inclined dipole; that is, a pair of positive and negative current sources. To represent the upper and lower edges of tabular deposits of metallic minerals, the negative and positive current sources would be horizontal lines at the top and bottom of the body, respectively. Figure 4. Profile plots of voltage versus distance for a brick in water. The depth to the top of the unwrapped brick is 15 and 30 mm, and the brick wrapped in aluminum foil is at a depth of 30 mm. SELF POTENTIAL MODEL Materials and Equipment - The self potential model consists of horizontal wires in the water tank. One wire is shallow and one is deep, representing the top and bottom of a tabular conductive body as shown in Figure 6. The wires are energized by a battery instead of natural chemical activity. The wires may be kept in place by any non-conducting improvised holder which does not float such as vertical columns of plastecine modelling clay, drinking glasses, etc. Because the voltages in the model are higher than those in the field, it is not necessary to use non-polarizing electrodes; the multimeter probe tips can serve as the electrodes. Figure 5. Conceptual diagram for field measurement of self potential. SAMPLE RESULTS FOR SELF POTENTIAL PROFILING Figure 7 contains two pots, one is a plot of voltage obtained over the submerged pair of wires for one wire directly over the other and the other is a plot of data with for the wires offset. The depth to the top wire is 15 mm and the depth to the deeper wire is 60 mm. For the vertical pair, the voltage is primarily due to the top wire and the plot is symmetrical. The response is similar to theoretical computations presented in Figure 8.8 part A, 596 Journal of Geoscience Education, v. 50, n. 5, November, 2002, p

4 Figure 6. Arrangement of equipment for model self potential profiling. Figure 7. Profile plot of voltage versus distance for subsurface self potential sources. page 505 of Reynolds (1997). The voltage is asymmetrical for the offset wires, with the steepest side in the direction of the offset of the deeper wire. The response is similar to theoretical computations presented in Figure 8.8 part B, page 505 of Reynolds (1997). ELECTROMAGNETICS MODEL Electromagnetic measurements are widely used in environmental work to locate electrically conductive zones associated with leachate leaking from landfill, and in mining to locate conductive ore bodies. The field measurement has been duplicated in a tabletop model using small coils. The subsurface conductor is a sheet of aluminum. The signal from the receiver is recorded by a digital voltmeter connected to a computer. Measurements may be carried out across vertical and dipping tabular bodies, and at varying heights above a horizontal conductor. To understand the experiment the students need at least an appreciation of the following physics concepts: electrical conductivity and resistivity the magnetic field around a loop of wire energized with direct and alternating current the ability of a coil of wire to detect an oscillating magnetic field measurement of amplitude and phase of an AC signal, and the addition and subtraction of sinusoids of the same frequency but differing magnitudes and phases (phasor arithmetic) the concept of eddy currents induced in a conductor by an oscillating magnetic field An introduction to commerical electromagnetic terrain conductivity meters modeled here may be read online or downloaded at (from McNeil, 1980). The paper presents principles of electromagnetic terrain measurement and presents data from sites surveyed with DC resistivity and with electromagnetic terrain conductivity. The point of the comparison is that an electromagnetic terrain conductivity survey is much quicker to carry out than the resistivity survey but obtains very similar information. ELECTROMAGNETIC GEOPHYSICS PRINCIPLES The most common electromagnetic method is called horizontal loop electromagnetics (HLEM). A conceptual diagram of HLEM being used to detect a subsurface conductor is shown in Figure 8. HLEM utilizes a transmitter loop energized with an alternating current. Usually the loop is placed so that the axis is vertical (and the plane of the loop is horizontal). The transmitter creates an oscillating magnetic field which resembles a small bar magnet held vertically in the center of the loop along the axis. The important difference between the field of the loop and the field of a magnet is that the field of the loop is oscillating, and thus can be detected by an induction coil. A second loop is used to receive the signal some distance away from the transmitter, also held with its axis vertical (and the plane horizontal). In field equipment, the distance between the transmitter and receiver is typically 4 to 100 meters. In the model the distance is 4.5 cm. The primary field from the transmitter loop penetrates into the ground. In conductive ground, it creates eddy currents, creating a secondary field. The receiver loop detects the sum of the primary and the secondary fields. Data shown in mining geophysics literature show two components of received data, an in-phase and a quadrature component (e.g. Beck, 1991), which are used in quantitative interpretation of data, but the model uses the received signal unresolved into components. When data are acquired along a profile, a narrow vertical conductor produces a Young - Tabletop Models for Electrical and Electromagnetic Geophysics 597

5 Figure 9. Detail of transmitter and receiver coil mounting. Figure 8. Conceptual diagram of transmitter and receiver loops, primary field, eddy currents, and secondary field. From Grant and West (1965). characteristic anomaly shaped like a smoothed, stretched out letter M (Figure 7.21 in Beck (1991) and Strangway (1966), and in model data shown later). Physical arguments for the shape of the anomaly are given in Figure 7.22 of Beck (1991). When the apparatus encounters a broad moderately conducting zone, such as a plume of conductive contaminants leaking from a landfill, the response is mainly on the quadrature channel (McNeil, 1980). Some commercial electromagnetic terrain conductivity instruments which are manufactured primarily for the environmental market convert the quadrature channel signal to apparent conductivity, which is displayed on the operating console or recorded on a digital data logger. This electromagnetic terrain conductivity measurement is probably the single most commonly used geophysical tool for environmental site characterization over the past 20 years. The reason it is so popular is that the measurement is fast and simple and the instrument manufacturers have promoted their equipment effectively with case studies and notes. MODEL TRANSMITTER AND RECEIVER The transmitter coil is 28 AWG solid enameled copper wire wound on a plastic sewing machine bobbin, and the receiver is an induction coil sold for recording telephone conversations. Both coils are hot-glued with 45 mm between centers on a thin scrap of plastic or perforated board of approximate dimensions 3 cm by 10 cm by 2 mm, as shown in Figure 2. The transmitter is energized by a 1000 Hz sine wave. This signal from a function Figure 10. Suggested mounting of conductors. generator is connected to an optional step-down audio output transformer, and in turn to the transmitter coil. The output of the pickup coil can be viewed on a digital voltmeter or an oscilloscope. The oscilloscope allows visualization of the phase shift in the waveform, but the digital voltmeter is quicker and easier to read. There are two essential demonstrations or experiments with the apparatus: The response of a buried horizontal conductor as a function of the height of the coils above the conductor like Figures 5 and 6 in McNeil (1980), and the response of a vertical or dipping conductor as a function of horizontal coil position., like figures in Strangway (1966). RESPONSE TO A VERTICAL OR DIPPING SHEET The physical model - The conductive target for the coils is a scrap piece of aluminum sheet approximately 6 by 230 by 150 mm. The aluminum sheet can be mounted inside a inverted shallow plywood box or plastic tub, as suggested in Figure 10, and may be attached to wooden blocks by duct tape. A grid or traverse lines may be 598 Journal of Geoscience Education, v. 50, n. 5, November, 2002, p

6 Figure 11. Top: Data over vertical and dipping conductor as a function of horizontal coil location. The data were originally recorded in units of millivolts but have been converted to percent of the primary signal. Bottom: The configuration of the subsurface conductor. marked on the outside of the top of the box to guide data acquisition. Signal detection and recording - A digital multimeter is used to measure the output of the pickup coils to acquire data along a profile over the model. To produce the plots shown here, data were acquired with the voltmeter attached to a computer. The data were written to a text file, then the file was read into a spread sheet, and a distances were added. The signal voltage was converted to percent of the primary signal as follows: Percent of primary field = 100*(signal along profile - primary signal)/primary signal The primary signal is the coil voltage when it is far away from the conductor. The secondary signal is expressed as a percent of the primary field because it is common practice, and some commercial HLEM geophysics equipment is calibrated to read out in percent. In the tabletop experiment, the primary signal was about 10 millivolts, and the signal when traversing the conductor changed by about plus or minus 5 millivolts. The top panel of Figure 11 shows the results of a profile over the aluminum sheet positioned vertically, and dipping at 45 degrees. The bottom panel shows the subsurface configurations of the conductor. Note that for Figure 12. top: Conceptual oscilloscope display middle: Data over horizontal sheet conductor as a function of coil height with the coils axis horizontal. The coil height was originally measured in millimeters but has been normalized by dividing by the coil spacing. bottom: Definition of coil configurations. (Side view). the dipping conductor, the profile data are asymmetrical with the bigger shoulder in the direction of the dip. These plots are essentially identical to sample curves found in the references, except that the signal is not resolved into in-phase and quadrature components. Small irregularities in the data are probably due to 1. the fact that the signal strength is close to the limit of detection of the digital voltmeter. The data are accurate to only two significant figures, and 2. the difficulty of positioning the (hand held) coils at the correct position along the line. Depending on time and student interest, the experiment can be repeated for coils traversing the edge of a horizontal aluminum sheet. Young - Tabletop Models for Electrical and Electromagnetic Geophysics 599

7 RESPONSE TO A BROAD HORIZONTAL CONDUCTOR The purpose of this set of measurements is to visualize the physical setting and response which produces curves such as Figures 4, 5, and 6 in McNeil (1980). The importance of the curves is that they illustrate the depth sensitivity of the two coil configurations. A broad horizontal conductor may be encountered as a contaminant plume in environmental work, or as conductive overburden in mining exploration. The aluminum sheet is placed flat on the table top. The coils are held at heights above the sheet from zero to about 60 mm. Two sets of data are obtained, one set with the coil axes vertical, and the other with the coil axes horizontal. There is a possibility for confusion regarding the nomenclature of these coil orientations. In the literature from Geonics, (McNeil, 1980) the configuration with the coil axes vertical is termed vertical dipole, in other literature, the same configuration is termed horizontal loops, presumably because the plane containing the coil windings is horizontal for a large hoop-shaped coil. The Geonics nomenclature is used here. McNeil (1980) described the curves in his Figures 4, 5 and 6 as Relative response versus depth for vertical (or horizontal) dipoles. [The] plotted value represents the relative contribution to H s [the secondary magnetic field] from material in a very thin layer dz located at normalized depth z. For the purpose of this set of measurements the secondary field as percent of the primary field may be substituted for relative response. The normalization factor for the horizontal axis in the figures is the intercoil spacing, that is, the depth to the thin plate divided by the coil spacing. In the model, the thin layer is a 6 mm thick plate of aluminum, and the intercoil spacing is 4.5cm. Some discussion with students is necessary to clarify that the signal received by the pickup coil is actually the sum of both the primary signal from the transmitter coils and the secondary signal that is created by eddy currents in the aluminum plate. The sum is not simply the sum of the magnitude of the two signals, but is a sum of two sinusoids with different phases. For the model, it is adequate to simply work with the magnitude of the total received signal. The coils should be held with their axes vertical, and the received signal should be demonstrated at a great height above the conducting plate, in which case the signal is only the primary signal, and at a range of heights, ending with the coils sitting directly on the plate. If a digital oscilloscope is used instead of a digital voltmeter, the signal with the coils high above the plate should be stored in memory for later comparison. It is quite evident in the demonstration that at an intermediate height above the plate (5 to 10 cm) the received signal is larger than the primary signal alone by several percent. As the coils come closer to the plate, the received signal becomes smaller, and returns to the same amplitude as the primary field or less. With the coils setting directly on the plate, the received signal is slightly smaller than the primary signal alone. The configuration of coils and conductor are shown in the bottom panel of Figure 12. The top panel is a simulated oscilloscope display of the signals for various heights of the coils above the conductive plate. The sequence of measurements is similar to that previously described, except that the plate was horizontal and the coils were moved vertically, over a height from about 0 to 60 mm above the plate. The data were processed as described earlier to yield percent of the primary field, resulting in the plots in the center panel of Figure 12. These are essentially identical to Figure 5,6 and 7 in McNeil, with the exception being that values could not be obtained at zero height above the plate due to the finite thickness of the coils, and there is a small amount of noise in the data. The lessons to be learned from the curves are: 1. Measurements made with the coil axes vertical have their geatest sensitivity to conductive material at a depth of about 0.55 times the coil spacing (0.4 in McNeil (1980), 2. Measurements made with the coil axes horizontal have their greatest sensitivity to conductive material near the surface, 3. Both coil configurations are sensitive to conductive material over a range of depths. The measurement should also be repeated over ferrous metal (e.g. a scrap of angle iron). The response is large and the received signal is larger than primary signal alone. The results could lead to a discussion about how to discriminate between ferrous and non-ferrous metal. This principle is used in metal detectors. CONCLUSIONS Table top models have been described which demonstrate electrical resistivity, self potential and electromagnetic geophysics responses. The models are made of simple materials and can be used to supplement introductory classes in geology, mining, or environmental studies. The results give data plots similar to theoretical computations and field data. This approach should be useful in classes which cover geophysical methods, but which may not have the opportunity for outdoor work. An electronic expanded version of this paper is available from the author which contains more detailed instructions for carrying out the experiment and a list of materials. AKNOWLEDGMENTS The concept of the use of models to obtain characteristic response curves for electromagnetic prospecting is a classic subject which was well established at the time of Strangway (1966). The author s interest in the subject 600 Journal of Geoscience Education, v. 50, n. 5, November, 2002, p

8 was stimulated by a attention-getting demonstration of a model time domain electromagnetic transient system demonstrated in the convention booth of Electromagnetic Systems Inc, a commercial electromagnetic geophysics service company, and by quantitative work by Clay et al (1974). REFERENCES CITED Avants, B., Soodak, D., Ruppeiner, G., 1999, Measuring the electrical conductivity of the earth, Am. J. Phys, v. 67, p Beck, A. E., 1991, Physical Principles of Exploration Methods, Wuerz Publishing Ltd, Winnepeg, Manitoba, Canada Boyd, T., 2000, Introduction to Geophysical Exploration, /tboyd/gp311/. Burger, H. R., 1992, Exploration Geophysics of the Shallow Subsurface, Prentice Hall, Englewood Cliffs, New Jersey, 489 p. Clay, C. S. and Greisher, L. l., and Kan, T. K., 1974, Matched filter detection of electromagnetic transient reflections, Geophysics, v. 39, p Grant, F. S., and West, G. F., 1965, Interpretation Theory in Applied Geophysics, McGraw Hill, New York, 584 p. McNeill, J. D., 1980, Electromagnetic Terrain Conductivity Measurement at Low Induction Numbers, Technical Note TN-6, Geonics Ltd., 1745 Meyerside Drive, Ontario, Canada. Can be downloaded from lit.html. Reynolds, J. M., 1997, An Introduction to Applied and Environmental Geophysics, Wiley, New York, 796 p. Strangway, D., 1966, Electromagnetic parameters of some sulfide orebodies, p in Hansen, D.A., Heinrichs, W. E., Holmer, R. C., MacDougall, R. E., Rogers, G. R., Sumner, J.S., and Ward, S. H. eds, Mining Geophysics Volume I Case Histories, Society of Exploration Geophysicists, Tulsa, Oklahoma, 492 p. Telford, W. M., Geldart, L. P., Sheriff, R. E., 1990, Applied Geophysics, 2nd ed., Cambridge University Press, Cambridge, 770 p. Young - Tabletop Models for Electrical and Electromagnetic Geophysics 601