CN103278855B - Method for eliminating influence of roadways and terrains on apparent resistivity in direct-current exploration - Google Patents

Abstract

The invention discloses a method for eliminating the influence of roadway and topography on the apparent resistivity of direct current exploration, which specifically includes establishing a model according to the roadway shape, excavation depth, topographical fluctuation elevation, etc.; taking the minimum value of the stratum resistivity in the exploration area as the The resistivity of a uniform half-space with terrain; the power supply electrodes are placed at the corresponding positions in the model according to the device type and electrode layout method used in DC exploration; each time the power supply electrodes are moved, a three-dimensional numerical simulation is performed to obtain the potential response of the background field , and then interpolated to obtain the potential difference between the receiving electrodes as the potential difference of the background field; starting from the potential formula of the point current source located in the horizontal uniform half space, the apparent resistivity formula is derived; the measured potential difference is subtracted as the potential difference of the background field, The potential difference without the influence of roadway and topography is obtained, and then substituted into the half-space apparent resistivity formula where the current source is located underground to obtain the relative apparent resistivity. The invention can be widely used in direct current resistivity exploration engineering.

Description

A Method to Eliminate the Effect of Roadway and Terrain on Apparent Resistivity of DC Exploration

technical field

The invention belongs to the field of electrical and electromagnetic prospecting, and in particular relates to a technology for eliminating the influence of tunnels and topography on apparent resistivity in DC resistivity prospecting.

Background technique

Apparent resistivity is one of the important methods for interpretation of electrical prospecting data. In the detection of underground and surface direct current methods, the apparent resistivity distortion affected by the roadway and terrain is often mixed with the abnormality of geological targets, leading to interpretation errors and even misjudgments. The roadway effect is a distortion of the normal distribution of the constant current field, which is related to various factors such as the device form, the pole layout method, the degree of terrain undulation, the geometric shape of the roadway, and the conductivity of the formation. This effect is nonlinear with the change of the power supply electrode, and it is difficult to try to find the influence factor ^[1] to realize the correction. Topographical effects are also a distortion of the constant current field. The usual ratio correction method ^[2] is not easy to determine the uniform half-space resistivity value for simulating the pure terrain response. When the underground electrical structure becomes complex, the accuracy of this correction method decreases, and even leads to wrong results. If we completely rely on 3D numerical inversion including roadway and topography ^[3] , apparent resistivity, an essential component in data inversion interpretation, will be missing. Moreover, the ill-posed nature of geophysical inverse problems, the instability and multiple solutions in 3D inversion, and the huge amount of calculations have yet to be resolved. For this reason, according to the superposition property of the current field in the linear medium, the present invention uses three-dimensional numerical forward modeling to strip the influence of the roadway and terrain, and from the uniform half-space potential of the point current source in the ground, it provides the general conditions of various devices for underground and ground direct current exploration. Applicable apparent resistivity formula.

There is following defective in prior art:

1. In the underground and surface direct current detection, the apparent resistivity distortion affected by the roadway and terrain is often mixed with the abnormality of the geological target, resulting in interpretation errors or even misjudgments;

2. The impact of the roadway is related to various factors such as the device type, the pole layout method, the degree of terrain undulation, the geometric shape of the roadway, and the conductivity of the formation, and it changes nonlinearly with the distance between the power supply and the electrode. It is difficult to find the influencing factors to achieve correction;

3. The usual method of correcting terrain influence by ratio is not easy to determine the uniform half-space resistivity value for simulating pure terrain response. When the underground electrical structure becomes complex, the accuracy of this correction method is reduced, and even wrong results are obtained;

4. If one relies solely on 3D numerical inversion including roadways and topography, apparent resistivity, an essential component of data interpretation, will be missing. Moreover, the 3D inversion itself still has problems such as instability and high non-uniqueness;

5. The original underground and surface DC apparent resistivities are derived from the potential formula of the current source on the surface of the uniform half-space and the potential formula of the current source in the uniform full space, respectively, and cannot be used universally. For underground exploration close to the ground, the original apparent resistivity derived from the potential formula of the current source in uniform full space has a large error.

comparison file

[1] Yue Jianhua, Li Zhidan. The influence of roadway in mine direct current method exploration. Journal of Coal Science, 1999, 24(1): 7-10

[2] Holcomble HT, Jiracek G R. Three dimensional terrain correction in resistivity surveys. Geophysics, 1984, 49(4): 439~452

[3] Wu Xiaoping. Three-dimensional inversion of resistivity under non-flat terrain conditions. Acta Geophysics, 2005, 48(4): 932-936.

Contents of the invention

The purpose of the present invention is to provide a method for eliminating the influence of roadway and topography on the apparent resistivity of DC prospecting, so as to eliminate the influence of roadway and topography on apparent resistivity in DC resistivity prospecting, and improve the interpretation accuracy of direct current prospecting.

In order to solve the above technical problems, the present invention adopts the following technical solutions.

A method for eliminating the influence of roadways and topography on the apparent resistivity of DC exploration, characterized in that the roadway and topography in the uniform half-space are separated from the geoelectric structure according to the superposition of the constant current field in the linear medium, specifically including the following step:

Step 1, establish a model according to the roadway shape, excavation depth, terrain relief elevation, etc.;

Step 2, taking the minimum value of the formation resistivity in the exploration area as the resistivity of the uniform half-space including the roadway and the terrain;

Step 3, put the power supply electrode and Place it at the corresponding position in the model according to the device type and electrode layout method used in DC exploration;

Step 4, each time the power supply electrode moves, a three-dimensional numerical simulation is performed to obtain the potential response of the background field, and then interpolated to obtain the receiving electrode and potential difference between Potential difference as background field;

Step 5, starting from the potential formula where the point current source is located in the horizontal uniform half space, derive the apparent resistivity formula: the power supply electrode in the ground and To form a current loop, there is any point in the ground The potential formula of

(1)

In the formula is the earth resistivity, is the supply current, and power supply and virtual source arrive distance, and power supply and virtual source arrive distance from any point on the ground The potential is

(2)

Formula (1) and formula (2) are subtracted to get the receiving electrode and potential difference between

(3)

Equation (3) derived from As the apparent resistivity, the calculation formula is as follows

(4)

When formula (4) in When is the measured potential difference and the earth is a non-horizontal uniform half space, the earth resistivity in the formula is the apparent resistivity, and the above formula is the formula for calculating the apparent resistivity, where

(5)

is the device coefficient;

Step six, the measured potential difference Subtract the potential difference as the background field , get the potential difference without roadway and terrain influence , using the following formula

(6)

Calculate the relative apparent resistivity , which is the apparent resistivity with the influence of roadway and terrain eliminated.

Adding the relative apparent resistivity to the uniform half-space resistivity yields the absolute apparent resistivity with roadway and terrain effects eliminated.

The apparent resistivity derived from the current source potential formula in the uniform half-space in the fifth step can be applied to underground detection and ground detection at the same time.

The method can be applied to all DC resistivity detection methods underground and on the ground, including profile and sounding, advanced detection, roof, floor and side detection, etc., as well as monopole-dipole, dipole-monopole, monopole- Four basic device types, monopole, dipole-dipole, and any combination.

The invention has beneficial effects. The vast majority of rock-forming minerals except ferromagnetic minerals are linear media within the field strength range of direct current method exploration. Utilizing the superposition property of the constant current field, the influence of the roadway and terrain is eliminated by the separation method. This method of separation and elimination solves the difficulty of determining the influencing factors in correcting the impact of the roadway, and there is no error caused by the improper determination of the uniform half-space resistivity of the usual ratio method. The application of 3D numerical forward modeling in the inversion and interpretation of the apparent resistivity, which is an important component, avoids the problems of instability, multi-solution and huge amount of calculation caused by completely relying on 3D inversion. The apparent resistivity derived from the current source potential formula in a uniform half-space can be switched naturally between underground and surface detection, not only does not need to change the formula, but also ensures the accuracy of the apparent resistivity when the roadway is close to the ground. The present invention is suitable for all DC resistivity detection methods underground and on the ground, such as section and depth sounding, advanced detection, roof, floor and side detection, etc., and monopole-dipole, dipole-monopole, monopole-monopole, Dipole-dipole and other four basic device types and any combination.

Description of drawings

Fig. 1 is the distribution diagram of underground point current field, where is the midpoint current source, is a virtual source of symmetric position, are the distances from the source and virtual sources to the ground, is any point in the ground, and the dotted line with the arrow is the current line.

Figure 2 is a schematic diagram of a uniform half-space calculation model for undulating terrain with roadways, where is the interface between earth and air, is the roadway-air interface, is the subsurface truncation boundary, is the emitter electrode, where is the positive electrode of the power supply, is the negative pole of the power supply, is the receiving electrode, is the vector radius from the source point to the boundary point, is the outer normal vector of the boundary, and the arrow indicates the device direction of movement.

Detailed ways

The technical solution of the present invention will be described in further detail below in conjunction with the accompanying drawings.

Take the detection of symmetrical quadrupole profile in mountain roadway as an example.

According to step 1 in the technical scheme, a model is established according to the shape of the roadway, the excavation depth, and the elevation of the terrain, as shown in Figure 2;

According to step 2 in the technical plan, take the minimum value of formation resistivity in the survey area as a uniform half-space resistivity with roadways and with terrain;

According to step 3 in the technical scheme, the power supply electrode of the symmetrical quadrupole device and Placed in the corresponding position in the model, as shown in Figure 2;

According to step 4 in the technical solution, a three-dimensional numerical simulation is performed every time the power supply electrode moves. If the field element algorithm such as finite element is used, the following boundary conditions are available:

At the interface between the surface and the air superior

(7)

At the interface of roadway and air superior

(8)

Truncated Boundary in Subterranean Infinite Space , you can set the first type, the second type, and the third type of boundary conditions. Among them, the third type of boundary condition is the general form

(9)

In the above formula, is the potential, is the distance from the origin to the field point, is the radial vector from the source point to the boundary and the outer normal vector angle between. If the roadway is buried deeply, the ground-air boundary can be moved down to become the ground boundary, and the boundary condition of formula (9) can be used. The boundary conditions Equations (7) and (8) are exact, and the boundary condition (9) for the subsurface boundary is approximate. If possible, the upper boundary should be extended to the ground as far as possible to obtain higher-precision 3D numerical simulation results.

After the potential response of the background field is obtained by three-dimensional numerical simulation, the receiving electrode is obtained by interpolation and potential difference between Potential difference as background field;

Calculate the device coefficient according to the formula (5) in Step 5 of the technical plan, and the highest point of the roadway from the terrain is known ,if ,So

(10)

Substituting formula (10) into formula (5), the device coefficient is

(11)

According to step six in the technical plan, the measured potential difference Subtract the potential difference as the background field , get the potential difference without roadway and terrain influence , using formula (6)

(12)

Obtain the relative apparent resistivity without roadway and terrain influence;

According to the technical scheme, the relative apparent resistivity plus the half-space resistivity , to obtain the absolute apparent resistivity that eliminates the influence of roadway and topography.

Claims (4)

1. A method for eliminating the influence of roadway and terrain on the apparent resistivity of DC exploration, characterized in that the roadway and terrain in the uniform half space are separated from the geoelectric structure according to the superposition of the constant current field in the linear medium, specifically Include the following steps: Step 1, building a model according to the roadway shape, excavation depth, and terrain relief elevation; Step 2, taking the minimum value of the formation resistivity in the exploration area as the resistivity of the uniform half-space including the roadway and the terrain; Step 3, place the power supply electrodes A and B at the corresponding positions in the model according to the device type and electrode layout method used in DC exploration; Step 4, each time the power supply electrode moves, a three-dimensional numerical simulation is performed to obtain the potential response of the background field, and then interpolated to obtain the potential difference ΔU″ _MN between the receiving electrodes M and N as the potential difference of the background field; Step 5, starting from the potential formula of the point current source located in the horizontal uniform half space, deduce the apparent resistivity formula: the power supply electrodes A and B in the ground form a current loop, and there is the potential formula of any point M in the ground ${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&rho;\; I</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AM</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BM</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$ In the formula, ρ is the resistivity of the earth, I is the supply current, AM and A'M are the distances from the power source A and the virtual source A' to M respectively, and BM and B'M are the distances from the power source B and the virtual source B' to M respectively , the potential of any point N in the ground is ${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&rho;\; I</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AN</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BN</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$ Formula (1) and formula (2) are subtracted to obtain the potential difference ΔU _MN between the receiving electrodes M and N $\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; MN</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&rho;\; I</span>}}{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AM</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AN</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BM</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BN</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ The ρ derived from formula (3) is used as the apparent resistivity, and the calculation formula is as follows $\mathrm{<span\; class="notranslate">\; \&rho;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AM</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AN</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BM</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BN</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; MN</span>}}}{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; MN</span>}}}{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ When ΔU _MN in formula (4) is the measured potential difference and the earth is a non-horizontal uniform half space, the earth resistivity ρ in the formula is the apparent resistivity, and the above formula is the formula for calculating the apparent resistivity, where $\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AM</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AN</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BM</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BN</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$ is the device coefficient; Step 6: Subtract the measured potential difference ΔU _MN from the potential difference ΔU″ _MN of the background field to obtain the potential difference ΔU′ _MN without the influence of the roadway and terrain, using the following formula ${\mathrm{<span\; class="notranslate">\; \&rho;</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AM</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; AN</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; A</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BM</span>}}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; BN</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; B</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\mathrm{<span\; class="notranslate">\; N</span>}}}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; MN</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; K</span>}\frac{\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; MN</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{\mathrm{<span\; class="notranslate">\; I</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$ The calculated relative apparent resistivity ρ' is the apparent resistivity that eliminates the influence of roadway and topography. 2. The method for eliminating the impact of roadway and terrain on DC exploration apparent resistivity as claimed in claim 1, wherein adding said relative apparent resistivity to said uniform half-space resistivity eliminates the influence of roadway and terrain absolute apparent resistivity. 3. The method for eliminating the impact of roadway and topography on DC exploration apparent resistivity as claimed in claim 1, characterized in that the apparent resistivity derived from the current source potential formula in the uniform half space in said step 5 can be applied to both Subsurface detection and surface detection. 4. The method for eliminating the influence of roadway and topography on DC exploration apparent resistivity as claimed in claim 1, characterized in that, the method can be applied to all DC resistivity detection underground and on the ground, including profile and sounding, advanced Probing, roof, floor and side probing.