State educational institution of higher professional education

Tomsk Polytechnic University


Guidelines for the implementation of laboratory work on the topic: “Electrical prospecting installations. Calculation of the parameters of electrical exploration installations in the methods of resistance, induced polarization and charged body”

Tomsk 2008


The methods of resistance, induced polarization and charged body are widely used in prospecting and exploration of various minerals, as well as for solving engineering-geological and hydrogeological problems.

Due to the fact that the supply and receiving electrodes can be located differently in the measuring installations, these methods have many modifications that make up two large groups – electrical profiling (EP) and electrical probing (EP). In EP, the nature of the change in the studied parameter along the line of observation (profile) or within a certain area along a given network is investigated. The type and dimensions of the installation remain unchanged, i.e. the depth of research remains unchanged. With EZ, the change in the measured parameter with depth at a specific point on the ground is studied, while the position of the center of the installation remains unchanged.

Requirements for the quality of electrical exploration work are constantly increasing due to the need to solve more and more complex geological problems. At the same time, questions of the correct substantiation of the method and modifications of electrical prospecting, the type and size of the electrical prospecting installation, the design of electrodes and the magnitude of current and voltage, as well as the equipment used in this, come to the fore. All these questions must be scientifically substantiated and calculated.


An electrical exploration installation is a set of used mutual arrangements of supply A and B and receiving M and N electrodes (Fig. 1), where the length of the supply dipole AB determines the depth of penetration of the electric field into the ground, and the length of the receiving line MM determines the value of the measured potential difference, i.e. . the value of DU MN .

Knowing the values DU MN , J AB and K calculate the apparent electrical resistivity of the geological environment r to the formula:

r k u003d K DU MN / J AB , (Ohm m) (1.1)

where K is the coefficient of the electrical prospecting installation, which depends on the distance between the electrodes A, M, N, B and on their relative position. In the general case, for a four-electrode setup (Fig. 1), K is a coefficient that depends on the distance between the electrodes.

Fig.1. Schematic diagram of the installation for working by the resistance method

To determine r to (in Ohm m) according to the diagram in fig. 1, it is necessary to measure the potential difference DU (in mV) between two points of the profile M and N, where the receiving electrodes are located, divide it by the current J (in mA) flowing through the supply line, and multiply the resulting value by K (formula 1.1).

The electric potential and electric field strength created by a hemispherical point grounding in a homogeneous and isotropic medium are determined by the formulas:

U = r to J / 2pr (1.3); E = r to J / 2pr 2 (1.4),

where r is the distance from the supply ground to the test point (in m).

Using formula 1.3, you can calculate the potential difference DU between points M and N from two point sources + A and – B.

DU u003d U M U N u003d (U A M – U B M ) – (U A N – U B N ) u003d

u003d (r to J / 2pr AM – r to J / 2pr BM ) – (r to J / 2pr A N – r to J / 2pr BM ) =

= r to J / 2pr AM – r to J / 2pr BM – r to J / 2pr A N + r to J / 2pr BM =

= r to J [2p/ (1 / r AM – 1 / r BM – 1/ r A N + 1/ r BM ) ] = r to J K, where

the value in square brackets is a constant value for the installation of the same type and one size (distance between the electrodes) and is called the installation coefficient, denoted by the letter K.

K = 2p / (1/r AM – 1/r AN – 1/r BM + 1/r BN ), (m) (1.2)

In measuring setups, the supply and receiving electrodes can be arranged in different ways, forming different types of setups. The type of electrical exploration installation determines the type of resistivity method, the geological problems to be solved, and the type of equipment used.

All known electrical exploration installations can be divided into 4 groups:

1. installations of the symmetrical type;

2. dipole;

3. setting the median gradient;

4. focused.

Note: if the distance between the receiving electrodes r MN is small enough, the ratio DU MN / r MN tends to the value of E M N (projection of the electric field onto the MN line) at the measurement points. Such measuring installations are called limiting. They allow you to measure the electric field E on the surface of the earth:

E MN = DU MN / r MN , (1.5)

1.1. Symmetrical type installations (electrodes A and B, M and N are located on the same line (profile).

1. Rectilinear four-point installation AMNB , in this installation all the electrodes are located in one line (Fig. 2.1). In this case, the measuring electrodes are usually placed within the middle third of the segment AB, since in this case the setting is close to the limit.

2. Symmetrical four-point AMNB installation is currently the most common. In it, the receiving grounds are located on a straight line connecting the supply grounds symmetrically with respect to the center of segment A3 (Fig. 2.4).

If the distance between the receiving grounds r MN is less than one third of the distance between the supply grounds r AB (r MN < 1/3 AB), such an installation is called a Schlumberger installation, under this condition, the ratio DU MN / r MN can be considered with sufficient accuracy equal to the electric field strength in the center of the installation, i.e. consider it limiting.

If r AM u003d r MN u003d r N B u003d a, then such an installation is called a Venus installation (Fig. 2.3).

3. AMONB divergent installation . Its simplest view is shown in Fig. 2.6. It differs from the symmetrical one in that one more measuring electrode 0 is added to it in the center of the installation. This makes it possible to measure not only the potential difference DU MN , but also the potential difference DU MO and DU ON . It is obvious that in this case the difference DU MO – DU ON , referred to the distance r MN , is proportional to the second derivative of the potential in the middle of the setup. If we add a pair of M¢N¢ electrodes to the measuring electrodes MON, located along the line passing through the point 0 orthogonally to the line MN, we get a divergent setup for measuring two second derivatives of the potential along orthogonal directions. It is known from theories that the sum of these second derivatives is equal (with a minus sign) to the divergence of the horizontal component of the electric field vector E:


That is why this setup is called divergent (Fig. 2.7).

4. The three-point installation AMNB ¥ (Fig. 2.8) is learned in practice if electrode B is so far from the measurement points that the electric field it creates is negligibly small compared to the field of electrode A. This usually occurs when the ratio BO / AO ³ 5 times .

The limiting three-point setup is called the Hummel setup. For it, the formula for calculating the electric component of the field is written as

E MN = J r / 2pr 2 (1.7)

where r is the distance from point A to the measurement point of field 0.

5. A two-point (potential) setting AM, N ¥ B ¥ (Fig. 2.10) is obtained from a three-point one if the measuring electrode N is also taken to infinity (in practice, this means that the electrode N is located so far from the current source A that the potential of the point N would be close to zero). This condition is met if the ratio AH / AM is greater than 5. Therefore, a two-point installation allows you to directly measure the potential of the M point (this is what determines its name). In particular, on the surface of a homogeneous earth

U M = J r / 2pr, (1.8); K=2pr (1.9),

where r = r AM .

Rice. 2. Varieties of installations such as symmetrical

1.2. Dipole installations are those in which the measuring line MN (receiving dipole) is placed outside the supply dipole AB and can be arbitrarily oriented relative to it.

Rice. 3. Varieties of dipole installations

There are several modifications of such installations (Fig. 3), among which, depending on the angle q between the axis of the supply dipole AB and the radius vector r connecting the centers of the dipoles, as well as on the angle b between the axis of the measuring dipole MN and r, the following are distinguished:

1. radial installation (0

2. azimuthal (0

Z. axial (q=90, b=0);

4. equatorial (q=90, b=90);

5. parallel (0

6. perpendicular (0

The distance r u003d r O 1 O 2 between the centers of the supply and measuring dipoles is called the spacing of the dipole installation. The spacing value r (similar to the length of the AB/26 line in the first group setups) determines the depth of investigations with the dipole setup. The coefficient of any dipole installation can be calculated by the general formula (1.2).

1.3. The mid-gradient settings are obtained when the position of supply electrodes A and B is fixed, i.e. they remain motionless during the survey, and the receiving grounds and move along the profiles parallel to the lines AB. The combination of these profiles forms a tablet . The length of each profile should not exceed 0.5 of the distance AB. The tablet, usually consisting of 5 + 20 profiles, is positioned so that its central profile coincides with the line AB (Fig. 4), and the distance from the central to the extreme profiles does not exceed half the distance AB. After the completion of measurements on the first tablet P 1 , the supply grounds are moved to the second position A 2 B 2 so that adjacent tablets P 1 and P 2 overlap at the ends of the profiles. When moving the supply grounds to position A 3 V 3 , the corresponding plates P 1 and P 2 must overlap with the extreme profiles. The scheme of moving the SG installation is shown in fig. 5.

Rice. 4. Installation of median gradients (groundings A and B are fixed, and M and N move along profiles parallel to the line AB, forming a plate P 0 .
Rice. 5. The order of work when shooting median gradients: – the location of the profiles and the movement of the supply A and B in the measuring M and N groundings along the profile; – the location of the tablets.
Rice. 6. Explanation to the calculation of the SG installation coefficient The SG installation coefficient is determined from expression (1.2) or by the approximate formula (1.10).

When shooting median gradients, r k is calculated using formula (1.1); the installation factor is determined from expression (1.2) or by the approximate formula:


The designations adopted in this expression are explained in Fig. 6.

1.4. Focused installations are obtained when the supply AB and receiving MN electrodes are located on the same line, alternating with each other (Fig. 7).

If the distances AB and MN are equal to each other, then the installation is focused symmetrical, but if these distances are not multiple, then the installation is simply focused.

The installation coefficient is determined from the expression (1.2.).

Electrical exploration work with all of the above installations can be carried out both on direct and low-frequency alternating current, using special equipment for this.

Rice. 7. Varieties of installations such as focused

Be First to Comment

Leave a Reply

Your email address will not be published.