Method and system for measuring and calculating apparent resistivity of horizontally layered earth

Abstract

The invention relates to the technical field, and discloses a horizontally layered earth apparent resistivity measuring and calculating method and system, and the method comprises the steps: constructing a feature equation of a horizontally layered earth according to an integral variable set obtained through an index discrete sampling method and horizontally layered earth parameters; a first layered uplink electromagnetic wave amplitude kernel function of the characteristic equation under each integral variable is calculated, a horizontal layered earth integral upper limit is obtained, and the horizontal layered earth integral upper limit is set as the maximum value of the integral variable meeting a preset criterion; on the basis of the horizontal layered earth integral upper limit, the integral range of the constructed non-boundary-domain apparent resistivity relational expression is limited, and a boundary-domain apparent resistivity relational expression is obtained; and based on a 151-point Gaussian-Legendre integral algorithm and Euler transform, carrying out iterative solution on the apparent resistivity relational expression of the bounded domain to obtain an apparent resistivity measurement result. According to the method provided by the invention, the dual requirements of the apparent resistivity measurement and calculation of the horizontally layered earth on the precision and the efficiency are met.

Description

Technical Field

[0001] The present invention relates to the technical field of geological exploration, and in particular to a method and system for calculating the apparent resistivity of horizontally layered earth. Background Art

[0002] In geological exploration, the precise measurement of the apparent resistivity of horizontally layered earth is crucial for analyzing underground geological structures and exploring for resources. The apparent resistivity of horizontally layered earth is the resistivity of each layer calculated using the uniform earth resistivity measurement method when the underground medium is electrically heterogeneous and the surface is uneven. This resistivity is influenced by a variety of factors, including the actual resistivity of the underground medium, electrode spacing, electrode arrangement, and measurement depth.

[0003] Existing methods for measuring the apparent resistivity of horizontally layered earth include the complex mirror method and the 141 linear filtering method. The complex mirror method requires the use of a sampling law to obtain the dynamic waveform range of the first layer's uplink electromagnetic wave amplitude kernel function with respect to the integral variable. Currently, no relevant methods are described. The complex mirror method requires complex matrix calculations such as singular decomposition and projection transformation to determine the intensity and mode of the complex mirror image, which is computationally intensive and inefficient. The 141 linear filtering method uses logarithmic equal-interval sampling. To obtain the optimal filter coefficients and exponential sampling coefficients, extensive calculations are required. Furthermore, when operating conditions change, recalculation must be performed for the specific operating conditions, resulting in low measurement efficiency. Therefore, existing methods for measuring the apparent resistivity of horizontally layered earth cannot meet the dual requirements of accuracy and efficiency for measuring the apparent resistivity of horizontally layered earth.

[0004] It can be seen that how to meet the dual requirements of accuracy and efficiency in the measurement of apparent resistivity of horizontally layered earth has become a technical problem that needs to be solved urgently by those skilled in the art. Summary of the Invention

[0005] The present invention provides a method and system for measuring the apparent resistivity of horizontally layered earth to solve the technical problem of how to meet the dual requirements of accuracy and efficiency in measuring the apparent resistivity of horizontally layered earth, thereby achieving the effect of meeting the dual requirements of accuracy and efficiency in measuring the apparent resistivity of horizontally layered earth.

[0006] In a first aspect, the present invention provides a method for calculating the apparent resistivity of horizontally layered earth, the method comprising: Obtaining an integral variable set by an exponential discrete sampling method, and constructing a characteristic equation of the horizontally layered earth based on the integral variable set and the obtained horizontally layered earth parameters of the target earth region; According to the first layered uplink electromagnetic wave amplitude kernel function corresponding to the characteristic equation under each integral variable, a horizontal layered earth integral upper limit is obtained, the horizontal layered earth integral upper limit is set as the maximum value of the integral variable satisfying a preset criterion, the preset criterion is used to reflect the relationship between the local absolute error of the first layered uplink electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the integral variable set and the allowable error, and the allowable error is set as the fluctuation range determined according to the first layered uplink electromagnetic wave amplitude kernel function varying with the integral variable; According to the obtained pole distance of the Wenner quadrupole method, an apparent resistivity relationship formula of the unbounded domain of the horizontal layered earth is constructed; Based on the horizontal layered earth integral upper limit, the integral range of the apparent resistivity relationship formula of the unbounded domain is limited to obtain an apparent resistivity relationship formula of a bounded domain; Based on the 151-point Gauss-Legendre integral algorithm and Euler transformation, the apparent resistivity relationship formula of the bounded domain is iteratively solved to obtain the apparent resistivity calculation result.

[0007] Preferably, the characteristic equation of the horizontal layered earth is constructed according to the integral variable set and the obtained horizontal layered earth parameters of the target large area, comprising: The horizontal layered earth parameters of the target large area are obtained, the horizontal layered earth parameters include the soil resistivity of each layer and the z-axis coordinate of the layer boundary of each layer, and the reflection coefficient of each layer boundary is constructed according to the soil resistivity; Based on the electromagnetic characteristics of the horizontal layered earth, the interlayer relationship of the layer boundary of the horizontal layered earth is determined according to the reflection coefficient, the integral variable set and the z-axis coordinate of the layer boundary; Based on the electromagnetic field boundary condition, the characteristic equation of the horizontal layered earth is constructed, the characteristic equation is composed of a characteristic equation matrix, a characteristic equation vector and a to-be-solved characteristic vector, the elements of the characteristic equation matrix represent the interlayer relationship, the elements of the characteristic equation vector represent the known electromagnetic field boundary excitation condition, and the to-be-solved characteristic vector includes the first layered uplink electromagnetic wave amplitude kernel function.

[0008] Preferably, the first layered uplink electromagnetic wave amplitude kernel function of the characteristic equation under each integral variable is calculated to obtain the horizontal layered earth integral upper limit, comprising: The characteristic equation is iteratively solved according to the integral variable set to obtain the to-be-solved characteristic vector corresponding to each integral variable in the integral variable set, and the first layered uplink electromagnetic wave amplitude kernel function in each to-be-solved characteristic vector is obtained; According to each of the first layered uplink electromagnetic wave amplitude kernel function, a fluctuation range of the first layered uplink electromagnetic wave amplitude kernel function is obtained, and an allowable error is constructed according to the fluctuation range; According to each of the first layered uplink electromagnetic wave amplitude kernel function, a local absolute error of the first layered uplink electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the integral variable set is obtained; According to the local absolute error and the allowable error, a preset criterion is constructed, and the preset criterion is solved to obtain a maximum value of the integral variable that satisfies the preset criterion, and the maximum value is taken as a horizontal layered geodetic integral upper limit.

[0009] Preferably, the 151-point Gauss-Legendre integral algorithm and Euler transformation are used to iteratively solve the bounded domain apparent resistivity relationship to obtain an apparent resistivity calculation result, including: The 151-point Gauss-Legendre integral algorithm is used to solve the bounded domain apparent resistivity relationship to obtain an apparent resistivity Gauss calculation formula; An Euler transformation coefficient function is introduced into the apparent resistivity Gauss calculation formula to obtain an apparent resistivity Euler transformation calculation formula; The apparent resistivity Euler transformation calculation formula is iteratively solved to obtain an apparent resistivity calculation result.

[0010] Preferably, the apparent resistivity Euler transformation calculation formula is expressed as: wherein, denotes a pole distance, denotes a pole distance number of the Wenner quadrupole method, denotes a pole distance corresponding apparent resistivity, denotes a soil resistivity of a first layer, denotes an integral point index of the 151-point Gauss-Legendre integral, denotes a position coefficient of the 151-point Gauss-Legendre integral, denotes a horizontal layered geodetic integral upper limit, denotes a weight coefficient of the 151-point Gauss-Legendre integral, denotes a coefficient function of the Euler transformation, denotes an integral variable corresponding first layered uplink electromagnetic wave amplitude kernel function, denotes corresponding first type zero-order Bessel function, denotes corresponding first type zero-order Bessel function.

[0011] In a second aspect, the present application also provides a system for calculating apparent resistivity of horizontally layered earth, which implements the method for calculating apparent resistivity of horizontally layered earth, and comprises a characteristic equation construction unit, a horizontally layered earth integral upper limit calculation unit, an apparent resistivity relationship construction unit, an apparent resistivity relationship conversion unit and an apparent resistivity calculation unit. The characteristic equation construction unit is configured to obtain an integral variable set by an exponential discrete sampling method, and construct a characteristic equation of horizontally layered earth according to the integral variable set and acquired horizontally layered earth parameters of a target large area. The horizontally layered earth integral upper limit calculation unit is configured to calculate a first layered uplink electromagnetic wave amplitude kernel function of the characteristic equation under each integral variable, and obtain a horizontally layered earth integral upper limit, which is set as a maximum value of the integral variable satisfying a preset criterion, and the preset criterion is configured to reflect a relationship between a local absolute error of the first layered uplink electromagnetic wave amplitude kernel function corresponding to a highest integral variable in the integral variable set and an allowable error, which is set according to a fluctuation range of the first layered uplink electromagnetic wave amplitude kernel function with respect to the integral variable. The apparent resistivity relationship construction unit is configured to construct a non-bounded domain apparent resistivity relationship of the horizontally layered earth according to an acquired pole distance of the Wenner quadrupole method. The apparent resistivity relationship conversion unit is configured to limit an integral range of the non-bounded domain apparent resistivity relationship based on the horizontally layered earth integral upper limit, and obtain a bounded domain apparent resistivity relationship. The apparent resistivity calculation unit is configured to iteratively solve the bounded domain apparent resistivity relationship based on a 151-point Gauss-Legendre integral algorithm and Euler transformation, and obtain an apparent resistivity calculation result.

[0012] Preferably, the characteristic equation construction unit comprises a reflection coefficient calculation module, an interlayer relationship construction module and a characteristic equation construction module. The reflection coefficient calculation module is configured to acquire horizontally layered earth parameters of a target large area, the horizontally layered earth parameters comprising soil resistivity of each layer and z-axis coordinates of layer boundaries of each layer, and construct a reflection coefficient of each layer boundary according to the soil resistivity. The interlayer relationship construction module is configured to determine an interlayer relationship of layer boundaries of the horizontally layered earth according to the reflection coefficient, the integral variable set and the z-axis coordinates of the layer boundaries based on electromagnetic characteristics of the horizontally layered earth. The feature equation construction module is configured to construct a feature equation of the horizontally layered earth based on electromagnetic field boundary conditions, the feature equation being composed of a feature equation matrix, a feature equation vector, and a to-be-solved eigenvector, elements of the feature equation matrix representing the interlayer relationship, elements of the feature equation vector representing known electromagnetic field boundary excitation conditions, and the to-be-solved eigenvector including the first layered uplink electromagnetic wave amplitude kernel function.

[0013] Preferably, the horizontally layered earth integral upper limit calculation unit includes a first calculation module, an allowable error construction module, a local absolute error construction module, and a second calculation module. The first calculation module is configured to iteratively solve the feature equation according to the integral variable set to obtain the to-be-solved eigenvector corresponding to each integral variable in the integral variable set, and obtain the first layered uplink electromagnetic wave amplitude kernel function in each to-be-solved eigenvector. The allowable error construction module is configured to obtain a fluctuation range of the first layered uplink electromagnetic wave amplitude kernel function according to each first layered uplink electromagnetic wave amplitude kernel function, and construct an allowable error according to the fluctuation range. The local absolute error construction module is configured to obtain a local absolute error of the first layered uplink electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the integral variable set according to each first layered uplink electromagnetic wave amplitude kernel function. The second calculation module is configured to construct a preset criterion according to the local absolute error and the allowable error, and solve the preset criterion to obtain a maximum value of the integral variable that satisfies the preset criterion, and take the maximum value as the horizontally layered earth integral upper limit.

[0014] Preferably, the apparent resistivity calculation unit includes a third calculation module, an Euler transformation module, and a fourth calculation module. The third calculation module is configured to solve the bounded domain apparent resistivity relationship by using a 151-point Gauss-Legendre integral algorithm to obtain an apparent resistivity Gauss calculation formula. The Euler transformation module is configured to introduce an Euler transformation coefficient function into the apparent resistivity Gauss calculation formula to obtain an apparent resistivity Euler transformation calculation formula. The fourth calculation module is configured to iteratively solve the apparent resistivity Euler transformation calculation formula to obtain an apparent resistivity measurement result.

[0015] Preferably, the apparent resistivity Euler transformation calculation formula is expressed as: wherein, Indicates the pole distance, Indicates the pole distance number of the Wenner quadrupole method, Indicates pole distance The corresponding apparent resistivity, represents the soil resistivity of the first layer, Indicates the integration point index of the 151-point Gauss-Legendre integral, represents the position coefficient of the 151-point Gauss-Legendre integral, represents the upper limit of the horizontal layered geodetic integral, represents the weight coefficient of the 151-point Gauss-Legendre integral, represents the coefficient function of Euler transformation, The integral variable is The corresponding first layer uplink electromagnetic wave amplitude kernel function, express The corresponding zero-order Bessel function of the first kind is, express The corresponding zero-order Bessel function of the first kind.

[0016] This application provides a method and system for calculating the apparent resistivity of horizontally layered earth. Compared with the prior art, the embodiments of this application have the following beneficial effects: The method for calculating the apparent resistivity of horizontally layered earth disclosed in this application uses an equal exponential sampling method to determine the integral variable. This method can obtain dramatic changes in the first layer's upward electromagnetic wave amplitude kernel function in the low-frequency band, and can also obtain the asymptotic value of the first layer's upward electromagnetic wave amplitude kernel function in the high-frequency band, thereby obtaining the dynamically changing waveform of the entire first layer's upward electromagnetic wave amplitude kernel function, ensuring the accuracy of the measurement. At the same time, the exponential discretization step size of the integral variable is fixed, avoiding the influence of soil parameter changes on it. The upper limit of the horizontally layered earth integral is determined by the soil parameters, reflecting the differences in soil parameters. It does not require a large number of cases to find the optimal solution for the filter coefficient and the exponential sampling coefficient, significantly reducing the complexity of the measurement. The use of the 151-point Gauss-Legendre numerical integration algorithm combined with the Euler transformation coefficient to realize the Euler transformation of the apparent resistivity can effectively improve the efficiency of measuring the apparent resistivity of horizontally layered earth and reduce the complexity of the measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 This is a schematic diagram of the steps of a method for measuring the apparent resistivity of horizontally layered earth provided by a preferred embodiment of the present invention; Figure 2 A horizontal layered earth model diagram provided by a preferred embodiment of the present invention; Figure 3is a structure schematic diagram of a horizontal layered earth apparent resistivity measuring system provided by one preferred embodiment of the present application; Reference signs: 1 - characteristic equation construction unit, 2 - horizontal layered earth integral upper limit calculation unit, 3 - apparent resistivity relationship construction unit, 4 - apparent resistivity relationship conversion unit, 5 - apparent resistivity calculation unit. DETAILED DESCRIPTION

[0018] The embodiments of the present application will be described in detail below with reference to the drawings, and the embodiments are given only for the purpose of illustration and cannot be understood as limiting the present application, including the drawings are for reference and illustration only, and do not constitute a limitation on the scope of patent protection of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor belong to the scope of protection of the present application. In the description of the present application, the terms "first", "second", "third" and the like are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features limited by "first", "second", "third" and the like can be explicitly or implicitly included one or more features. In the description of the present application, unless otherwise specified, the meaning of "a plurality of" is two or more.

[0019] In the description of the present application, it should be noted that, unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium, it can be the communication inside two elements. The terms "vertical", "horizontal", "left", "right", "up", "down" and similar expressions used herein are only for the purpose of illustration, and are not intended to indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application. The term "and / or" used herein includes any and all combinations of one or more related listed items. For those of ordinary skill in the art, the specific meaning of the above terms in the present application can be understood in specific circumstances.

[0020] In the description of the present application, it should be noted that, unless otherwise defined, all technical and scientific terms used in the present application have the same meaning as understood by those skilled in the art. The terms used in the specification of the present application are only for the purpose of describing the specific embodiments, and are not intended to limit the present application. For those of ordinary skill in the art, the specific meaning of the above terms in the present application can be understood in specific circumstances.

[0021] See also Figure 1 FIG. 1 is a schematic diagram of steps of a method for calculating the apparent resistivity of horizontally layered earth. In an embodiment of the present invention, a method for calculating the apparent resistivity of horizontally layered earth is provided, comprising: S1. Obtain an integral variable set by an exponential discrete sampling method, and construct a characteristic equation of the horizontally layered earth based on the integral variable set and the acquired horizontally layered earth parameters of the target earth area; the technical solution of this application is implemented under the condition of known horizontally layered earth parameters and quadrupole method pole spacing arrangement, and the horizontally layered earth parameters include the soil resistivity of each layer, the thickness of each layer, and the boundary of each layer. Axis coordinates.

[0022] Furthermore, an equal exponential sampling method is used to determine the integral variable, and the integral variable is set as the integral variable. The integral variables form an integral variable set, and the integral variable set is expressed as follows: in, represents the integration variable, Represents the index of the integral variable exponential discretization step size.

[0023] Based on the electromagnetic properties of horizontally layered earth, through physical modeling and mathematical derivation, the boundary conditions for electromagnetic wave propagation in layered media within a horizontally layered earth are converted into matrix equations to construct the characteristic equation. To describe the electromagnetic wave propagation characteristics of each layer in a horizontally layered earth, the Hankel integral kernel function is used to represent the amplitude characteristics of the upward electromagnetic wave within the layer, which is the upward electromagnetic wave amplitude kernel function. The Hankel integral kernel function is used to represent the amplitude characteristics of the downward electromagnetic wave within the layer, which is the downward electromagnetic wave amplitude kernel function.

[0024] Furthermore, the reflection coefficient of each layer boundary is constructed based on the soil resistivity. The reflection coefficient of each layer boundary is expressed as: in, represents a hierarchical index, Indicates the The reflectance of the layers, Indicates the Layered soil resistivity, Indicates the Layered soil resistivity.

[0025] The upper and lower boundaries of each layer of the horizontally layered earth meet the electromagnetic field boundary conditions. The kernel function of the upgoing electromagnetic wave amplitude of the adjacent layers and the kernel function of the upgoing electromagnetic wave amplitude meet a linear relationship. The linear relationship is expressed to obtain the characteristic equation, which is expressed as: in, The characteristic equation matrix representing the relationship between the layers of the horizontally layered earth is formed by the layer boundaries. represents the desired eigenvector consisting of the kernel function of the upgoing electromagnetic wave amplitude and the kernel function of the downgoing electromagnetic wave amplitude of the horizontally layered earth, Represents the characteristic equation vector composed of known electromagnetic field boundary excitation conditions.

[0026] The eigenvector to be found is expressed as: in, represents the first layer downlink electromagnetic wave amplitude kernel function, represents the first layer uplink electromagnetic wave amplitude kernel function, Indicates the number of layers, Indicates the The kernel function of the electromagnetic wave amplitude of the layer downlink, Indicates the The kernel function of the amplitude of the electromagnetic wave in the upper layer.

[0027] Characteristic equation matrix for dimensional matrix, each element is represented as follows: in, Indicates the The z-axis coordinate of the layer boundary of the layer, Represents the surface normal boundary condition about The coefficient of The convergence boundary condition for the last layer of the layered earth is about The coefficient of Represents the surface normal boundary condition about The coefficient of The potential boundary condition of the ith layer of the layered earth is expressed as The coefficient of The continuous boundary condition of the normal current density of the ith layer of the layered earth is The coefficient of The potential boundary condition of the ith layer of the layered earth is expressed as The coefficient of The continuous boundary condition of the normal current density of the ith layer of the layered earth is about The coefficient of The potential boundary condition of the ith layer of the layered earth is expressed as The coefficient of The continuous boundary condition of the normal current density of the ith layer of the layered earth is The coefficient of .

[0028] Characteristic equation vector for dimensional column vector whose non-zero elements are: in, Represents the first element in the column, Represents the second element in the column.

[0029] S2. According to the first layered upward electromagnetic wave amplitude kernel function corresponding to the characteristic equation under each integral variable, the upper limit of the horizontal layered earth integration is obtained. The upper limit of the horizontal layered earth integration is set to the maximum value of the integral variable that meets the preset criterion. The preset criterion is used to reflect the relationship between the local absolute error and the allowable error of the first layered upward electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the integral variable set. The allowable error is set to be determined according to the fluctuation range of the first layered upward electromagnetic wave amplitude kernel function as the integral variable changes. In a preferred embodiment of the present application, the first layered upward electromagnetic wave amplitude kernel function of the characteristic equation of the horizontal layered earth for each integral variable is iteratively calculated, and the first layered upward electromagnetic wave amplitude kernel function is judged by the preset criterion to determine the upper limit of the horizontal layered earth integration.

[0030] make , solve the characteristic equation and get the integral variable as The corresponding feature vector to be found, and record the .

[0031] make , iteratively solve the characteristic equation until Get the desired eigenvector corresponding to each integral variable in the integral variable set, and record the corresponding eigenvector .

[0032] According to the kernel function of the amplitude of the upgoing electromagnetic wave of each first layer, the fluctuation range of the kernel function of the amplitude of the upgoing electromagnetic wave of the first layer as the integral variable changes is obtained, which is expressed as follows: in, represents the fluctuation range of the first layer's upgoing electromagnetic wave amplitude kernel function, represents the maximum value of the first layer's upgoing electromagnetic wave amplitude kernel function, represents a minimum value of the first layered uplink electromagnetic wave amplitude kernel function.

[0033] Further, according to the fluctuation range, an allowable error is constructed, and according to each first layered uplink electromagnetic wave amplitude kernel function, a local absolute error of the first layered uplink electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the integral variable set is obtained, and according to the allowable error and the local absolute error, a preset criterion is constructed, and the preset criterion is represented as follows: wherein, represents the first layered uplink electromagnetic wave amplitude kernel function corresponding to the highest integral variable, represents the integral variable satisfying the preset criterion, represents an integral variable index corresponding to the integral variable satisfying the preset criterion.

[0034] According to the preset criterion, a maximum value of the integral variable satisfying the preset criterion is obtained, and the maximum value is taken as the horizontal layered earth integral upper limit.

[0035] In the preferred embodiment of the present application, the equal index sampling method is used to determine the integral variable, which can obtain the sharp change of the first layered uplink electromagnetic wave amplitude kernel function in the low frequency band, and can also obtain the asymptotic value of the first layered uplink electromagnetic wave amplitude kernel function in the high frequency band, so as to obtain the dynamic change waveform of the entire first layered uplink electromagnetic wave amplitude kernel function, and ensure the accuracy of the measurement. At the same time, the integral variable index discretization step is determined, which avoids the influence of soil parameter change. The horizontal layered earth integral upper limit is determined by the soil parameter, which reflects the difference of the soil parameter, and does not need to use a large number of cases to solve the optimal solution of the filtering coefficient and the index sampling coefficient, which significantly reduces the complexity of the measurement.

[0036] S3, according to the obtained pole distance of the Wenner four-electrode method, a horizontal layered earth unbounded domain apparent resistivity relationship is constructed; in the preferred embodiment of the present application, the measurement of the horizontal layered earth parameter adopts the Wenner four-electrode method, including 2 power supply electrodes and 2 measurement electrodes, which are symmetrically arranged between the four electrodes, and the distance between the electrodes is the pole distance, a total of times of measurement, corresponding to groups of pole distances.

[0037] An apparent resistivity calculation formula of the pole distance is constructed, and the apparent resistivity calculation formula is represented as: wherein, represents the pole distance, represents the apparent resistivity corresponding to the pole distance represents the potential function. ​

[0038] As Figure 2 The horizontal layered earth model diagram is shown, and the potential function is solved according to the horizontal layered earth model diagram to obtain a potential function analytical expression: Wherein, The corresponding first-order zero-order Bessel function, The corresponding first-order zero-order Bessel function, The potential function integral variable is represented, The first layered soil resistivity is represented, The pole distance is represented The corresponding first-order zero-order Bessel function.

[0039] Because the range of the potential function integral variable of the potential function analytical expression is an infinite bound range, the apparent resistivity obtained according to the potential function analytical expression is an unbounded domain apparent resistivity relationship, and the unbounded domain apparent resistivity relationship is: S3, based on the upper limit of the horizontal layered earth integral, the integral range of the unbounded domain apparent resistivity relationship is limited to obtain a bounded domain apparent resistivity relationship; the upper limit of the potential function integral variable of the unbounded domain apparent resistivity relationship is set to the upper limit of the horizontal layered earth integral to obtain the bounded domain apparent resistivity relationship, and the bounded domain apparent resistivity relationship is represented as: Wherein, The upper limit of the horizontal layered earth integral is represented.

[0040] S4, based on the 151-point Gauss-Legendre integral algorithm and Euler transformation, the bounded domain apparent resistivity relationship is iteratively solved to obtain apparent resistivity calculation results; in the preferred embodiment of the present application, the 151-point Gauss-Legendre integral algorithm and Euler transformation are combined to iteratively solve the bounded domain apparent resistivity relationship, the 151-point Gauss-Legendre integral algorithm is a specific implementation form of the Gauss-Legendre integral algorithm using 151 nodes, and the 151-point Gauss-Legendre integral algorithm is used to solve the bounded domain apparent resistivity relationship to obtain an apparent resistivity Gauss calculation formula, and the apparent resistivity Gauss calculation formula is: Wherein, The integral point index of the 151-point Gauss-Legendre integral algorithm is represented, The corresponding first-order zero-order Bessel function, The corresponding first-order zero-order Bessel function, The corresponding first-order zero-order Bessel function, corresponding first type zero order Bessel function, denotes the weight coefficient of the 151-point Gauss-Legendre integral algorithm, denotes the position coefficient of the 151-point Gauss-Legendre integral algorithm, and the specific values of the weight coefficient and the position coefficient need to be determined through the position coefficient and the weight coefficient table of the 151-point Gauss-Legendre integral algorithm, which is public content and will not be specifically shown in the present application.

[0041] The Euler transformation coefficient function is introduced into the apparent resistivity calculation formula to obtain an apparent resistivity Euler transformation calculation formula, and the apparent resistivity Euler transformation calculation formula is: wherein, denotes the coefficient function of the Euler transformation, and wherein, denotes the complementary error function, denotes the integral variable, corresponding first layered uplink electromagnetic wave amplitude kernel function, denotes corresponding first type zero order Bessel function, denotes corresponding first type zero order Bessel function.

[0042] For the in the apparent resistivity Euler transformation calculation formula still adopts the method for determining the first layered uplink electromagnetic wave amplitude kernel function in S1, and the difference lies in that the integral variable is , so the specific solving process will not be repeated.

[0043] Let the pole distance number be , and the apparent resistivity Euler transformation calculation formula is solved to obtain the apparent resistivity measurement result measured by the first four-pole method.

[0044] Let , and the apparent resistivity Euler transformation calculation formula is iteratively solved until > to obtain the final apparent resistivity measurement result.

[0045] In the preferred embodiments of the present application, the 151-point Gauss-Legendre numerical integral algorithm is used in combination with the Euler transformation coefficient to realize the Euler transformation of the apparent resistivity, which can effectively improve the measurement efficiency of the apparent resistivity of the horizontal layered earth and reduce the complexity of the measurement.

[0046] The apparent resistivity calculation method of the horizontal layered earth of the application is compared with the calculation results of the complex mirror image method and the 141-point linear filtering method, and a 10-layer horizontal layered earth example is verified. The horizontal layered earth parameters of the 10-layer horizontal layered earth are as follows: the soil resistivity of the first layer is 100 Ω·m, the thickness is 1 m, the boundary z-axis coordinate of the soil of the first layer and the soil of the second layer is 1 m; the soil resistivity of the second layer is 1000 Ω·m, the thickness is 1 m, the boundary z-axis coordinate of the soil of the second layer and the soil of the third layer is 2 m; the soil resistivity of the third layer is 100 Ω·m, the thickness is 1 m, the boundary z-axis coordinate of the soil of the third layer and the soil of the fourth layer is 3 m; the soil resistivity of the fourth layer is 100 Ω·m, the thickness is 1 m, the boundary z-axis coordinate of the soil of the fourth layer and the soil of the fifth layer is 4 m; the soil resistivity of the fifth layer is 100 Ω·m, the thickness is 1 m, the boundary z-axis coordinate of the soil of the fifth layer and the soil of the sixth layer is 5 m; the soil resistivity of the sixth layer is 100 Ω·m, the thickness is 1 m, the boundary z-axis coordinate of the soil of the sixth layer and the soil of the seventh layer is 6 m; the soil resistivity of the seventh layer is 100 Ω·m, the thickness is 1 m, the boundary z-axis coordinate of the soil of the seventh layer and the soil of the eighth layer is 5 m; the soil resistivity of the eighth layer is 100 Ω·m, the thickness is 1 m, the boundary z-axis coordinate of the soil of the eighth layer and the soil of the ninth layer is 5 m; the soil resistivity of the ninth layer is 100 Ω·m, the thickness is 1 m, the boundary z-axis coordinate of the soil of the ninth layer and the soil of the tenth layer is 9 m; the soil resistivity of the tenth layer is 100 Ω·m, the thickness is 1 m.

[0047] The calculation results of the complex mirror image method, the 141-point linear filtering method and the apparent resistivity calculation method of the horizontal layered earth of the application are shown in the following table: As can be seen from Table 1, the error of the calculation results of the application and the calculation results of the complex mirror image method and the 141-point linear filtering method is within 0.07, the error is very small, so the apparent resistivity calculation method of the horizontal layered earth of the application can effectively improve the calculation efficiency, and also has high calculation accuracy.

[0048] In the preferred embodiment of the present application, the integral variable set is obtained by the exponential discrete sampling method, the characteristic equation of the horizontally layered earth is constructed according to the integral variable set and the horizontal layered earth parameters of the target large area region obtained, the upper limit of the horizontally layered earth integral is obtained according to the first layered uplink electromagnetic wave amplitude kernel function corresponding to the characteristic equation under each integral variable, the upper limit of the horizontally layered earth integral is set as the maximum value of the integral variable satisfying the preset criterion, the preset criterion is used to reflect the relationship between the local absolute error of the first layered uplink electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the integral variable set and the allowable error, the allowable error is determined according to the fluctuation range of the first layered uplink electromagnetic wave amplitude kernel function with the integral variable, the unbounded domain apparent resistivity relationship of the horizontally layered earth is constructed according to the pole distance of the Wenner quadrupole method, the integral range of the unbounded domain apparent resistivity relationship is limited based on the upper limit of the horizontally layered earth integral, the bounded domain apparent resistivity relationship is obtained, and the apparent resistivity calculation result is obtained by iteratively solving the bounded domain apparent resistivity relationship based on the 151-point Gauss-Legendre integral algorithm and Euler transformation. The apparent resistivity calculation method of the horizontally layered earth disclosed in the present application determines the integral variable by using the equal exponential sampling method, can obtain the sharp change of the first layered uplink electromagnetic wave amplitude kernel function at a low frequency band, can also obtain the asymptotic value of the first layered uplink electromagnetic wave amplitude kernel function at a high frequency band, and thus can obtain the dynamic change waveform of the entire first layered uplink electromagnetic wave amplitude kernel function, thereby ensuring the accuracy of the calculation. At the same time, the integral variable exponential discretization step is determined, avoiding the influence of soil parameter changes. The upper limit of the horizontally layered earth integral is determined by the soil parameters, reflecting the difference of the soil parameters, and there is no need to use a large number of cases to solve the optimal solution of the filtering coefficient and the exponential sampling coefficient, thereby significantly reducing the complexity of the calculation. The Euler transformation of the apparent resistivity is realized by using the 151-point Gauss-Legendre numerical integral algorithm combined with the Euler transformation coefficient, which can effectively improve the calculation efficiency of the apparent resistivity of the horizontally layered earth and reduce the complexity of the calculation.

[0049] Correspondingly, as Figure 3 shown is an apparent resistivity calculation system of a horizontally layered earth, based on an apparent resistivity calculation method of a horizontally layered earth, the embodiment of the present application further provides an apparent resistivity calculation system of a horizontally layered earth, realizes the apparent resistivity calculation method of the horizontally layered earth disclosed in the embodiment of the present application, and comprises a characteristic equation construction unit 1, a horizontally layered earth integral upper limit calculation unit 2, an apparent resistivity relationship construction unit 3, an apparent resistivity relationship conversion unit 4 and an apparent resistivity calculation unit 5. The characteristic equation construction unit 1 is used to obtain an integral variable set by an exponential discrete sampling method, and construct a characteristic equation of a horizontally layered earth according to the integral variable set and the horizontal layered earth parameters of a target large area region obtained. The horizontal layered earth integral upper limit calculation unit 2 is configured to obtain a horizontal layered earth integral upper limit according to a first layered uplink electromagnetic wave amplitude kernel function corresponding to the characteristic equation under each integral variable, the horizontal layered earth integral upper limit being set as a maximum value of the integral variable satisfying a preset criterion, the preset criterion being configured to reflect a relationship between a local absolute error of the first layered uplink electromagnetic wave amplitude kernel function corresponding to a highest integral variable in the integral variable set and an allowable error, the allowable error being set according to a fluctuation range of the first layered uplink electromagnetic wave amplitude kernel function with respect to the integral variable; The apparent resistivity relationship formula construction unit 3 is configured to construct an unbounded domain apparent resistivity relationship formula of the horizontal layered earth according to the obtained pole distance of the Wenner quadrupole method. The apparent resistivity relationship formula conversion unit 4 is configured to limit an integral range of the unbounded domain apparent resistivity relationship formula based on the horizontal layered earth integral upper limit, to obtain a bounded domain apparent resistivity relationship formula. The apparent resistivity calculation unit 5 is configured to iteratively solve the bounded domain apparent resistivity relationship formula based on a 151-point Gauss-Legendre integral algorithm and Euler transformation, to obtain an apparent resistivity calculation result.

[0050] Further, the characteristic equation construction unit 1 includes a reflection coefficient calculation module, an interlayer relationship construction module, and a characteristic equation construction module. The reflection coefficient calculation module is configured to obtain horizontal layered earth parameters of a target large area, the horizontal layered earth parameters including soil resistivity of each layer and z-axis coordinates of layer boundaries of each layer, and construct reflection coefficients of each layer boundary according to the soil resistivity. The interlayer relationship construction module is configured to determine an interlayer relationship of layer boundaries of the horizontal layered earth according to the reflection coefficients, the integral variable set, and the z-axis coordinates of the layer boundaries based on electromagnetic characteristics of the horizontal layered earth. The characteristic equation construction module is configured to construct a characteristic equation of the horizontal layered earth based on electromagnetic field boundary conditions, the characteristic equation being composed of a characteristic equation matrix, a characteristic equation vector, and a to-be-solved characteristic vector, elements of the characteristic equation matrix representing the interlayer relationship, elements of the characteristic equation vector representing known electromagnetic field boundary excitation conditions, and the to-be-solved characteristic vector including the first layered uplink electromagnetic wave amplitude kernel function.

[0051] Further, the horizontal layered earth integral upper limit calculation unit 2 includes a first calculation module, an allowable error construction module, a local absolute error construction module, and a second calculation module. The first calculation module is configured to iteratively solve the characteristic equation according to the integral variable set to obtain the to-be-solved characteristic vector corresponding to each integral variable in the integral variable set, and obtain the first layered uplink electromagnetic wave amplitude kernel function in each to-be-solved characteristic vector. The allowable error construction module is configured to obtain a fluctuation range of the first layered uplink electromagnetic wave amplitude kernel function according to each first layered uplink electromagnetic wave amplitude kernel function, and construct an allowable error according to the fluctuation range. The local absolute error construction module is configured to obtain a local absolute error of the first layered uplink electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the integral variable set according to each first layered uplink electromagnetic wave amplitude kernel function. The second calculation module is configured to construct a preset criterion according to the local absolute error and the allowable error, and solve the preset criterion to obtain a maximum value of the integral variable satisfying the preset criterion, and take the maximum value as a horizontal layered earth integral upper limit.

[0052] Further, the apparent resistivity calculation unit 3 comprises a third calculation module, an Euler transformation module and a fourth calculation module. The third calculation module is configured to solve the bounded domain apparent resistivity relationship by using a 151-point Gauss-Legendre integral algorithm to obtain an apparent resistivity Gauss calculation formula. The Euler transformation module is configured to introduce an Euler transformation coefficient function into the apparent resistivity Gauss calculation formula to obtain an apparent resistivity Euler transformation calculation formula. The fourth calculation module is configured to iteratively solve the apparent resistivity Euler transformation calculation formula to obtain an apparent resistivity calculation result.

[0053] Further, the apparent resistivity Euler transformation calculation formula is expressed as: wherein, denotes a pole distance, denotes a pole distance number of the Wenner quadrupole method, denotes a pole distance corresponding apparent resistivity, denotes a soil resistivity of a first layer, denotes an integral point index of the 151-point Gauss-Legendre integral, denotes a position coefficient of the 151-point Gauss-Legendre integral, denotes a horizontal layered earth integral upper limit, denotes a weight coefficient of the 151-point Gauss-Legendre integral. a coefficient function representing the Euler transform, representing the integral variable a corresponding first layered upgoing electromagnetic wave amplitude kernel function, representing a corresponding first kind zero order Bessel function, representing a corresponding first kind zero order Bessel function The specific limitation of the apparent resistivity measuring system for a horizontally layered earth can refer to the above-mentioned limitation of the apparent resistivity measuring method for a horizontally layered earth, which will not be repeated here. Those skilled in the art can realize that the various modules and steps described in combination with the embodiments disclosed in the present application can be realized in hardware, software or a combination of both. Whether the functions are realized in hardware or software depends on the specific application and design constraints of the technical solution. The skilled person can use different methods to realize the described functions for each specific application, but such implementation should not be considered as beyond the scope of the present application.

[0054] In summary, the application provides a kind of apparent resistivity measurement method and system of horizontal layered earth, which solves the technical problem of how to meet the dual requirements of precision and efficiency of apparent resistivity measurement of horizontal layered earth, the method comprises: obtaining integral variable set by exponential discrete sampling method, and constructing the characteristic equation of horizontal layered earth according to the integral variable set and the horizontal layered earth parameters of the target large area region obtained;According to the first layered uplink electromagnetic wave amplitude kernel function corresponding to the characteristic equation under each integral variable, the upper limit of horizontal layered earth integral is obtained, the upper limit of horizontal layered earth integral is set as the maximum value of integral variable that meets the preset criterion, the preset criterion is used to reflect the relationship between the local absolute error of the first layered uplink electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the integral variable set and the allowable error, and the allowable error is determined according to the fluctuation range of the first layered uplink electromagnetic wave amplitude kernel function with integral variable;According to the pole distance of Wenner quadrupole method obtained, the unbounded domain apparent resistivity relationship of horizontal layered earth is constructed;Based on the upper limit of horizontal layered earth integral, the integral range of unbounded domain apparent resistivity relationship is limited to obtain bounded domain apparent resistivity relationship;Based on 151-point Gauss-Legendre integral algorithm and Euler transformation, the bounded domain apparent resistivity relationship is iteratively solved to obtain the apparent resistivity calculation result.The apparent resistivity measurement method of horizontal layered earth disclosed in the application uses equal exponential sampling method to determine the integral variable, which can obtain the sharp change of the first layered uplink electromagnetic wave amplitude kernel function in low frequency band, and can also obtain the asymptotic value of the first layered uplink electromagnetic wave amplitude kernel function in high frequency band, so as to obtain the dynamic change waveform of the entire first layered uplink electromagnetic wave amplitude kernel function, and ensure the accuracy of the calculation.At the same time, the integral variable exponential discretization step is determined, which avoids the influence of soil parameter change on it.The upper limit of horizontal layered earth integral is determined by soil parameters, which reflects the difference of soil parameters, and does not need to use a large number of cases to solve the optimal solution of filtering coefficient and exponential sampling coefficient, which significantly reduces the complexity of calculation.Using 151-point Gauss-Legendre numerical integral algorithm combined with Euler transformation coefficient to realize the Euler transformation of apparent resistivity can effectively improve the calculation efficiency of apparent resistivity of horizontal layered earth and reduce the complexity of calculation.

[0055] Each embodiment in this specification is described in a progressive manner, and the same or similar parts of each embodiment can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. It should be noted that the various technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the various technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0056] The above-described embodiments merely represent several preferred implementations of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that a person skilled in the art could make several improvements and substitutions without departing from the technical principles of the present application, and such improvements and substitutions should also be considered within the scope of protection of the present application. Therefore, the scope of protection of the present patent application shall be based on the scope of protection of the claims.

Claims

1. A method for calculating the apparent resistivity of horizontally layered earth, characterized in that: The method comprises: Obtaining an integral variable set by an exponential discrete sampling method, and constructing a characteristic equation of the horizontally layered earth based on the integral variable set and the obtained horizontally layered earth parameters of the target earth region; Obtaining a horizontal layered geodetic integral upper limit based on the first layered upward electromagnetic wave amplitude kernel function corresponding to the characteristic equation under each integral variable, wherein the horizontal layered geodetic integral upper limit is set to the maximum value of the integral variable that satisfies a preset criterion, wherein the preset criterion is used to reflect the relationship between the local absolute error of the first layered upward electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the set of integral variables and an allowable error, wherein the allowable error is set to be determined based on the fluctuation range of the first layered upward electromagnetic wave amplitude kernel function as the integral variable changes; Constructing an apparent resistivity relationship of the unbounded domain of the horizontally layered earth based on the obtained pole distance of the Wenner quadrupole method; Based on the upper limit of the horizontal layered geodetic integration, the integration range of the unbounded domain apparent resistivity relationship is limited to obtain the bounded domain apparent resistivity relationship; Based on the 151-point Gauss-Legendre integral algorithm and Euler transformation, the apparent resistivity relationship of the bounded domain is iteratively solved to obtain the apparent resistivity measurement result.

2. The method for calculating apparent resistivity of horizontally layered earth according to claim 1, wherein: The step of constructing a characteristic equation of the horizontally layered earth based on the set of integral variables and the acquired horizontally layered earth parameters of the target earth region includes: Acquire horizontal layered geodetic parameters of the target geodetic region, the horizontal layered geodetic parameters including soil resistivity of each layer and a z-axis coordinate of a layer boundary of each layer, and construct a reflection coefficient of each layer boundary based on the soil resistivity; Determining, based on the electromagnetic characteristics of the horizontally layered earth and the reflection coefficient, the set of integral variables, and the z-axis coordinate of the layer boundary, an interlayer relationship of the layer boundary of the horizontally layered earth; Based on the electromagnetic field boundary conditions, the characteristic equation of the horizontally layered earth is constructed. The characteristic equation consists of a characteristic equation matrix, a characteristic equation vector and a characteristic vector to be determined. The elements of the characteristic equation matrix represent the inter-layer relationship, and the elements of the characteristic equation vector represent the known electromagnetic field boundary excitation conditions. The characteristic vector to be determined includes the first layered upward electromagnetic wave amplitude kernel function.

3. The method for calculating apparent resistivity of horizontally layered earth according to claim 2, wherein: The upper limit of the horizontal layered earth integral is obtained according to the first layered uplink electromagnetic wave amplitude kernel function corresponding to the characteristic equation under each integral variable, including: Iteratively solving the characteristic equation according to the set of integral variables to obtain the desired eigenvector corresponding to each integral variable in the set of integral variables, and obtaining the first layered uplink electromagnetic wave amplitude kernel function in each of the desired eigenvectors; Obtaining a fluctuation range of the first-layered upward electromagnetic wave amplitude kernel function according to each first-layered upward electromagnetic wave amplitude kernel function, and constructing an allowable error according to the fluctuation range; Obtaining, according to each first-layered upward electromagnetic wave amplitude kernel function, a local absolute error of the first-layered upward electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the set of integral variables; According to the local absolute error and the allowable error, a preset criterion is constructed, and the preset criterion is solved to obtain the maximum value of the integral variable that meets the preset criterion, and the maximum value is used as the upper limit of the horizontal layered geodetic integral.

4. The method for calculating apparent resistivity of horizontally layered earth according to claim 1, wherein: The apparent resistivity relationship of the bounded domain is iteratively solved based on the 151-point Gauss-Legendre integral algorithm and Euler transformation to obtain the apparent resistivity measurement result, including: The 151-point Gauss-Legendre integral algorithm is used to solve the apparent resistivity relationship of the bounded domain, and the Gauss calculation formula of the apparent resistivity is obtained; Introducing the Euler transformation coefficient function into the apparent resistivity Gaussian calculation formula to obtain the apparent resistivity Euler transformation calculation formula; The apparent resistivity Euler transform calculation formula is iteratively solved to obtain the apparent resistivity measurement result.

5. The method for calculating apparent resistivity of horizontally layered earth according to claim 4, wherein: The calculation formula of the apparent resistivity Euler transform is expressed as: in, Indicates the pole distance, Indicates the pole distance number of the Wenner quadrupole method, Indicates pole distance The corresponding apparent resistivity, represents the soil resistivity of the first layer, Indicates the integration point index of the 151-point Gauss-Legendre integral, represents the position coefficient of the 151-point Gauss-Legendre integral, represents the upper limit of the horizontal layered geodetic integral, represents the weight coefficient of the 151-point Gauss-Legendre integral, represents the coefficient function of Euler transformation, The integral variable is The corresponding first layer uplink electromagnetic wave amplitude kernel function, express The corresponding zero-order Bessel function of the first kind is, express The corresponding zero-order Bessel function of the first kind.

6. A system for measuring apparent resistivity of horizontally layered earth, for implementing the method for measuring apparent resistivity of horizontally layered earth according to any one of claims 1 to 7, characterized in that: The system comprises: a characteristic equation construction unit, a horizontal layered earth integral upper limit calculation unit, an apparent resistivity relationship construction unit, an apparent resistivity relationship conversion unit and an apparent resistivity calculation unit; The characteristic equation construction unit is used to obtain an integral variable set by an exponential discrete sampling method, and construct a characteristic equation of the horizontally layered earth based on the integral variable set and the obtained horizontally layered earth parameters of the target earth region; The horizontal layered geodetic integral upper limit calculation unit is configured to obtain a horizontal layered geodetic integral upper limit based on the first layered upward electromagnetic wave amplitude kernel function corresponding to the characteristic equation under each integral variable, wherein the horizontal layered geodetic integral upper limit is set to the maximum value of the integral variable that satisfies a preset criterion, wherein the preset criterion is used to reflect the relationship between the local absolute error of the first layered upward electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the set of integral variables and the allowable error, wherein the allowable error is set to be determined based on the fluctuation range of the first layered upward electromagnetic wave amplitude kernel function as the integral variable changes; The apparent resistivity relationship constructing unit is used to construct the unbounded domain apparent resistivity relationship of the horizontally layered earth according to the pole distance obtained by the Wenner quadrupole method; an apparent resistivity relation conversion unit, configured to limit the integration range of the unbounded domain apparent resistivity relation based on the horizontal layered earth integral upper limit, and obtain the bounded domain apparent resistivity relation; The apparent resistivity calculation unit is used to iteratively solve the bounded domain apparent resistivity relationship based on a 151-point Gauss-Legendre integral algorithm and Euler transformation to obtain an apparent resistivity measurement result.

7. The system for calculating apparent resistivity of horizontally layered earth according to claim 6, wherein: The characteristic equation construction unit includes: a reflection coefficient calculation module, an interlayer relationship construction module and a characteristic equation construction module; The reflection coefficient calculation module is used to obtain horizontal layered earth parameters of the target earth area, wherein the horizontal layered earth parameters include the soil resistivity of each layer and the z-axis coordinate of the layer boundary of each layer, and construct the reflection coefficient of each layer boundary based on the soil resistivity; The interlayer relationship building module is configured to determine the interlayer relationship of the layer boundary of the horizontally layered earth based on the electromagnetic characteristics of the horizontally layered earth, the reflection coefficient, the set of integral variables, and the z-axis coordinate of the layer boundary; The characteristic equation construction module is used to construct the characteristic equation of the horizontally layered earth based on the electromagnetic field boundary conditions. The characteristic equation consists of a characteristic equation matrix, a characteristic equation vector and a characteristic vector to be determined. The elements of the characteristic equation matrix represent the inter-layer relationship, and the elements of the characteristic equation vector represent the known electromagnetic field boundary excitation conditions. The characteristic vector to be determined includes the first layered upward electromagnetic wave amplitude kernel function.

8. The system for calculating apparent resistivity of horizontally layered earth according to claim 7, wherein: The horizontal layered geodetic integral upper limit calculation unit includes: a first calculation module, an allowable error construction module, a local absolute error construction module and a second calculation module; The first calculation module is configured to iteratively solve the characteristic equation according to the set of integral variables to obtain the desired eigenvector corresponding to each integral variable in the set of integral variables, and obtain the first hierarchical uplink electromagnetic wave amplitude kernel function in each of the desired eigenvectors; The allowable error construction module is configured to obtain a fluctuation range of the first layered uplink electromagnetic wave amplitude kernel function according to each first layered uplink electromagnetic wave amplitude kernel function, and construct the allowable error according to the fluctuation range; The local absolute error construction module is configured to obtain, based on each first-layered uplink electromagnetic wave amplitude kernel function, the local absolute error of the first-layered uplink electromagnetic wave amplitude kernel function corresponding to the highest integral variable in the set of integral variables; The second calculation module is used to construct a preset criterion based on the local absolute error and the allowable error, and solve the preset criterion to obtain the maximum value of the integral variable that meets the preset criterion, and use the maximum value as the upper limit of the horizontal layered geodetic integral.

9. The system for calculating apparent resistivity of horizontally layered earth according to claim 6, wherein: The apparent resistivity calculation unit includes: a third calculation module, an Euler transformation module and a fourth calculation module; The third calculation module is used to solve the apparent resistivity relationship of the bounded domain using a 151-point Gauss-Legendre integral algorithm to obtain a Gauss calculation formula for apparent resistivity; The Euler transformation module is used to introduce the Euler transformation coefficient function into the apparent resistivity Gaussian calculation formula to obtain the apparent resistivity Euler transformation calculation formula; The fourth calculation module is used to iteratively solve the apparent resistivity Euler transform calculation formula to obtain the apparent resistivity measurement result.

10. The system for calculating apparent resistivity of horizontally layered earth according to claim 9, wherein: The calculation formula of the apparent resistivity Euler transform is expressed as: in, Indicates the pole distance, Indicates the pole distance number of the Wenner quadrupole method, Indicates pole distance The corresponding apparent resistivity, represents the soil resistivity of the first layer, Indicates the integration point index of the 151-point Gauss-Legendre integral, represents the position coefficient of the 151-point Gauss-Legendre integral, represents the upper limit of the horizontal layered geodetic integral, represents the weight coefficient of the 151-point Gauss-Legendre integral, represents the coefficient function of Euler transformation, The integral variable is The corresponding first layer uplink electromagnetic wave amplitude kernel function, express The corresponding zero-order Bessel function of the first kind is, express The corresponding zero-order Bessel function of the first kind.

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