Groundwater Geophysics Phần 3 docx

96 Kord Ernstson, Reinhard Kirsch (layer i) with thickness h i in a sounding curve supplies a substitute resistiv- ity ρ* i and substitute thickness h * i : LTi ρ⋅ρ=ρ ∗ (3.6) L T ii hh ρ ρ ⋅= ∗ (3.7) While for the substitute resistivity ρ L < ρ* i < ρ T , the substitute thickness h* i is larger than the true thickness h i by a multiplier of λ=(ρ T/ ρ L ) 1/2 , λ be- ing the coefficient of anisotropy (Fig. 3.9). Fig. 3.9. Electrical anisotropy on different scales: a macroanisotropic resistivity section with average transverse and longitudinal resistivities ρ T and ρ L (left) and a single microanisotropic layer with transverse and longitudinal resistivities ρ T and ρ L (right). Interpretation of the sounding curve leads to higher thickness of the mi- croanisotropic layer (h 3 * ) than in reality Geoelectric anisotropy is a matter of scale and of the resolution of a ver- tical resistivity section. While graphite, a slate or a lake sediment may be termed microanisotropic, a sequence of well-defined electrically isotropic beds can behave macroanisotropic if they are not resolved in a geoelectric sounding curve (see, e.g., the ten-layer case in Fig. 3.8). 3 Geoelectrical methods 97 For a macroanisotropic section, average longitudinal and average trans- verse resistivities can be calculated from the parameters of the single beds (Fig. 3.9): iiiL /h/h ρ ∑∑ =ρ ∗ (3.8) ∑ ρ ∑ =ρ ∗ iiiT h/h (3.9) Substitute resistivity and thickness as well as coefficient of anisotropy are the same as for microanisotropic behavior (3.6, 3.7). Equivalence between true resistivity sections and sections with substi- tute layers due to anisotropy may cause serious modeling and interpreta- tion errors if the anisotropy (both macro and micro) is not recognized. As can be calculated from Eqs. 3.6 - 3.9, intermittently occurring high- and low-resistivity beds may lead to large coefficients of anisotropy and, cor- respondingly, to large errors in modeled thicknesses. Anisotropy also leads to discrepancies between results of vertical elec- trical soundings and electromagnetic induction measurements (horizontal current flow-lines). Comparing VES date with data from resistivity bore- hole logging (mostly horizontal flow lines), anisotropy must also be taken into consideration. 3.2.5 Geological and hydrogeological interpretation The discussion of the principle of equivalence shows that singular depth soundings are in general little meaningful. Likewise, the sometimes used term "electrical drilling" should basically be avoided, because VES is not intended to and cannot replace boreholes but is methodically a different complex. VES interpretation comprises the more or less synchronous han- dling of measured sounding curves in the survey area and their modeling results. Continuity of layers in the area should be checked as well as the reality of obvious breaks in the geologic layering. With regard to equivalence, reinterpretation of some soundings can be necessary, and additional field measurements may be helpful. In areas of young Cenozoic unconsolidated deposits (molasse, glacial sediments) with rapidly changing thicknesses (Fig. 3.10A), data of a key borehole may be required to fix modeling parameters and thus to get absolute depths inde- pendent of equivalence. In hard sedimentary rocks where stratigraphic standard thicknesses and rock resistivities are frequently well known and constant over large areas, VES modeling and interpretation may be easier leading to a detailed knowledge of the tectonics in many cases (Fig. 3.10B). 98 Kord Ernstson, Reinhard Kirsch As the final result, a resistivity model of the project area which is geologi- cally and hydrogeologically reasonable and without discrepancies with drilling or other geophysical results should be obtained. Fig. 3.10. Resistivity depth profiles from vertical electrical soundings. A: Quater- nary sandy aquifer partly covered with till, B: tectonic graben as a fractured and partially karstified limestone aquifer 3.3 Resistivity mapping Targets of resistivity mapping (or profiling) are near surface resistivity anomalies, caused by, e.g., fracture zones, cavities or waste deposits. Any common electrode configuration (e.g., Wenner or Dipole-Dipole) can be used for mapping purposes. In general, the chosen four-point configuration 3 Geoelectrical methods 99 is kept constant and moved along profiles, while apparent resistivity is recorded (Fig. 3.11). Prior to the field works, optimum electrode spacing of the configuration can be determined by model calculations, if assump- tions on resistivity and depth of the target and on resistivity of the sur- rounding material are possible. I U apparent resistivity distance Fig. 3.11. Resistivity mapping with a dipole-dipole configuration Another common array is the gradient array (Fig. 3.12). Here electrodes A and B are fixed and only electrodes M and N are moved, and a rectangular area between the electrodes is mapped. The apparent resistivities are calcu- lated from (3.1, 3.2) and plotted as a map of isoohms (Fig. 3.13). Instead of point electrodes line electrodes may be used for current injection (e.g. grounded cables or a number of lined-up connected steel rods). Although the mapping response of an arbitrary resistivity distribution can be calculated, interpretation is in general done qualitatively by locating structures of interest and outlining their extension and strike. Nevertheless, a study of resistivity mapping model curves (see, e.g., Keller & Frischknecht 1970, Schulz 1985) may be very useful to learn that even simple geometries may produce complex apparent-resistivity profiles and that anomalies may be quite different when measured with different electrode configurations. 100 Kord Ernstson, Reinhard Kirsch Fig. 3.12. Gradient array for resistivity mapping 0 20406080100120140 0 10 20 30 40 90 105 120 135 150 m m Ohmm Fig. 3.13. Apparent resistivities over fracture zones in limestone mapped by gra- dient array 3.3.1 Square array configuration The square array configuration is especially designed for the mapping of resistivity anisotropy, caused by e.g. fracture zones. Fracture zones may behave electrically anisotropic, because the resistivity parallel to strike is in general lower than perpendicular. The electrodes are arranged to form a square (Fig. 3.14) whose side length is a, and the apparent resistivity as- signed to the midpoint is computed from I U K A ⋅=ρ (3.10) with the geometric factor of the square array defined by 22 a2 K − π = (3.11) At each location, the square is rotated by 45°, and four apparent resistivity values ρ A1 ρ A4 are measured (Fig. 3.14). They depend on the resistivity 3 Geoelectrical methods 101 anisotropy and on the strike of the fracture zone which can be deduced graphically or analytically (Lane et al. 1995, Habberjam 1975). Using ani- sotropy as defined by Habberjam (1975), secondary porosity (porosity of the fractures) can also be estimated from the measured apparent resistivi- ties (Taylor 1984). Fig. 3.14. Field layout of square array configuration For mapping purposes, square arrays are positioned to form a conti- nuous row (Fig. 3.15). Side length a of the squares depends on the penetra- tion required, a typical value is a=5m. Fig. 3.15. Square array mapping 102 Kord Ernstson, Reinhard Kirsch For the assessment of secondary porosity the following quantities are calculated from the measured apparent resistivities: ()() [ ] [ ] 2/12/1 2A4A1A3A )2(2)2/(2/3A +⋅ρ+ρ+ρ+ρ= (3.12) ()() [ ] [ ] 2/12/1 4A2A3A1A )2(2)2/(2/3B +⋅ρ+ρ+ρ+ρ= ()() [ ] [ ] 2/12/1 3A1A2A4A )2(2)2/(2/3C +⋅ρ+ρ+ρ+ρ= ()() [ ] [ ] 2/12/1 1A3A4A2A )2(2)2/(2/3D +⋅ρ+ρ+ρ+ρ= 2222 DCBAT −−−− +++= [] 2/1 222222 )CD()BA(2S −−−− −+−= [] 2/1 )ST/()ST(N −+= Secondary porosity Φ can then be calculated after )(CN )1N)(1N(1041.3 minmax 2 24 ρ−ρ −−⋅ =φ (3.13) with: C conductivity of groundwater (microsiemens/cm) ρ max , ρ min maximum and minimum apparent resistivity. However, it should be kept in mind that only a rough estimate of frac- ture pore space can be obtained. Fracture fillings of clay or clay/water can lead to incorrect results. 3.3.2 Mobile electrode arrays Mobile electrode arrays are useful for mapping of large areas, and in some circumstances they may be an alternative to electromagnetic soundings with moving transmitter - moving receiver arrays. A number of ingenious instruments has been developed, e.g., with electrodes mounted on wheels or pushed into the ground pneumatically. Two instrumentations especially designed for groundwater exploration and brownfield mappings are pre- sented here: the pulled array by the Hydrogeophysics Group, University of Aarhus, and the OhmMapper by Geometrics Inc. 3 Geoelectrical methods 103 Pulled array configurations To cover large areas with spatially dense measurements, a towed electrode array was developed by Hydrogeophysics Group, Aarhus University. Orig- inally designed for resistivity mapping (pulled array continuous electrical profiling, PACEP) in Wenner configuration with electrode spacing of 10m, 20m, and 30m, the electrode array has been extended to allow resistivity soundings with 8 electrode spacing ranging from 2m to 30m in Wenner and dipole-dipole configuration (pulled array continuous electrical sound- ing, PACES). Electrodes are steel cylinders coupled by weight to the ground. Measurements are typically made at 1m intervals along the survey lines, with the distance between lines being 50-300m. With the PACEP method, two people can complete 10 to 15km of profile in one day. Fig. 3.16. PACES electrode configuration, activated electrodes for Wenner mea- surements are in black OhmMapper OhmMapper is also a towed instrument, but without galvanic ground coupling. The basic principle is shown in Fig. 3.17. Two conducting plates on the ground are electrically charged like a capacitor by AC current. In the ground, the opposite charge occur leading to balancing currents. As in classical resistivity methods, the resulting potential difference is measured. For practical use, the capacitors for energizing the ground are replaced by electrified cables acting as transmitter dipole. The instrument is operated in dipole-dipole configuration, penetration depth depends on dipole spacing. Instrument frequency is 16.5 Hz. 104 Kord Ernstson, Reinhard Kirsch Fig. 3.17. Basic principle of capacitively coupled OhmMapper system 3.3.3 Mise-à-la-masse method The mise-à-la-masse method originally used as a geophysical technique in mining only, has enjoyed some revival in environmental geophysics and hydrogeology. It is a kind of cross between resistivity and self-potential measurements. The technique uses a four-point electrode configuration as shown in Fig. 3.18. One current electrode (B) and one potential electrode (N) are (theoretically) set to infinity, and the potential electrode M serves to measure the potential field related with the current that is injected at electrode A. In an electrically homogeneous ground, the equipotentials are hemispherical (Fig. 3.18A). If, however, a buried conductive body is con- tacted by the current electrode A (Fig. 3.18B), then the potential distribu- tion at the surface will reflect the shape of the body and its spatial position which is the objective of a mise-à-la-masse survey. Different from other geophysical methods, the target must be known at one point at least in order to contact it, e.g., by a borehole. While in min- ing the electrically charged body is an ore body, groundwater is normally mise-à-la-masse-contacted for hydrogeological and environmental geo- physical purposes. Mise-à-la-masse is used to track groundwater flow paths, to evaluate contaminant plumes near waste disposal sites, and to de- lineate the migration of conductive tracers (Nimmer & Osiensky 2002). 3 Geoelectrical methods 105 Fig. 3.18. Principle of the mise-à-la-masse method 3.4 Self- potential measurements Self-potential (or spontaneous potential, SP) measurements belong to the earliest methods used in applied geophysics. Originally applied in mining to ore body exploration, SP became a standard tool with borehole logging and is now of increasing interest in environmental geophysics, geothermal application, and hydrogeology. Self potentials describe natural electrical direct currents originating from various electrochemical, electrophysical, and bioelectrical processes in the ground. Reduction and oxidation processes above and below the ground- water table define mineralization potentials of some 100 millivolts related with highly conductive ore bodies or graphite deposits. Electrochemical potentials in the order of ten millivolts result from ion flow in connection with variable electrolytic concentrations of the ground water and with clay mineral membrane effects. Heat flow may produce SP anomalies, and hy- drogeologically most relevant are streaming (or electrokinetic or filtration) potentials from ground-water flow in porous rocks. 3.4.1 Basic principles of streaming potential measurements In porous rocks, the contact between rock matrix and pore fluid is charac- terized by an electric double layer (Helmholtz double layer). Electrically charged, this double layer usually fixes pore fluid anions while cations re- main mobile. On water flow, the cations are transported, synonymous with [...]... Geophysics 4:1 13- 1 23 Edwards LS (1977) A modified pseudosection for resistivity and induced polarisation Geophysics 42:1020-1 036 Ernstson K, Scherer HU (1986) Self-potential variations with time and their relation to hydrogeologic and meteorological parameters Geophysics 51:1967-1977 Fox RC, Hohmann GW, Killpack TJ, Rijo L (1980) Topographic effects in resistivity and induced-polarization surveys Geophysics. .. and 150 m 116 Markus Janik, Heinrich Krummel 3. 6 References Advanced Geosciences Inc (2002) EarthImager, 2D Resistivity and IP Inversion Software Baker SS, Cull JP (2004) Streaming potential and groundwater contamination Exploration Geophys 35 :41-44 Barker RD (1989) Depth of investigation of collinear symmetrical four-electrode arrays Geophysics 54:1 031 -1 037 Barker RD (1992) A simple algorithm for electrical... flow, diffusion, and advection in a laboratory sand box Vadose Zone J 3: 1180-1192 3 Geoelectrical methods 117 Mundry E (1985) Gleichstromverfahren In: Bender F (ed) Angewandte Geowissenschaften Bd 2 Enke Verlag, Stuttgart, pp 299 -33 8 Mundry E, Dennert U (1980) Das Umkehrproblem in der Geophysik Geologisches Jahrbuch, Reihe E19:19 -39 Nimmer RE, Osiensky JL (2002) Using mise-a-la-masse to delineate the... (20 03) Principles of electrography applied to self-potential sources and hydrogeological applications Water Resources Res 39 : 1114,doi:10.1029/2001WR000916 Rizzo E, Suski B, Revil A, Straface S, Troisi S (2004) Self-potential signals associated with pumping tests experiments J Geophys Res 109:B102 03, doi:10.1029/2004JB0 030 49 Roy A, Apparao A (1971) Depth of investigation in direct current methods Geophysics. .. Geophys Res 109:B102 03, doi:10.1029/2004JB0 030 49 Roy A, Apparao A (1971) Depth of investigation in direct current methods Geophysics 36 :9 43- 959 Schulz R (1985) Interpretation and depth of investigation of gradient measurements in direct current geoelectrics Geoph Prosp 33 :1240-12 53 Taylor RW (1984) The determination of joint orientation and porosity from azimuthal resistivity measurements In: Nielsen DM,... Water 36 :779-782 Bogoslowsky VA, Ogilvy AA (1972) The study of streaming potentials on fissured media models Geophys Prosp 20:109-117 Buselli G, Lu K (2001) Groundwater contamination monitoring with multichannel electrical and electromagnetic methods J Appl Geophys 48:11- 23 Corvin RF (1990) The self-potential method for environmental and engineering applications Geotechnical and Environmental Geophysics, ... ground (Rizzo et al 2004) and with the contours of the ground-water table (Birch 1998, Revil et al 20 03) m MILLIVOLT 140 16 120 14 12 100 W 80 10 8 60 6 40 4 20 0 2 0 20 40 60 80 100 120 140 160 m 0 Fig 3. 21 Self-potential anomalies around a well (w) during a pumping test 3 Geoelectrical methods 109 3. 5 2D measurements Markus Janik, Heinrich Krummel Sounding and profiling can be combined in a single... bedrock in New Hampshire Ground Water 33 :476-485 Lange G (1997) Geoelektrik In: Knödel K, Krummel H, Lange G (eds) Handbuch zur Erkundung des Untergrundes von Deponien und Altlasten, Bd 3 Geophysik Springer, Heidelberg, pp 122-165 Loke MH, Barker R D (1996) Rapid least-squares inversion of apparent resistivity pseudosections using a quasi-Newton method Geophys Prosp 44: 131 –152 Maineult A, Barnabé Y, Ackerer... profile should be determined 3. 5 .3 Data Processing and Interpretation For many groundwater- related problems it is preferable to carry out 2D resistivity measurements instead of 1D soundings and/or profiling The aim of a geoelectrical survey at the Earth surface is to provide detailed information about the lateral and vertical resistivity distribution in the ground Unfortunately 3D measurements still are... the data 3 Geoelectrical methods 1 13 3.5.4 Examples The following example describes the investigation of a dyke The objective was to map a marl layer, which is the first low permeable layer and was used as the base of the dyke Depth profile of this layer and sandy intrusions within the marl were targets of this measurement Parameters of the dc resistivity survey example: Profile length: 135 m Electrode . ()() [ ] [ ] 2/12/1 2A4A1A3A )2(2)2/(2/3A +⋅ρ+ρ+ρ+ρ= (3. 12) ()() [ ] [ ] 2/12/1 4A2A3A1A )2(2)2/(2/3B +⋅ρ+ρ+ρ+ρ= ()() [ ] [ ] 2/12/1 3A1A2A4A )2(2)2/(2/3C +⋅ρ+ρ+ρ+ρ= ()() [ ] [ ] 2/12/1 1A3A4A2A )2(2)2/(2/3D. Ernstson, Reinhard Kirsch Fig. 3. 12. Gradient array for resistivity mapping 0 20406080100120140 0 10 20 30 40 90 105 120 135 150 m m Ohmm Fig. 3. 13. Apparent resistivities over fracture. (Fig. 3. 9): iiiL /h/h ρ ∑∑ =ρ ∗ (3. 8) ∑ ρ ∑ =ρ ∗ iiiT h/h (3. 9) Substitute resistivity and thickness as well as coefficient of anisotropy are the same as for microanisotropic behavior (3. 6,