Layered medium electromagnetic field calculation method and device, electronic equipment and medium

Abstract

The invention discloses a layered medium electromagnetic field calculation method and device, electronic equipment and a medium. The method comprises the following steps: establishing a Bessel function integral expression of a uniform layered medium electromagnetic field; segmenting an integral region according to the distance from an emission source to a receiving point, and further carrying out segmented discretization on a Bessel function; performing quadratic interpolation on the Bessel function integral expression of each integral unit through a shape function to obtain an integral expression corresponding to the integral unit; an integral expression corresponding to each integral unit is calculated, and an integral result of the layered medium electromagnetic field is obtained through accumulation calculation. The method is suitable for high-precision calculation of a complex layered electromagnetic field, and solves the problem of low universality and precision of an algorithm in the prior art.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic field calculation, and more specifically, to a layered medium electromagnetic field calculation method, device, electronic equipment and medium. Background Art

[0002] In the numerical simulation of layered electromagnetic fields, the analytical expression of electromagnetic fields contains Bessel functions. As the parameters such as the transmission and reception distance and frequency change, the Bessel functions change rapidly and are difficult to calculate. This results in reduced accuracy of numerical simulation calculations. In order to achieve high-precision calculations of integrals containing Bessel functions, the most widely used methods are digital filtering and direct integration.

[0003] For the digital filtering method, the numerical calculation accuracy of Bessel functions under different changing trend kernel functions of five numerical filtering algorithms was compared. The results showed that the calculation accuracy of Anderson801 filter coefficient was high and stable, but the disadvantage was low calculation efficiency. Zhang Yawei compared the interpretation depth and calculation accuracy that could be achieved by several filter coefficients. Werthmüller used the direct matrix inversion method to derive the filter coefficients and designed a digital filter that can be used for diffusion field and wave field. He tested it with 250MHz ground penetrating radar as an example to prove the effectiveness of this method. For the direct integration method, Zhou Jianmei used cubic spline function to interpolate the integral kernel function, and obtained a series of simple Sommerfeld integrals with kernel functions as polynomials, and then used the recursive formula of Bessel function and the asymptotic expansion of Lommel formula to solve the value of the integral; Li Lei used the wavelet transform method to transform the integral containing Bessel function into an integral that can be solved by special functions. This method improves the convergence property of the integral, accelerates the integral calculation, and improves the calculation efficiency; Kye proposed an ISE method - the orthogonal interpolation quadrature method (QWE) of Shanks transform, which is applied to the integral calculation containing Bessel function; Xi Jianjun et al. rewrote the electromagnetic field formula into the sum of the integral formula containing Bessel function transformation and the ordinary integral or hypergeometric function, and analyzed the attenuation law of the reflection coefficient existing in the kernel function with the integrand; Gao et al. used numerical methods to calculate the high-frequency integral transformation containing Bessel function, and derived an asymptotic quadrature rule based on the variable upper bound integral, and verified the effectiveness of the scheme through examples; Dai Shikun et al. proposed a cubic spline interpolation method for calculating Bessel function integral, which solved the layered medium simulation problem to a certain extent.

[0004] The above methods can generally be well applied to the calculation of electromagnetic fields in uniform layered media at low frequencies and certain transmission and reception distances. However, as the frequency and transmission and reception distance increase, the calculation accuracy of these methods decreases or even fails, and they are not universal.

[0005] Therefore, it is necessary to develop a layered medium electromagnetic field calculation method, device, electronic equipment and medium.

[0006] The information disclosed in the background technology section of the present invention is only intended to deepen the understanding of the general background technology of the present invention, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to those skilled in the art. Summary of the invention

[0007] The present invention proposes a method, device, electronic device and medium for calculating the electromagnetic field of a layered medium. The integral containing the Bessel function can be divided into two intervals and expanded with high precision using different polynomials. The integral of each interval can be discretized into the sum of multiple unit integrals. Each unit integrand is represented by quadratic shape function interpolation, thereby obtaining an analytical expression for the high-oscillation unit integral, and all discrete units are superimposed and summed to obtain a high-precision numerical solution.

[0008] In a first aspect, an embodiment of the present disclosure provides a method for calculating electromagnetic fields of layered media, comprising:

[0009] Establish the Bessel function integral expression of the electromagnetic field of uniform layered medium;

[0010] The integration area is segmented according to the distance from the transmitting source to the receiving point, and then the Bessel function is discretized piecewise;

[0011] The integral expression of the Bessel function of each integral unit is interpolated quadratically through the shape function to obtain the integral expression corresponding to the integral unit;

[0012] The integral expression corresponding to each integral unit is calculated, and the integral result of the electromagnetic field of the layered medium is obtained by cumulative calculation.

[0013] Preferably, the Bessel function integral expression of the electromagnetic field of the uniform layered medium is:

[0014]

[0015] Where g(m) represents the earth response function, m represents the integral parameter, r represents the distance from the transmitting source to the receiving point, mr represents the quantity, and J n Represents the nth-order Bessel function.

[0016] Preferably, piecewise discretizing the Bessel function comprises:

[0017] The Bessel function is divided into two intervals:

[0018] When 0≤mr≤4, let t=(mr / 4) 2 , the Bessel function expansion is:

[0019]

[0020] When 4≤mr≤∞, let t=(4 / mr) 2 , the Bessel function expansion is:

[0021]

[0022] Among them, θ0=mr-π / 4, θ1=mr-3π / 4,

[0023]

[0024] Among them, |ε0|≤10 -9 ,|ε1|≤3×10 -10 ,|ε2|≤3×10 -9 ,|ε3|≤4×10 -9 ,|ε4|≤6×10 -9 ,|ε5|≤6×10 -9 .

[0025] Preferably, the Bessel function integral expression of the electromagnetic field is expressed by the Bessel function integral of the integral unit as follows:

[0026]

[0027] Among them, I ei represents the Bessel function integral expression of the i-th integration unit, m i ,m i+2 They represent the lower limit and upper limit of the i-th integration unit respectively, and M represents the number of units.

[0028] Preferably, the Bessel function integral expression of each integral unit is interpolated quadratically by a shape function to obtain an integral expression corresponding to the integral unit, which includes:

[0029] When 0≤mr≤4, the integral region of the Bessel function integral expression is discretized, and quadratic interpolation is performed within the unit through the shape function;

[0030] The integral expression corresponding to the integral unit obtained according to the interpolated integral region is:

[0031]

[0032] Among them, N1 = (2L1-1)L1, N2 = 4L1L3, N3 = (2L3-1)L3, L3=1-L1,l=m i+2 -m i .

[0033] Preferably, the Bessel function integral expression of each integral unit is interpolated quadratically by a shape function to obtain an integral expression corresponding to the integral unit, which includes:

[0034] When 4≤mr≤∞, the integral region of the Bessel function integral expression of each integral unit is discretized, and quadratic interpolation is performed within the unit through the shape function;

[0035] The integral expression corresponding to the integral unit obtained according to the interpolated integral region is:

[0036]

[0037] Among them, the coefficient A 11 ,A 12 ,A 13 ,A 14 ,A 15 ,A 16 The expression is:

[0038]

[0039]

[0040] Where l is the length of the integration unit.

[0041] Preferably, according to the integral expression corresponding to each integral unit, the integral result of the electromagnetic field of the layered medium is calculated as:

[0042]

[0043] Wherein, M represents the number of units.

[0044] In a second aspect, the present disclosure also provides a layered medium electromagnetic field calculation device, including:

[0045] Modeling module, which establishes the Bessel function integral expression of the electromagnetic field of uniform layered media;

[0046] Discrete module, which divides the integral area into segments according to the distance from the transmitting source to the receiving point, and then discretizes the Bessel function piecewise;

[0047] The integration module performs quadratic interpolation on the Bessel function integral expression of each integration unit through the shape function to obtain the integral expression corresponding to the integration unit;

[0048] The calculation module calculates the integral expression corresponding to each integral unit and obtains the integral result of the electromagnetic field of the layered medium by cumulative calculation.

[0049] In a third aspect, an embodiment of the present disclosure further provides an electronic device, the electronic device comprising:

[0050] A memory storing executable instructions;

[0051] A processor runs the executable instructions in the memory to implement the layered medium electromagnetic field calculation method.

[0052] In a fourth aspect, an embodiment of the present disclosure further provides a computer-readable storage medium, which stores a computer program, and when the computer program is executed by a processor, the layered medium electromagnetic field calculation method is implemented.

[0053] The methods and apparatus of the present invention have other features and advantages that will be apparent from, or will be described in detail in, the accompanying drawings and subsequent detailed descriptions incorporated herein, which together serve to explain the specific principles of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] The above and other objects, features and advantages of the present invention will become more apparent through a more detailed description of exemplary embodiments of the present invention in conjunction with the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present invention.

[0055] Figure 1 A flow chart showing the steps of a method for calculating electromagnetic fields of layered media according to an embodiment of the present invention.

[0056] Figure 2 shows a frequency 10 according to an embodiment of the present invention 4 Schematic diagram of analytical solution, numerical solution and relative error contour map of different electric field components at Hz.

[0057] Figure 3 A schematic diagram showing relative errors compared with a filter coefficient method according to an embodiment of the present invention is shown.

[0058] Figure 4 A schematic diagram showing relative errors of four filter coefficient methods according to an embodiment of the present invention is shown.

[0059] Figure 5 A block diagram of a layered medium electromagnetic field calculation device according to an embodiment of the present invention is shown.

[0060] Description of reference numerals:

[0061] 201, modeling module; 202, discrete module; 203, integration module; 204, calculation module. DETAILED DESCRIPTION

[0062] The preferred embodiments of the present invention will be described in more detail below. Although the preferred embodiments of the present invention are described below, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0063] The present invention provides a layered medium electromagnetic field calculation method, comprising:

[0064] Establish the Bessel function integral expression of the electromagnetic field of uniform layered medium;

[0065] The integration area is segmented according to the distance from the transmitting source to the receiving point, and then the Bessel function is discretized piecewise;

[0066] The integral expression of the Bessel function of each integral unit is interpolated quadratically through the shape function to obtain the integral expression corresponding to the integral unit;

[0067] The integral expression corresponding to each integral unit is calculated, and the integral result of the electromagnetic field of the layered medium is obtained by cumulative calculation.

[0068] In one example, the Bessel function integral expression of the electromagnetic field of a uniform layered medium is:

[0069]

[0070] Where g(m) represents the earth response function, m represents the integral parameter, r represents the distance from the transmitting source to the receiving point, mr represents the quantity, and J n Represents the nth-order Bessel function.

[0071] In one example, piecewise discretizing the Bessel function includes:

[0072] The Bessel function is divided into two intervals:

[0073] When 0≤mr≤4, let t=(mr / 4) 2 , the Bessel function expansion is:

[0074]

[0075] When 4≤mr≤∞, let t=(4 / mr) 2 , the Bessel function expansion is:

[0076]

[0077] Among them, θ0=mr-π / 4, θ1=mr-3π / 4,

[0078]

[0079] Among them, |ε0|≤10-9 ,|ε1|≤3×10 -10 ,|ε2|≤3×10 -9 ,|ε3|≤4×10 -9 ,|ε4|≤6×10 -9 ,|ε5|≤6×10 -9 .

[0080] In one example, the Bessel function integral expression of the electromagnetic field is expressed by the Bessel function integral of the integration unit as follows:

[0081]

[0082] Among them, I ei represents the Bessel function integral expression of the i-th integration unit, m i ,m i+2 They represent the lower limit and upper limit of the i-th integration unit respectively, and M represents the number of units.

[0083] In one example, the Bessel function integral expression of each integral unit is interpolated quadratically through the shape function to obtain the integral expression corresponding to the integral unit, including:

[0084] When 0≤mr≤4, the integral region of the Bessel function integral expression is discretized, and quadratic interpolation is performed within the unit through the shape function;

[0085] The integral expression corresponding to the integral unit obtained according to the interpolated integral region is:

[0086]

[0087] Among them, N1 = (2L1-1)L1, N2 = 4L1L3, N3 = (2L3-1)L3, L3=1-L1,l=m i+2 -m i .

[0088] In one example, the Bessel function integral expression of each integral unit is interpolated quadratically through the shape function to obtain the integral expression corresponding to the integral unit, including:

[0089] When 4≤mr≤∞, the integral region of the Bessel function integral expression of each integral unit is discretized, and quadratic interpolation is performed within the unit through the shape function;

[0090] The integral expression corresponding to the integral unit obtained according to the interpolated integral region is:

[0091]

[0092] Among them, the coefficient A11 ,A 12 ,A 13 ,A 14 ,A 15 ,A 16 The expression is:

[0093]

[0094]

[0095] Where l is the length of the integration unit.

[0096] In one example, according to the integral expression corresponding to each integral unit, the integral result of the electromagnetic field of the layered medium is calculated as follows:

[0097]

[0098] Wherein, M represents the number of units.

[0099] Specifically, the analytical expression of the electromagnetic field of a uniform layered medium can generally be expressed as the following Bessel function integral as formula (1).

[0100] To represent the integral containing Bessel function piecewise discretely, first divide the Bessel function into two intervals:

[0101] When 0≤mr≤4, let t=(mr / 4) 2 , the Bessel function expansion is formula (2), when 4≤mr≤∞, let t=(4 / mr) 2 , the Bessel function expansion is formula (3).

[0102] The shape function quadratic interpolation is used for the integral part of the Bessel function in the integral unit, and the Bessel function expression of the integral unit can be expressed as formula (4).

[0103] When the integration area is in the first interval (0≤mr≤4), Formula (4) can be rewritten as:

[0104]

[0105] Among them, P(m)=g(m), Q(m)=J0(mr).

[0106] The quadratic shape function interpolation is used for the unit integration of formula (8):

[0107]

[0108] Among them, N i =(2L i -1)L i , Ni+1 =4L i L i+2 , N i+2 =(2L i+2 -1)L i+2 , L i+2 =1-L i .

[0109] Therefore, the integral expression is formula (5).

[0110] When the integration area is in the second interval (4≤mr≤∞), t=(4 / mr) 2 , substituting the Bessel function J0(mr) into formula (4) yields:

[0111]

[0112] Using trigonometric function expansion formula:

[0113]

[0114] Formula (10) can be expanded as:

[0115]

[0116] make: Then formula (12) can be expressed as

[0117]

[0118] The P(m) and Q(m) in the unit of formula (13) are expressed by quadratic shape function interpolation:

[0119]

[0120] Among them, N i =(2L i -1)L i , N i+1 =4L i L i+2 , N i+2 =(2L i+2 -1)L i+2 ,

[0121] Substituting formula (14) into formula (13), the integral expression is formula (6).

[0122] Calculate the above discrete unit expression formula (6), and then perform integral unit accumulation to obtain the calculation result of formula (7), which is the integral result of the electromagnetic field of the layered medium.

[0123] The present invention also provides a layered medium electromagnetic field calculation device, comprising:

[0124] Modeling module, which establishes the Bessel function integral expression of the electromagnetic field of uniform layered media;

[0125] Discrete module, which divides the integral area into segments according to the distance from the transmitting source to the receiving point, and then discretizes the Bessel function piecewise;

[0126] The integration module performs quadratic interpolation on the Bessel function integral expression of each integration unit through the shape function to obtain the integral expression corresponding to the integration unit;

[0127] The calculation module calculates the integral expression corresponding to each integral unit and obtains the integral result of the electromagnetic field of the layered medium by cumulative calculation.

[0128] In one example, the Bessel function integral expression of the electromagnetic field of a uniform layered medium is:

[0129]

[0130] Where g(m) represents the earth response function, m represents the integral parameter, r represents the distance from the transmitting source to the receiving point, mr represents the quantity, and J n Represents the nth-order Bessel function.

[0131] In one example, piecewise discretizing the Bessel function includes:

[0132] The Bessel function is divided into two intervals:

[0133] When 0≤mr≤4, let t=(mr / 4) 2 , the Bessel function expansion is:

[0134]

[0135] When 4≤mr≤∞, let t=(4 / mr) 2 , the Bessel function expansion is:

[0136]

[0137] Among them, θ0=mr-π / 4, θ1=mr-3π / 4,

[0138]

[0139] Among them, |ε0|≤10 -9 ,|ε1|≤3×10 -10 ,|ε2|≤3×10 -9 ,|ε3|≤4×10 -9,|ε4|≤6×10 -9 ,|ε5|≤6×10 -9 .

[0140] In one example, the Bessel function integral expression of the electromagnetic field is expressed by the Bessel function integral of the integration unit as follows:

[0141]

[0142] Among them, I ei represents the Bessel function integral expression of the i-th integration unit, m i ,m i+2 They represent the lower limit and upper limit of the i-th integration unit respectively, and M represents the number of units.

[0143] In one example, the Bessel function integral expression of each integral unit is interpolated quadratically through the shape function to obtain the integral expression corresponding to the integral unit, including:

[0144] When 0≤mr≤4, the integral region of the Bessel function integral expression is discretized, and quadratic interpolation is performed within the unit through the shape function;

[0145] The integral expression corresponding to the integral unit obtained according to the interpolated integral region is:

[0146]

[0147] Among them, N1 = (2L1-1)L1, N2 = 4L1L3, N3 = (2L3-1)L3, L3=1-L1,l=m i+2 -m i .

[0148] In one example, the Bessel function integral expression of each integral unit is interpolated quadratically through the shape function to obtain the integral expression corresponding to the integral unit, including:

[0149] When 4≤mr≤∞, the integral region of the Bessel function integral expression of each integral unit is discretized, and quadratic interpolation is performed within the unit through the shape function;

[0150] The integral expression corresponding to the integral unit obtained according to the interpolated integral region is:

[0151]

[0152] Among them, the coefficient A 11 ,A 12 ,A 13 ,A 14 ,A 15 ,A16 The expression is:

[0153]

[0154]

[0155] Where l is the length of the integration unit.

[0156] In one example, according to the integral expression corresponding to each integral unit, the integral result of the electromagnetic field of the layered medium is calculated as follows:

[0157]

[0158] Wherein, M represents the number of units.

[0159] Specifically, the analytical expression of the electromagnetic field of a uniform layered medium can generally be expressed as the following Bessel function integral as formula (1).

[0160] To represent the integral containing Bessel function piecewise discretely, first divide the Bessel function into two intervals:

[0161] When 0≤mr≤4, let t=(mr / 4) 2 , the Bessel function expansion is formula (2), when 4≤mr≤∞, let t=(4 / mr) 2 , the Bessel function expansion is formula (3).

[0162] The shape function quadratic interpolation is used for the integral part of the Bessel function in the integral unit, and the Bessel function expression of the integral unit can be expressed as formula (4).

[0163] When the integration area is in the first interval (0≤mr≤4), Formula (4) can be rewritten as formula (8). Formula (9) is obtained by using quadratic shape function interpolation to integrate the unit of formula (8). Therefore, the integral expression is formula (5).

[0164] When the integration area is in the second interval (4≤mr≤∞), t=(4 / mr) 2 , Substituting the Bessel function J0(mr) into formula (4), we get formula (10). Using the trigonometric function expansion formula of formula (11), formula (10) can be expanded into formula (12), where: Then formula (12) can be expressed as formula (13), and P(m) and Q(m) in the unit of formula (13) can be expressed as formula (14) by using quadratic shape function interpolation. Substituting formula (14) into formula (13), the integral expression is formula (6).

[0165] Calculate the above discrete unit expression formula (6), and then perform integral unit accumulation to obtain the calculation result of formula (7), which is the integral result of the electromagnetic field of the layered medium.

[0166] The present invention also provides an electronic device, which includes: a memory storing executable instructions; and a processor, which runs the executable instructions in the memory to implement the above-mentioned layered medium electromagnetic field calculation method.

[0167] The present invention also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above-mentioned layered medium electromagnetic field calculation method is implemented.

[0168] To facilitate understanding of the solutions and effects of the embodiments of the present invention, four specific application examples are given below. Those skilled in the art should understand that the examples are only for facilitating understanding of the present invention, and any specific details thereof are not intended to limit the present invention in any way.

[0169] Example 1

[0170] Figure 1 A flow chart showing the steps of a method for calculating electromagnetic fields of layered media according to an embodiment of the present invention.

[0171] like Figure 1 As shown, the layered medium electromagnetic field calculation method includes: step 101, establishing a Bessel function integral expression of a uniform layered medium electromagnetic field; step 102, segmenting the integral region according to the distance from the transmitting source to the receiving point, and then discretizing the Bessel function in segments; step 103, performing quadratic interpolation on the Bessel function integral expression of each integral unit through a shape function to obtain an integral expression corresponding to the integral unit; step 104, calculating the integral expression corresponding to each integral unit, and obtaining the integral result of the layered medium electromagnetic field by cumulative calculation.

[0172] The calculation results of this method are given below to verify that the method proposed in the present invention is correct and has high accuracy when used for numerical simulation.

[0173] In the uniform full space, the conductivity σ=0.0001S / m, the relative dielectric constant εr=1, the electric dipole source coordinates are set to (0,0,0.1), and the dipole moment is one unit.

[0174] Figure 2 shows a frequency 10 according to an embodiment of the present invention 4 Schematic diagram of analytical solution, numerical solution and relative error contour map of different electric field components at Hz, z = 2m.

[0175] Figure 2 Shown is frequency 104 The analytical solution, numerical solution and relative error of the electric field component at Hz. From the comparison between the numerical solution and the analytical solution, it can be seen that the two have the same shape and a high degree of agreement. The maximum relative error of different electric field components is about 0.003%. The calculation results show that the algorithm of the present invention is correct and has a high calculation accuracy.

[0176] The comparison cases of this method with the existing filter coefficient method are shown below, among which the mainstream filter coefficient methods selected for comparison are shown in Table 1.

[0177] Table 1 Four high-precision long filter coefficients

[0178]

[0179] The algorithm of the present invention is compared with the above four digital filtering algorithms to verify the frequency applicability. The parameters are as follows:

[0180] Figure 3 A schematic diagram showing relative errors compared with a filter coefficient method according to an embodiment of the present invention is shown.

[0181] In the uniform full space, the frequency range is selected as 10-1~1010Hz (logarithmically equally spaced sampling), the conductivity σ=0.0001S / m, the relative dielectric constant εr=1, the electric dipole source coordinates are (0,0,0), and the dipole moment is one unit. The calculation results are as follows Figure 3 shown.

[0182] Figure 4 A schematic diagram showing relative errors of four filter coefficient methods according to an embodiment of the present invention is shown.

[0183] The algorithm of the present invention is compared with the above four digital filtering algorithms to verify the applicability of the transmission and reception distance. The parameters are as follows: in the uniform full space, the horizontal distance R from the transmitting source to the receiving point in the x direction ranges from 0.1 to 500m, the conductivity σ = 0.0001S / m, the relative dielectric constant ε r =1, the electric dipole source coordinates are (0,0,0), and the dipole moment is one unit. The calculation results are as follows Figure 4 shown.

[0184] From the above calculation results, it can be seen that the calculation accuracy of this method is similar to that of the filtering method at low frequency and short transmission and reception distance, but it is more stable. The calculation accuracy is similar when the frequency is low, and the calculation accuracy is more than 2 orders of magnitude higher when the frequency is high. The calculation accuracy of this method is similar but more stable at short transmission and reception distance, and the calculation accuracy is more than 2 orders of magnitude higher at long transmission and reception distance.

[0185] Example 2

[0186] Figure 5A block diagram of a layered medium electromagnetic field calculation device according to an embodiment of the present invention is shown.

[0187] like Figure 5 As shown, the layered medium electromagnetic field calculation device comprises:

[0188] Modeling module 201, establishing a Bessel function integral expression of the electromagnetic field of a uniform layered medium;

[0189] Discretization module 202, segmenting the integration area according to the distance from the transmitting source to the receiving point, and then discretizing the Bessel function piecewise;

[0190] An integration module 203 performs quadratic interpolation on the Bessel function integral expression of each integration unit through a shape function to obtain an integral expression corresponding to the integration unit;

[0191] The calculation module 204 calculates the integral expression corresponding to each integral unit, and obtains the integral result of the electromagnetic field of the layered medium by cumulative calculation.

[0192] Example 3

[0193] The present disclosure provides an electronic device, which includes: a memory storing executable instructions; and a processor, which runs the executable instructions in the memory to implement the above-mentioned layered medium electromagnetic field calculation method.

[0194] An electronic device according to an embodiment of the present disclosure includes a memory and a processor.

[0195] The memory is used to store non-temporary computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory (cache), etc. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc.

[0196] The processor may be a central processing unit (CPU) or other forms of processing units having data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the present disclosure, the processor is used to run the computer-readable instructions stored in the memory.

[0197] Those skilled in the art should be able to understand that in order to solve the technical problem of how to obtain a good user experience, the present embodiment may also include well-known structures such as a communication bus and an interface, and these well-known structures should also be included in the protection scope of the present disclosure.

[0198] For detailed description of this embodiment, reference may be made to the corresponding descriptions in the aforementioned embodiments, which will not be repeated here.

[0199] Example 4

[0200] The embodiment of the present disclosure provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the layered medium electromagnetic field calculation method is implemented.

[0201] According to the computer-readable storage medium of the embodiment of the present disclosure, non-transitory computer-readable instructions are stored thereon. When the non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the above-mentioned methods of each embodiment of the present disclosure are executed.

[0202] The above-mentioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or mobile hard disk), media with built-in rewritable non-volatile memory (e.g., memory card) and media with built-in ROM (e.g., ROM box).

[0203] Those skilled in the art should understand that the purpose of the above description of the embodiments of the present invention is only to exemplarily illustrate the beneficial effects of the embodiments of the present invention, and is not intended to limit the embodiments of the present invention to any given examples.

[0204] The embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for calculating electromagnetic fields of layered media, characterized in that: include: Establish the Bessel function integral expression of the electromagnetic field of uniform layered medium; The integration area is segmented according to the distance from the transmitting source to the receiving point, and then the Bessel function is discretized piecewise; The integral expression of the Bessel function of each integral unit is interpolated quadratically through the shape function to obtain the integral expression corresponding to the integral unit; The integral expression corresponding to each integral unit is calculated, and the integral result of the electromagnetic field of the layered medium is obtained by cumulative calculation.

2. The method for calculating electromagnetic fields of layered media according to claim 1, wherein: The Bessel function integral expression of the electromagnetic field of a uniform layered medium is: Where g(m) represents the earth response function, m represents the integral parameter, r represents the distance from the transmitting source to the receiving point, mr represents the quantity, and J n Represents the nth-order Bessel function.

3. The layered medium electromagnetic field calculation method according to claim 2, wherein: The piecewise discretization of Bessel functions includes: The Bessel function is divided into two intervals: When 0≤mr≤4, let t=(mr / 4) 2 , the Bessel function expansion is: When 4≤mr≤∞, let t=(4 / mr) 2 , the Bessel function expansion is: Among them, θ0=mr-π / 4, θ1=mr-3π / 4, where, |ε0| ≤ 10 -9 , |ε1| ≤ 3×10 -10 , |ε2| ≤ 3×10 -9 , |ε3| ≤ 4×10 -9 , |ε4| ≤ 6×10 -9 , |ε5| ≤ 6×10 -9 .

4. The layered medium electromagnetic field calculation method according to claim 1, wherein: The Bessel function integral expression of the electromagnetic field is expressed by the Bessel function integral of the integral unit as follows: Among them, I ei represents the Bessel function integral expression of the i-th integration unit, m i ,m i+2 They represent the lower limit and upper limit of the i-th integration unit respectively, and M represents the number of units.

5. The method for calculating electromagnetic fields of layered media according to claim 4, wherein: The Bessel function integral expression of each integral unit is interpolated quadratically by the shape function to obtain the integral expression corresponding to the integral unit, including: When 0≤mr≤4, the integral region of the Bessel function integral expression is discretized, and quadratic interpolation is performed within the unit through the shape function; The integral expression corresponding to the integral unit obtained according to the interpolated integral region is: Among them, N1 = (2L1-1)L1, N2 = 4L1L3, N3 = (2L3-1)L3, L3=1-L1,l=m i+2 -m i .

6. The layered medium electromagnetic field calculation method according to claim 4, wherein: The Bessel function integral expression of each integral unit is interpolated quadratically by the shape function to obtain the integral expression corresponding to the integral unit, including: When 4≤mr≤∞, the integral region of the Bessel function integral expression of each integral unit is discretized, and quadratic interpolation is performed within the unit through the shape function; The integral expression corresponding to the integral unit obtained according to the interpolated integral region is: Among them, the coefficient A 11 ,A 12 ,A 13 ,A 14 ,A 15 ,A 16 The expression is: Where l is the length of the integration unit.

7. The layered medium electromagnetic field calculation method according to claim 1, wherein: According to the integral expression corresponding to each integral unit, the integral result of the electromagnetic field of the layered medium is calculated as follows: Wherein, M represents the number of units.

8. A layered medium electromagnetic field calculation device, characterized in that: include: Modeling module, which establishes the Bessel function integral expression of the electromagnetic field of uniform layered media; Discrete module, which divides the integral area into segments according to the distance from the transmitting source to the receiving point, and then discretizes the Bessel function piecewise; The integration module performs quadratic interpolation on the Bessel function integral expression of each integration unit through the shape function to obtain the integral expression corresponding to the integration unit; The calculation module calculates the integral expression corresponding to each integral unit and obtains the integral result of the electromagnetic field of the layered medium by cumulative calculation.

9. An electronic device, characterized in that: The electronic device comprises: A memory storing executable instructions; A processor, wherein the processor runs the executable instructions in the memory to implement the layered medium electromagnetic field calculation method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the layered medium electromagnetic field calculation method according to any one of claims 1 to 7 is implemented.

Images