A method, system and storage medium for calculating apparent resistivity of layered earth

Abstract

The present invention relates to the field of power system grounding measurement and evaluation, and provides a method, system, and storage medium for calculating apparent resistivity of layered earth. The method comprises the following steps: initializing a pole distance a according to the Wenner quadrupole method, inputting a test current I, obtaining a test voltage ΔV corresponding to the pole distance a, and calculating an apparent resistivity measurement value ρ. am ; The Euler transformation method is introduced to obtain the surface potential difference ΔV′(a) between the two voltage poles and the calculated value of apparent resistivity ρ as ; According to whether the relative error ε exceeds the preset threshold, confirm the update of the pole distance a or output the calculated value of the apparent resistivity ρ at this time as The present invention converts the infinite Bessel function integral of the spatial potential into the weighted sum of a finite number of surface characteristic impedances by introducing the Euler transformation method. The processing time is short, it is not limited by the number of soil layers, is applicable to complex earth stratification, and can be quickly applied on engineering sites.

Description

Technical Field

[0001] The present invention relates to the field of power system grounding measurement and evaluation, and more particularly to a method, system and storage medium for calculating apparent resistivity of layered earth. Background Art

[0002] The grounding grid is a large-scale metal interconnected network buried underground at the substation site. It is an important part of the substation's safety protection. Its grounding resistance / grounding impedance is closely related to the earth resistivity of the site. The survey and analysis of earth resistivity is the most basic, most critical and most difficult part. Since the earth resistivity in nature is often uneven, ordinary sampling measurement methods cannot meet the resistivity measurement needs of a large-scale site. In engineering, the following methods can be used: Figure 1 The horizontal layered structure shown is used as a model for an inhomogeneous earth to approximate and invert the earth's resistivity. Layers are numbered according to their resistivity, starting at the surface and extending along the z-axis to infinity (layer n). However, the earth's resistivity ρ and thickness h in the horizontal layered structure are unknown, so specialized measurement methods are required for layered earth parameter inversion. Currently, the quadrupole method is often used in conjunction with earth resistivity measurement and inversion.

[0003] The Wenner quadrupole method, also known as the equidistant quadrupole method, is to arrange four equally spaced electrodes C1-C2-P1-P2 in a straight line at the same depth, and adjust the electrode spacing a to obtain the apparent resistivity ρ of the earth corresponding to different C1-C2-P1-P2 positions. a (a), and when inverting the measured data, it is necessary to calculate the surface potential difference ΔV′ between the voltage poles P1 and P2. However, processing the surface potential difference ΔV′ between the voltage poles P1 and P2 involves the infinite integral of the first-kind zero-order Bessel function. Currently, numerical integration or complex mirroring methods are commonly used for this purpose. However, due to factors such as the large number of soil layers, these methods are complex and time-consuming, making them unable to meet the requirements of rapid application on-site. Summary of the Invention

[0004] In order to overcome the problems of the above-mentioned prior art in measuring the earth resistivity for layered earth, such as complicated steps, long processing time, and inability to meet the needs of rapid application on engineering sites, the present invention provides a method, system and storage medium for measuring the apparent resistivity of layered earth.

[0005] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0006] In a first aspect, a method for calculating apparent resistivity of layered earth includes the following steps:

[0007] S1. According to the Wenner quadrupole method, initialize the pole distance a, input the test current I to the current electrode, obtain the test voltage ΔV corresponding to the pole distance a, and calculate the apparent resistivity measurement value ρ am ;

[0008] S2. Introduce the Euler transformation method to obtain the surface potential difference ΔV′(a) between the two voltage poles, and calculate the apparent resistivity value ρ of the layered earth corresponding to the pole distance a based on the surface potential difference ΔV′(a) as ; Wherein, when the surface potential difference ΔV′(a) is calculated using the Euler transformation method, the parameters corresponding to the pole distance a are sampled at a preset interval and a preset number;

[0009] S3. Calculate the measured value ρ am and the calculated value ρ as The relative error ε between the two electrodes is determined. The electrode spacing a is updated based on whether the relative error ε exceeds the preset threshold. If it exceeds the preset threshold, the electrode spacing a is updated and the process goes to step S1. If it does not exceed the preset threshold, the electrode spacing a is not updated, the calculation is terminated, and the apparent resistivity calculation value ρ is output. as .

[0010] As a preferred solution, in step S1, the test current I is 0.1 mA-10 mA.

[0011] As a preferred solution, in step S1, the pole distance a is greater than 1 m.

[0012] As a preferred solution, in step S2, the Euler transformation method includes the following steps:

[0013] S2.1. Construct a model for the ground potential difference ΔV′(a) corresponding to the pole spacing a:

[0014]

[0015] Where λ is the integral variable, representing the electromagnetic field propagation coefficient; ρ1 represents the resistivity of the first layer of the horizontally layered earth; J0 is the first-kind zero-order Bessel function; and R1 is a function expressing the characteristic impedance of the earth's surface, which is in the following form:

[0016]

[0017] Among them, R i represents the characteristic impedance of the i-th layer of the horizontally layered earth; ρ i represents the resistivity of the i-th layer of earth; h i represents the thickness of the i-th layer of the earth; m represents the number of the deepest layer of the horizontally layered earth;

[0018] S2.2. Perform Hankel transformation on equation (1). The result of the Hankel transformation is expressed as follows:

[0019]

[0020]

[0021] Where J0 is the zero-order Bessel function of the first kind;

[0022] S2.3. Introducing the Euler transformation method, the transformation results of equations (3.1) and (3.2) are:

[0023]

[0024] Where λ = e -y ; a=e x ;x,y∈(-∞,∞);

[0025] S2.4, according to the interval Δ, the e in formula (4) x-y Sampling is performed, and the output of formula (4) is a discrete signal as follows:

[0026]

[0027] Among them, H n is the filter coefficient; Δ n is the sampling point position; at this time, the integral kernel function f=R1;

[0028] S2.5. Take 90 sampling points, perform truncated summation on equation (5), and update the surface potential difference ΔV′(a) model, which is expressed as follows:

[0029]

[0030] Among them, Δ k is the preset position coefficient, H k is the preset weight coefficient.

[0031] As a possible design of this preferred solution, in step S2.4, the sampling interval Δ is less than 0.5 times the cutoff frequency of the integral kernel function f. In this case, the discrete signal obtained by sampling can be restored to a continuous signal without distortion.

[0032] As a possible design of this preferred solution, the position coefficients Δ corresponding to the 90 sampling points in step S2.5 are preset. k and the preset weight coefficient H k As shown in the following table:

[0033]

[0034]

[0035] As a preferred solution, in step S3, the relative error ε is expressed as:

[0036]

[0037] In a second aspect, the present invention further provides a system for calculating apparent resistivity of layered earth, which is used to implement the method for calculating apparent resistivity of layered earth proposed in any of the above technical solutions, and includes the following modules:

[0038] The data acquisition module is used to obtain the pole distance a, test voltage ΔV and test current I based on the Wenner quadrupole method, and calculate the apparent resistivity measurement value ρ during the quadrupole method test am ;

[0039] The Euler transformation module is used to input the pole distance a and test current I obtained by the data acquisition module, and output the calculated apparent resistivity value ρ of the horizontal layered earth corresponding to the pole distance a according to the preset surface potential difference ΔV′(a) model based on Euler transformation. as ;

[0040] The error calculation module is used to calculate the apparent resistivity measurement value ρ obtained by the data acquisition module and the Euler transformation module respectively. am and the calculated value ρ as , judge the measured value ρ am and the calculated value ρ as Whether the relative error ε between the two meets the preset threshold, and output the error judgment result;

[0041] The iterative processing module is used to input the relative error ε judgment result of the error calculation module. If the relative error ε exceeds the preset threshold, the pole distance a is updated and input into the data acquisition module. If the relative error ε does not exceed the preset threshold, the calculation is terminated and the apparent resistivity calculation value ρ is output. as .

[0042] In a third aspect, the present invention further provides a computer-readable storage medium for storing a computer program, which can be executed by a processor to implement the apparent resistivity measurement method for layered earth proposed in any technical solution described in the first aspect above.

[0043] Compared with the prior art, the beneficial effects of the technical solution of the present invention are: by introducing the Euler transformation method and setting the sampling of the parameters corresponding to the pole distance a at a preset interval and a preset number, the present invention converts the infinite Bessel function integral of the spatial potential into a weighted sum of a finite number of surface characteristic impedances, which has a short processing time and is not limited by the number of soil layers. It is suitable for complex earth stratification and can be quickly applied on engineering sites. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a schematic diagram of the horizontal layered earth model;

[0045] Figure 2 This is a flow chart of the apparent resistivity calculation method for layered earth;

[0046] Figure 3 This is a framework diagram of the apparent resistivity measurement system for layered earth. DETAILED DESCRIPTION

[0047] The accompanying drawings are for illustrative purposes only and are not to be construed as limiting this patent;

[0048] In order to better illustrate this embodiment, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product size;

[0049] It is understandable to those skilled in the art that some well-known structures and descriptions thereof may be omitted in the drawings.

[0050] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0051] Example 1

[0052] This embodiment provides a method for calculating apparent resistivity of layered earth. Figure 2 FIG. 1 is a flow chart of the method for calculating apparent resistivity of layered earth according to the present embodiment.

[0053] The method for calculating apparent resistivity of layered earth proposed in this embodiment includes the following steps:

[0054] S1. According to the Wenner quadrupole method, initialize the pole distance a, input the test current I to the current electrode, obtain the test voltage ΔV corresponding to the pole distance a, and calculate the apparent resistivity measurement value ρ am ;

[0055] S2. Introduce the Euler transformation method to obtain the surface potential difference ΔV′(a) between the two voltage poles, and calculate the apparent resistivity value ρ of the layered earth corresponding to the pole distance a based on the surface potential difference ΔV′(a) as ; Wherein, when the surface potential difference ΔV′(a) is calculated using the Euler transformation method, the parameters corresponding to the pole distance a are sampled at a preset interval and a preset number;

[0056] S3. Calculate the measured value ρ am and the calculated value ρ as The relative error ε between the two electrodes is determined. The electrode spacing a is updated based on whether the relative error ε exceeds the preset threshold. If it exceeds the preset threshold, the electrode spacing a is updated and the process goes to step S1. If it does not exceed the preset threshold, the electrode spacing a is not updated, the calculation is terminated, and the apparent resistivity calculation value ρ is output. as.

[0057] This embodiment is based on the Wenner quadrupole method and is aimed at horizontally layered earth. The Euler transformation method is introduced and the parameters corresponding to the pole distance a are sampled at a preset interval and a preset number. The infinite Bessel function integral of the spatial potential in the existing technology (such as the complex mirror method) is converted into a weighted summation of the surface characteristic impedance of a specific sampling point. The apparent resistivity calculation value ρ corresponding to the pole distance a is determined by the relative error. as With the measured value ρ am to confirm whether it is necessary to continue updating the pole distance a to obtain a better fitting apparent resistivity calculation value ρ. as This embodiment is not limited by the number of soil layers, and effectively reduces the difficulty of obtaining the calculated apparent resistivity value.

[0058] In an optional embodiment, in step S1, the test current I is 0.1 mA-10 mA.

[0059] In an optional embodiment, in step S1, the pole distance a is greater than 1 m.

[0060] In a specific implementation process, including but not limited to setting the preset threshold to 5%, that is, when the relative error ε exceeds 5%, the pole distance a is updated and the process goes to step S1; when the relative error ε does not exceed the preset threshold, the pole distance a is not updated, the calculation is terminated and the apparent resistivity calculated value ρ at this time is output. as .

[0061] In an optional embodiment, in step S2, the Euler transformation method includes the following steps:

[0062] S2.1. Construct a model for the ground potential difference ΔV′(a) corresponding to the pole spacing a:

[0063]

[0064] Where λ is the integral variable, representing the electromagnetic field propagation coefficient; ρ1 represents the resistivity of the first layer of the horizontally layered earth; J0 is the first-kind zero-order Bessel function; and R1 is a function expressing the characteristic impedance of the earth's surface, which is in the following form:

[0065]

[0066] Among them, R i represents the characteristic impedance of the i-th layer of the horizontally layered earth; ρ i represents the resistivity of the i-th layer of earth; h i represents the thickness of the i-th layer of the earth; m represents the number of the deepest layer of the horizontally layered earth;

[0067] That is, in a horizontally layered earth with m layers, the characteristic impedance R1 of the first layer is expressed as:

[0068]

[0069] The expression of the characteristic impedance R2 of the second layer is:

[0070] ...

[0072] The characteristic impedance expression of the m-2 layer is:

[0073]

[0074] The characteristic impedance expression of the m-1 layer is:

[0075]

[0076] Among them, ρ1~ρ m are the resistivities of the earth from the 1st layer to the mth layer, h1~h m-1 are the thickness of the earth layers from the 1st layer to the m-1th layer respectively;

[0077] S2.2. Perform Hankel transformation on equation (1). The result of the Hankel transformation is expressed as follows:

[0078]

[0079]

[0080] Where J0 is the zero-order Bessel function of the first kind;

[0081] S2.3. Introducing the Euler transformation method, the transformation results of equations (3.1) and (3.2) are:

[0082]

[0083] Where λ = e -y ; a=e x ;x,y∈(-∞,∞);

[0084] S2.4, according to the interval Δ, the e in formula (4) x-y Sampling is performed, and the output of formula (4) is a discrete signal as follows:

[0085]

[0086] Among them, H n is the filter coefficient; Δ n is the sampling point position; at this time, the integral kernel function f=R1;

[0087] S2.5. Take 90 sampling points, perform truncated summation on equation (5), and update the surface potential difference ΔV′(a) model, which is expressed as follows:

[0088]

[0089] Among them, Δ k is the preset position coefficient, H k is the preset weight coefficient.

[0090] Furthermore, in step S2.4, the sampling interval Δ is smaller than 0.5 times the cutoff frequency of the integral kernel function f.

[0091] Preferably, the position coefficient Δ preset in step S2.5 k and the preset weight coefficient H k As shown in the following table:

[0092]

[0093]

[0094]

[0095] In an optional embodiment, in step S3, the relative error ε is expressed as:

[0096]

[0097] In a specific implementation process, a horizontal 10-layer soil model is set, and its parameters are shown in the following table:

[0098] Layer number Resistivity (Ω●m) Thickness (m) 1 100 1 2 1000 1 3 100 1 4 1000 1 5 100 1 6 1000 1 7 100 1 8 1000 1 9 100 1 10 1000 1

[0099] When a test current of I=1 mA is applied and other conditions are the same, the results of using the complex image method and the method of the present invention are shown in the following table:

[0100]

[0101]

[0102] Judging from the results, compared with obtaining the calculated apparent resistivity value that fits the measured value through the complex mirror method, the method of the present invention greatly reduces the difficulty of obtaining the calculated apparent resistivity value, and the maximum error is controlled within 2%, meeting the requirements of engineering applications. It is particularly suitable for data processing operations based on the quadrupole method at engineering sites.

[0103] Example 2

[0104] This embodiment provides a system for calculating apparent resistivity of layered earth, and applies the method for calculating apparent resistivity of layered earth proposed in Example 1. Figure 3 FIG. 1 shows a framework diagram of the apparent resistivity calculation system for layered earth according to this embodiment.

[0105] The apparent resistivity measurement system for layered earth proposed in this embodiment includes a data acquisition module, an Euler transformation module, an error calculation module and an iterative processing module.

[0106] The data acquisition module is used to obtain the pole distance a, test voltage ΔV and test current I based on the Wenner quadrupole method, and calculate the apparent resistivity measurement value ρ during the quadrupole method test. am .

[0107] The Euler transformation module is used to input the pole distance a and test current I obtained by the data acquisition module, and output the calculated apparent resistivity value ρ of the horizontal layered earth corresponding to the pole distance a according to the preset surface potential difference ΔV′(a) model based on Euler transformation. as .

[0108] In a specific implementation process, the surface potential difference ΔV′(a) model expression based on Euler transformation built into the Euler transformation module is:

[0109]

[0110] Among them, Δ k is the preset position coefficient, H k is the preset weight coefficient, and R1 represents the surface characteristic impedance function.

[0111] The error calculation module is used to calculate the apparent resistivity measurement value ρ obtained by the data acquisition module and the Euler transformation module respectively. am and the calculated value ρ as , judge the measured value ρ am and the calculated value ρ as Whether the relative error ε between the two meets the preset threshold, the error judgment result is output.

[0112] The iterative processing module is used to input the relative error ε judgment result of the error calculation module. If the relative error ε exceeds the preset threshold, the pole distance a is updated and input into the data acquisition module. If the relative error ε does not exceed the preset threshold, the calculation is terminated and the apparent resistivity calculation value ρ is output. as .

[0113] Example 3

[0114] This embodiment provides a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the processor executes the apparent resistivity measurement method for layered earth proposed in the above-mentioned embodiment 1.

[0115] The same or similar reference numerals correspond to the same or similar components;

[0116] The terms used in the drawings to describe positional relationships are for illustrative purposes only and should not be construed as limiting this patent;

[0117] Obviously, the above embodiments of the present invention are merely examples for the purpose of clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Those skilled in the art will appreciate that other variations or modifications can be made based on the above description. It is not necessary and impossible to enumerate all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A method for calculating apparent resistivity of layered earth, characterized in that: The following steps are involved: S1. According to the Wenner quadrupole method, initialize the pole distance a, input the test current I to the current electrode, obtain the test voltage ΔV corresponding to the pole distance a, and calculate the apparent resistivity measurement value ρ am ; S2. Introduce the Euler transformation method to obtain the surface potential difference ΔV′(a) between the two voltage poles, and calculate the apparent resistivity value ρ of the layered earth corresponding to the pole distance a based on the surface potential difference ΔV′(a) as ; Wherein, when the surface potential difference ΔV′(a) is calculated using the Euler transformation method, the parameters corresponding to the pole distance a are sampled at a preset interval and a preset number; S3. Calculate the measured value ρ am and the calculated value ρ as The relative error ε between the two electrodes is determined. The electrode spacing a is updated based on whether the relative error ε exceeds the preset threshold. If it exceeds the preset threshold, the electrode spacing a is updated and the process goes to step S1. If it does not exceed the preset threshold, the electrode spacing a is not updated, the calculation is terminated, and the apparent resistivity calculation value ρ is output. as ;in, In step S2, the Euler transformation method includes the following steps: S2.

1. Construct a model for the ground potential difference ΔV′(a) corresponding to the pole spacing a: Where λ is the integral variable, representing the electromagnetic field propagation coefficient; ρ1 represents the resistivity of the first layer of the horizontally layered earth; J0 is the first-kind zero-order Bessel function; and R1 is a function expressing the characteristic impedance of the earth's surface, which is in the following form: Among them, R i represents the characteristic impedance of the i-th layer of the horizontally layered earth; ρ i represents the resistivity of the i-th layer of earth; h i represents the thickness of the i-th layer of the earth; m represents the number of the deepest layer of the horizontally layered earth; S2.

2. Perform Hankel transformation on equation (1). The result of the Hankel transformation is expressed as follows: Where J0 is the zero-order Bessel function of the first kind; S2.

3. Introducing the Euler transformation method, the transformation results of equations (3.1) and (3.2) are: Among them, l=e -y ;a=e x ;x,y∈(-∞,∞); S2.4, according to the interval Δ, the e in formula (4) x-y Sampling is performed, and the output of formula (4) is a discrete signal as follows: Among them, H n is the filter coefficient; Δ n is the sampling point position; at this time, the integral kernel function f=R1; S2.

5. Take 90 sampling points, perform truncated summation on equation (5), and update the surface potential difference ΔV′(a) model, which is expressed as follows: Among them, Δ k is the preset position coefficient, H k is the preset weight coefficient.

2. The method for calculating apparent resistivity of layered earth according to claim 1, characterized in that: In step S1, the test current I is 0.1 mA-10 mA.

3. The method for calculating apparent resistivity of layered earth according to claim 1, characterized in that: In step S1, the pole distance a is greater than 1 m.

4. The method for calculating apparent resistivity of layered earth according to claim 1, characterized in that: In step S2.4, the sampling interval Δ is less than 0.5 times the cutoff frequency of the integral kernel function f.

5. The method for calculating apparent resistivity of layered earth according to claim 1, characterized in that: The Δ preset in step S2.5 k and the preset H k As shown in the following table:

6. The method for calculating apparent resistivity of layered earth according to claim 1, characterized in that: In step S3, the relative error ε is expressed as:

7. A system for measuring apparent resistivity of layered earth, used to implement the method for measuring apparent resistivity of layered earth according to any one of claims 1 to 6, characterized in that: The system comprises: The data acquisition module is used to obtain the pole distance a, test voltage ΔV and test current I based on the Wenner quadrupole method, and calculate the apparent resistivity measurement value ρ during the quadrupole method test am ; The Euler transformation module is used to input the pole distance a and test current I obtained by the data acquisition module, and output the calculated apparent resistivity value ρ of the horizontal layered earth corresponding to the pole distance a according to the preset surface potential difference ΔV′(a) model based on Euler transformation. as ; The error calculation module is used to calculate the apparent resistivity measurement value ρ obtained by the data acquisition module and the Euler transformation module respectively. am and the calculated value ρ as , judge the measured value ρ am and the calculated value ρ as Whether the relative error ε between the two meets the preset threshold, and output the error judgment result; The iterative processing module is used to input the relative error ε judgment result of the error calculation module. If the relative error ε exceeds the preset threshold, the pole distance a is updated and input into the data acquisition module. If the relative error ε does not exceed the preset threshold, the calculation is terminated and the apparent resistivity calculation value ρ is output. as .

8. The apparent resistivity measurement system for layered earth according to claim 7, characterized in that: The surface potential difference ΔV′(a) model expression based on Euler transformation built into the Euler transformation module is: Among them, Δ k is the preset position coefficient, H k is the preset weight coefficient, and R1 represents the surface characteristic impedance function.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the processor is caused to perform the method according to any one of claims 1 to 6.

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