## 1. Introduction

The piezoelectric and seismo-electrokinetic phenomena are manifested by electrical and electromagnetic processes that occur in rocks under the influence of elastic oscillations triggered by shots or mechanical impacts (hits) [

1,

2,

3,

4,

5,

6,

7,

8,

9,

10,

11,

12,

13,

14,

15,

16,

17,

18,

19,

20,

21,

22,

23,

24,

25,

26,

27,

28,

29,

30,

31,

32].

Because the manifestation patterns of the above phenomena are different in different rocks, these phenomena can be used as a basis for geophysical exploration techniques. In this paper, it is assumed that the studied piezoelectric and seismoelectric anomalies cannot be separated from one another, since the anomalous targets with the contrast piezoelectric properties as a rule occur in sedimentary host deposits where the seismoelectric effects take a place.

The piezoelectric method is an example of a successful application of piezoelectric/seismo-electrokinetic phenomena in exploration geophysics. It has been successfully applied in mineral exploration and environmental features research in Russia, USA, Canada, USA, Australia and other countries. The greatest contribution to the piezoelectric method application in subsurface geophysics (since the mid-1950s) was made by Naum Neishtadt (1929–2016) (

Figure 1).

Interpretation of seismoelectric/piezoelectric anomalies is often carried out using procedures similar to those employed in seismic prospecting. In the paper, it is shown that quantitative interpretation of expressed anomalies observed in near-surface may be performed using the methods developed for potential geophysical fields.

## 2. A Brief Background

This method is based on the piezoelectric activity of rocks, ores, and minerals. It enables direct exploration for pegmatite, apatite-nepheline, essentially sphalerite, and ore-quartz deposits of gold, tin, tungsten, molybdenum, zinc, crystal, and other raw materials. This method also enables differentiation of rocks such as bauxites, kimberlites, etc., from the host rocks, by their electrokinetic properties [

14].

Classification of some rocks, ores, and minerals by their piezoactivity is given in

Table 1. These objects (targets) transform wave elastic oscillations into electromagnetic ones. It should be take into account that, sometimes, anomalous bodies may be detected not by positive, but by negative anomalies, if low-piezoactive body occurs in the higher piezoactive medium.

The piezoelectric method is an example of successful application of piezoelectric/seismo-electrokinetic phenomena in exploration and environmental geophysics and designed for delineation of targets differing from the host media by piezoelectric properties [

14,

30]. This method can be employed in surface, downhole, and underground modes.

Experimental investigations enabled obtaining the main equation of the piezoelectric effect [

30]:

where

ε is the dielectric constant, and

σ is the electric conductivity of rock. It explains why the piezoelectric effect may be registered by both observations of intensities of electric field

E and magnetic field

H.

Recent testing of piezeoelectric effects of archaeological samples composed from the fired clay have shown values of (3.0–4.0) × 10^{−14} C/N (Coulomb/Newton).

An observation scheme for ground surveys using the piezoelectric method is presented in

Figure 2. The conventional piezoelectric measurements are conducted using electrodes, while the geophones play a subsidiary role for monitoring intensity of the elastic oscillation generation and behavior of the initial seismic field.

## 3. Can Piezoelectric and Seismoelectric Effects Be Related to Potential Fields?

The seismo-electrokinetic (electrokinetic) phenomenon

E in rocks is triggered by the potential gradient due to the displacement of liquid phase relative to the solid “skeleton” of the rock under the elastic wave influence. Essential similarity of this phenomenon to potential produced by water flow in rocks proposes a similar origin for these phenomena [

33].

Firstly, Ivanov [

34] discovered the seismoelectric effect

E in the rocks of sedimentary complex. He proposed a filtration hypothesis consisting of that in the sedimentary rocks occurs a double diffusion layer at the boundary between hard particles and liquid. A propagation of elastic waves causes a relative distortion of electrolyte and hard phase; thus, equilibrium condition in the double electric layer is distorted. This effect generates appearance of so-called filtration potential

U, flow (streaming) potential, an instantaneous value of which is determined over a part of the length of the elastic wave by the equation of Helmholtz–Smoluchowsky [

35]:

where

ρ_{1} and

ρ_{2} are the instantaneous pressure values in the section under consideration;

k is the coefficient calculating the dynamics of the elastic wave distribution,

ε is the dielectric constant,

ζ is the potential of the double electric layer,

η is the solution viscosity, and

σ is the conductivity.

Frenkel [

36] offered a mathematical description of the seismo-electric phenomenon

E, which was based on the Ivanov’s [

34] hypothesis regarding the electro-filtration nature of this phenomenon. Frenkel described compression and stretching of rock particles and pores, as well as of the pore moisture, under the influence of the elastic wave propagation. Moreover, he proposed an equation that described the propagation of elastic waves in moisturized soil. For calculating electro-kinetic potential, this equation uses the Helmholtz–Smoluchowski equation that describes the intensity of longitudinal electric field for stationary flow of liquid through the pores of the solid “skeleton”:

where

μ is the coefficient of viscosity of the medium,

i is the complex-valued electric field intensity,

$\beta =\frac{1}{f\left(1+\alpha \right)},$ α is the parameter that describes the mechanical properties of the medium,

${\beta}^{\prime}=1+\left(\beta -1\right)\frac{{K}_{2}}{{K}_{0}},$ K_{0} is the coefficient of compressibility of the solid phase,

$\alpha =\frac{{K}_{1}}{f}$ is the coefficient of permeability,

r is the pore radius,

f is the porosity,

K_{1} is the coefficient of permeability of the soil,

ρ_{2} is the true specific gravity of the pore moisture,

K_{2} is the coefficient of compressibility of the liquid phase,

ω_{0} is the propagation velocity of the longitudinal elastic wave, and

u is the displacement.

Equation (2) shows that the electric field intensity is proportional to porosity and is independent of the pore radius, because the α coefficient is proportional to the square of this radius. With the assumed values of displacement, the electric field intensity is proportional to the square of frequency of the elastic oscillations. In the above formula, the author assumes that the period of time required to produce the electro-kinetic potential gradient is negligibly short compared to the oscillation period 2π/ω. This is why the value of E at any given moment practically coincides with the value corresponding to the instantaneous value of the relative velocity.

To confirm Ivanov’s [

34] suggestion on the nature of this effect in rocks, Volarovich and Parkhomenko [

1] put experiments to reproduce this phenomenon on the artificially moistened rock samples under the laboratory conditions. They found that before the artificial moistening, the dolomite sample did not show any elastic oscillations when electrified; after the moistening, the appearance of an electric potential was observed on its faces. At the same time, the sign of the charge did not depend on which side of the sample the charges were taken from, but determined by the gradient of the pressure drop.

Parkhomenko [

5] stated that further study of the phenomenon

E will advance the current perception of electrokinetic phenomena, and that it may lead to the development of a new geophysical exploration technique for determination of porosity properties of rocks. The author emphasized the importance of studying the behavior of the phenomenon

E in various sedimentary rocks, its dependencies on the medium saturation, chemical composition of the pore moisture, and the values of

ζ-potential, apparent conductivity and polarizability.

Parkhomenko [

6] established that the magnitude of the phenomenon

E is a function of several variables, the most important of which are the medium saturation, concentration of salts in the liquid phase, electrochemical properties of the solid phase, texture of the rock, and the frequency of the applied seismic field. Specific surface of the electric double layer was found to be the key factor.

Butler [

37] applied the Laplace equation to solve some problems of seismoelectric effects. Haines et al.’s [

26] constructions in seismoelectric imaging are based on the potential electric quasi-static current dipole. Jardani et al. [

38] several times underlined the role of electrostatic potential in seismoelectric imaging. Mahardika and Revil [

39] noted a necessity employment of electrostatic potential for calculation of seismoelectric response generated at the boundary of two mediums.

Antonova [

40] applied the Laplace equation for calculation of finite piezoelectric body with open electric boundaries. Jandaghian and Jafari [

41] assumed that the electric potential field in the piezoelectric layer is satisfied to the Maxwell static electricity equation. Jouniaux and Zyserman [

32] gave a description of the electric potential within the electric double layer by seismo-electric and electro-seismic measurements.

All the aforementioned facts testify that the seismoelectric and piezoelectric anomalies observed in subsurface can be considered as anomalies of quasi-potential field.

Absence of reliable procedures for solving the direct and inverse problems of piezoelectric anomalies (PEA) drastically hampers further progression of the method. Therefore, it was suggested to adapt the tomography procedure, widely used in the seismic prospecting, to the PEA modeling. Diffraction of seismic waves has been computed for models of circular cylinder, thin inclined bed and thick bed [

42]. As a result, spatial-time distribution of the electromagnetic field caused by the seismic wave has been found. The computations have shown that effectiveness and reliability of PEA analysis may be critically enhanced by considering total electro- and magnetograms as differentiated from the conventional approaches. Distribution of the electromagnetic field obtained by solving the direct problem was the basis for an inverse problem, i.e., revealing depth of a body occurrence, its location in a space as well as determining physical properties. At the same time, this method has not received a wide practical application taking into account complexity of real geological media.

## 4. Short Description of the Interpretation Methodology Developed in Magnetic Prospecting

Careful analysis of piezoelectric/seismoelectric anomalies shows (see

Section 3) the possibility of application for quantitative analysis of these effects in advanced methodologies developed for magnetic prospecting in complex physical-geological conditions: rugged terrain relief, oblique polarization and complex media [

43,

44,

45,

46,

47,

48]. Employment of these methodologies (improved modifications of tangents, characteristic points and areal methods) for obtaining quantitative characteristics of ore bodies, environmental features and archaeological targets (models of horizontal circular cylinder, sphere, thin bed, thick bed and thin horizontal plate were utilized) may have significant importance [

49].

According to analogy with magnetic field, such parameter as “piezoelectric moment” (PM) can be calculated. The formulas for calculation of PM for the models of thin bed, horizontal circular cylinder (HCC) and thick bed are presented below.

- (1)
Thin bed:

where

A_{e} is the piezoelectric moment,

A_{T} is the total intensity of the piezoelectric (seismoelectric) anomaly, and

h is the depth of the upper edge of a thin bed.

- (2)
HCC:

where

${h}_{c}$ is the depth to the center of the HCC, and parameter

θ indicates some generalized parameter (its determination is given in detail in [

43,

50].

- (3)
Thick bed:

where

k’

_{m} is determined from special relationships [

48].

If anomalies are observed on an inclined profile, then the obtained parameters characterize a certain fictitious body. The transition from fictitious body parameters to those of the real body is performed using the following expressions (the subscript “

r” stands for a parameter of the real body) [

43]:

where

h is the depth of the upper edge (center of HCC) occurrence,

x_{0} is the location of the source’s projection to plan relative to the extremum having the greatest magnitude, and

ω_{0} is the angle of the terrain relief inclination (

ω_{0} > 0 when the inclination is toward the positive direction of the

x-axis).

## 6. Discussion and Conclusions

The presented physical characteristics of piezoactive rocks, ores and minerals give a wide spectrum of targets for searching of which seismo/piezoelectric method may be employed. Examined peculiarities of seismo/piezoelectric signals propagation in near-surface enable accepting these observations as quasi-potential ones.

For the first time, it was shown in detail that seismoelectric/piezoelectric anomalies in the near-surface geophysics may be analyzed using effective and reliable methods (improved version of characteristic points, tangents and areal) earlier developed in magnetic prospecting. It was proposed to employ such parameter as “piezoelectric moment” for classification of seismoelectric/piezoelectric anomalies. Effectiveness of this methodology was tested on several ore targets (Russia) and archaeological object (Israel). Obviously, further employment of seismoelectric/piezoelectric modifications in archaeology may include (besides quartz bodies), first, any clay (fired clay) targets (clay was widely used in antiquity as a building material and as a matter for construction of various domestic targets). Boulytchov [

19] has shown applicability of seismoelectric/piezoelectric method for delineation of underground caves (ancient caves account for at least 5–7% of archaeological targets).

At the same time, it must be underlined that proposed technology does not contradict to the conventional methodologies of piezoelectric/seismoelectric data analysis and could be applied as independent interpretation “method”.

For effective integration of piezo/seismoelectric interpretation results with other geophysical methods, some apparatus developed in theory of information [

51] and wavelet theory [

52] can be effectively applied.