Quantitative analysis of self-potential anomalies: Review of case studies from various SP applications


 Self-potential (SP) method is one of the most non-expensive and unsophisticated geophysical methods. However, its application limits absence of reliable interpreting methodology, first for the complex geological-environmental conditions. The typical disturbances appearing in the SP method are discussed. To exclude these noise components before the quantitative analysis, some ways for their removing (elimination) are presented. Some brief review of the available interpretation methods is presented. For the magnetic method of geophysical prospecting, special quantitative procedures applicable under complex physical-geological environments (oblique polarization, uneven terrain relief and unknown level of the normal field), have been recently developed. Earlier detected common peculiarities between the magnetic and SP fields have been extended. These common aspects make it possible to apply the advanced procedures developed in magnetic prospecting to SP method. Besides the reliable determination of the depth of anomalous targets, these methodologies enable to calculate the corrections for non-horizontal SP observations and direction of polarization vector. For classification of SP-anomalies is proposed to use a new parameter – 'self-potential moment'. These quantitative procedures (improved modifications of characteristic point, tangent techniques and areal method) have been successfully tested on SP models and employed in real situations in mining, archaeological, environmental and technogenic geophysics. The obtained results indicate practical importance of the developed methodologies.

reliable determination of the depth of anomalous targets, these methodologies enable  conductors. An appearance of these conditions is usually impossible without the 46 underground water contact (Sato and Mooney, 1960). 47 In the geological section, the conditions for the formation of a galvanic cell arise 48 on targets with electronic conductivity, if these bodies are in the water-saturated rocks 49 with ionic conductivity. The change in the redox conditions at the contact of the 50 electronic conductor (anomalous target) and the surrounding medium is associated 51 with a decrease in the oxygen content with a depth. 52 Fox's (1830) SP observations at copper vein deposits in Cornwall (England) laid 53 the foundation of the application of all electric methods in geophysics as a whole. SP 54 is an effective, prompt and comparatively simple geophysical method. Equipment for 55 SP method is one of the most non-expensive in the field geophysics (Table 1).  Table 1. Averaged prices for geophysical potential field equipment 58 Takum, 2015; Cui et al., 2017). Application of quantitative analysis in the SP method 79 for solving other geological-geophysical problems is beyond the scope of this study.  83 Main kinds of noise appearing in the SP method are shown in a block-scheme ( Figure   84 1). Some of these noise effects are considered below in detail.  86 Although the fact that SP electrode is called as "non-polarizable", after some time it 87 accomplishes some polarization effects from the surrounding media. However, taking 88 into account that we measure the value DU (U1 -U2), the most is important is to keep 89 not absolute non-polarizability, but an equivalent polarization on the both applied 90 electrodes. For checking this equivalent, the following procedure can be employed in 91 field conditions (of course, measurements in a physical laboratory are more precise). 92 We can write a trivial equation for first electrode: U1 + e1 (U1 is the first "medium" 93 signal, and e1 is the noise accumulated in the first electrode). For second electrode, 94 correspondingly we have U2 + e2 (U2 is the second "medium" signal, and e2 is the noise 95 of accumulated in the second electrode). According to (Semenov, 1980), we measure 96 (1) 97 Let us will change electrodes by their places. In this case we will obtain 98 (2) 99 After this, calculating a difference between DU1 and DU2, we receive    (Khesin et al., 1996).

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From other side, as follows from the very detailed SP measurements of Ernstson 130 and Schrerer (1986), at the inclined topographic surface the SP field directly increases 131 with relief form heightening (Figure 2). In the last case, for elimination of the terrain 132 relief influence, a correlation method developed in magnetic prospecting (Khesin et 133 al., 1996) and VLF studies (Eppelbaum and Mishne, 2011) can be applied 134 (employment of other methods to reduce the relief influence is also possible). The where h is the height of relief, b is the angle coefficient, and c is the free member.

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Value DUappr approximates the observed field as a function of elevation h 141 (anomalous zones usually do not include to the correlation field) and then we obtain 142 corrected (residual) field DUcorr, where the relief influence is essentially eliminated:   Many scientists note that after rains the intensity of SP anomalies increases (e.g., 164 Semenov, 1980;Parasnis, 1986;Revil and Jardani, 2013). Therefore, occasionally an 165 artificial irrigation of site intended for SP research is recommended.

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An extensive literature is devoted to the interpretation of self-potential anomalies. were not included in this review.

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The calculation of theoretical anomalies due to SP has long been based primarily 199 on Petrovsky's (1928) solution derived for a vertically polarized sphere (Zaborovsky,200 1963). Later on, some substantial solutions for sheet-like bodies and inclined plates 201 were obtained (Semenov, 1980). The electric polarization vector was generally 202 considered to be directed along the sheet-like body dipping (along the longer axis of 203 the conductive body).

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Other method of SP anomaly quantitative interpretation includes anomalous 205 body with a simple geometrical shape which approximates the anomaly source. Its comparison of the observed anomaly with a set of master curves (Semenov, 1980). where j is the current per unit length, r is the host medium resistivity, r1 and r2 are the       The procedure based on interpretation of self-potential anomalies due to simple

SOME COMMON ASPECTS OF MAGNETIC AND SP FIELDS 290
The magnetic field is a potential one (when value of target's magnetization is not very 291 high) and satisfies Poisson's equation:

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where Ua is the anomalous magnetic field and V represents the magnetic potential.

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Analytical expressions for some interpreting models for magnetic and SP fields 308 are presented in Table 2. . grad on SP anomalies method of the total normalized gradient developed in gravity     Table 3).     Besides the geometric parameters of anomalous target, the self-potential moment 388 can also be determined (see Table 3). For the models of thin bed and HCC, the self- Here the subscripts "r" and "f" stand for a parameter of real and fictitious self-potential 406 moments, respectively.

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Undoubtedly, calculation of all aforementioned parameters from SP data 408 should be joined to a unified computerized system with a minimal participation of an 409 interpreter.

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For testing some SP anomalies, software for 3D computation of magnetic field 411 may be applied. In this case, magnetic vector orientation can be utilized as analogue 412 of self-potential vector.     Obviously, absence of reliable methodologies for quantitative analysis of SP 509 anomalies, weak SP anomalies and different kinds of noise impedes a wide 510 employment of self-potential method in archaeological prospection.

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The territory of Israel contains more than 35,000 discovered archaeological sites 512 of different age and origin. For SP observations several typical archaeological sites 513 located in different areas of the country were selected (Eppelbaum et al., 2003b(Eppelbaum et al., , 2004.

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All SP measurements were performed using microVoltmeter with high input 515 impedance and distinctive non-polarizable electrodes (Cu in CuSO4 solution). The 516 interpretation results obtained earlier at these sites were revised and generalized (the 517 unified methodologies were employed). 518 519 The remains of the city of Banias are located in northern Israel, at the foot of Mt.

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Hermon. Banias was the principal city of the Golan and Batanaea regions in the Roman 521 period and occupied an area of more than 250 acres (Reich, 1992;Meyers, 1996). Here and was founded as a way-station for Nabatean (7 th -2 nd centuries BC) traders traveling 545 between Petra (Jordan) and Gaza. This site was occupied mainly throughout the 546 Byzantine period (4 th -7 th centuries AD) (Kenyon, 1979;Kempinski and Reich, 1992).  Biblical history. The site is situated roughly halfway between Jerusalem and Tel Aviv 564 (central Israel). The Crusaders rebuilt it on a smaller scale in the 12th century (Meyers, 565 1996). Nikopolis is displayed in almost all Christian Pilgrim texts from the 4 th century 566 onward; in majority of archaeological sources this site is named as Emmaus-Nikopolis. 567 Many scientists note that this site is characterized by multilayer sequence (e.g.,

Buried cavities in dolomitic limestone (southern Italy)
Several impressive examples of SP application for detection of underground cavities 588 in southern Italy were displayed in Quarto and Schiavone (1996). Let us will consider 589 one of these field cases, where the buried karst cavity exists in dolomitic limestones 590 ( Figure 17). The cavity is horizontally extended and over it a significant SP anomaly 591 (up to 100 mV) was observed. Quantitative examination along profile A -B crossing 592 a center of this anomaly has been performed ( Figure 18). For interpretation models of 593 thin bed (upper edge) and center of HCC were obtained depths of 6.0 and 9.5 meters, 594 respectively. Self-potential vector is oriented near-vertically. Self-potential moment of 595 anomaly from this cave is about .   The calculated self-potential moments for the variety of investigated targets are 643 compiled in Table 5. Values of self-potential momentpresented in Table 5  Self-potential method is one of the oldest and simultaneously non-expensive 657 geophysical methods. One of its main preferences is that the presence of water in Emmaus-Nikopolis (SP map is presented in Figure 15). Black arrow shows direction of