Terrain correction method, device and equipment based on electric field three-dimensional forward modeling and medium

Abstract

The invention discloses a terrain correction method and device based on electric field three-dimensional forward modeling, equipment and a medium. The method comprises the following steps: constructing a three-dimensional geoelectric model according to existing logging information and elevation data of a measuring area; performing mesh generation on the three-dimensional geoelectric model by adopting a non-structural tetrahedral mesh to obtain a three-dimensional mesh geoelectric model; obtaining an electric field linear equation set according to a three-dimensional forward modeling algorithm; calculating an initial electric field, solving an electric field linear equation set, and calculating a terrain electric field response value and a terrain-free electric field response value; and calculating an electric field response result after terrain correction according to the actually measured electric field response value, the terrain electric field response value and the terrain-free electric field response value. According to the method, the non-structural tetrahedral mesh is adopted for three-dimensional modeling, the electric field values of the terrain and the electric field values of the terrain are calculated in a forward modeling mode, the corrected electromagnetic field response is obtained through the two different model field values and the actual measurement response, and the influence of the terrain on transient electromagnetic data can be effectively eliminated.

Description

Technical Field

[0001] The present invention relates to the field of electromagnetic exploration of oil and gas resources, and more specifically, to a terrain correction method, device, equipment and medium based on three-dimensional forward modeling of electric fields. Background Art

[0002] When detecting by the electrical source transient electromagnetic (TEM), the collected electromagnetic signals are secondary induced fields. The change of the secondary induced field of the formation medium is different from the geometric sounding. It has a strong ability to adapt to complex terrain changes. However, this does not mean that the undulating changes of the terrain have no influence on the TEM data. In the electromagnetic exploration in mountainous areas, the terrain undulation not only deviates the observation points from the horizontal positions, but also changes the distribution of the electromagnetic fields in the earth, resulting in the inclusion of target body anomalies and terrain anomalies in the observed data, causing interference to the inference and interpretation, that is, the so-called terrain influence generally.

[0003] In the past, in TEM exploration, due to the certain difficulty in terrain influence correction and the lack of automated software, generally no correction was made. If the terrain influence was very serious, most of them only made manual correction to the abnormal parts. When making correction, the method of directly introducing the azimuth angle calculation by measuring the geometric coordinates was often adopted. This method required a large amount of measurement data support, was complex in operation, had a low working speed, and the correction accuracy was not high, affecting the efficiency of the exploration work and the accuracy of the interpretation, and further affecting the popularization and application of the TEM method in mountainous areas. The existing electromagnetic exploration terrain influence correction technologies also include the ratio method and the two-dimensional or three-dimensional inversion methods with terrain. Among them, the ratio method uses numerical methods such as boundary element, finite element, finite difference, and finite difference time domain to simulate the pure terrain response of a homogeneous earth, and then multiplies the measured apparent resistivity by the ratio of the resistivity of the homogeneous half-space to the pure terrain response to obtain the corrected apparent resistivity. However, in addition to the necessary point position measurement work in field exploration, a quite dense geodesic work is still required in the vast area between the transmitter and the receiver.

[0004] Therefore, it is necessary to develop a terrain correction method, device, equipment and medium based on three-dimensional forward modeling of electric fields.

[0005] The information disclosed in the background art part of the present invention is only intended to deepen the understanding of the general background art of the present invention, and should not be regarded as an admission or any form of implication that this information constitutes the prior art known to those skilled in the art. Summary of the Invention

[0006] The present invention proposes a terrain correction method, device, equipment and medium based on three-dimensional forward modeling of electric fields. It uses unstructured tetrahedral meshes for three-dimensional modeling, forward calculates the electric field values with and without terrain, and obtains the corrected electromagnetic field response through the field values of the two different models and the measured response, which can effectively eliminate the influence of terrain on transient electromagnetic data.

[0007] In a first aspect, an embodiment of the present disclosure provides a terrain correction method based on three-dimensional forward modeling of electric fields, including:

[0008] Construct a three-dimensional geoelectric model according to the existing logging information and elevation data in the survey area;

[0009] Use an unstructured tetrahedral mesh to perform mesh dissection on the three-dimensional geoelectric model to obtain a three-dimensional mesh geoelectric model;

[0010] According to the three-dimensional forward modeling algorithm, obtain a system of linear equations for the electric field;

[0011] Calculate the initial electric field, and then solve the system of linear equations for the electric field to calculate the electric field response values with and without terrain;

[0012] According to the measured electric field response value, the electric field response value with terrain, and the electric field response value without terrain, calculate the electric field response result after terrain correction.

[0013] As a specific implementation manner of the embodiment of the present disclosure, obtaining a system of linear equations for the electric field according to the three-dimensional forward modeling algorithm includes:

[0014] According to the three-dimensional forward modeling algorithm, calculate the electric field response at any point in space in the three-dimensional mesh geoelectric model;

[0015] Based on the electric field response, determine the electric field equation according to the Galerkin weighted residual method;

[0016] Use the second-order backward Euler difference scheme to discretize time to obtain a discrete equation;

[0017] Substitute the discrete equation into the electric field equation to obtain a system of linear equations for the electric field.

[0018] As a specific implementation manner of the embodiment of the present disclosure, the electric field response at any point in space in the three-dimensional mesh geoelectric model is:

[0019]

[0020] where E(r, t) is the electric field vector at position r at time t, and E j (t) is the tangential electric field value on the j-th edge of the tetrahedral element, which is the degree of freedom; N j (r) is the vector interpolation basis function.

[0021] As a specific implementation manner of the embodiment of the present disclosure, the electric field equation is:

[0022]

[0023] where S and M are the global stiffness matrix and mass matrix, and J is the source term,

[0024] As a specific implementation manner of the embodiment of the present disclosure, the discrete equation is:

[0025]

[0026] where Δt is the time step of the two time steps before the i-th moment.

[0027] As a specific implementation manner of the embodiment of the present disclosure, the electric field linear equations are:

[0028]

[0029] As a specific implementation manner of the embodiment of the present disclosure, according to the measured electric field response value, the electric field response value with terrain and the electric field response value without terrain, the electric field response result after terrain correction is calculated as:

[0030]

[0031] where r(t) is the correction coefficient, E 1 ′(t) is the measured electric field response value, E 1 (t) is the electric field response value with terrain, E 0 (t) is the electric field response value without terrain, E 0 ′(t) is the electric field response result after terrain correction.

[0032] In a second aspect, the embodiment of the present disclosure further provides a terrain correction device based on three-dimensional forward modeling of the electric field, including:

[0033] A model construction module, which constructs a three-dimensional geoelectric model according to the existing well logging information and elevation data in the surveyed area;

[0034] A grid meshing module, which meshes the three-dimensional geoelectric model with unstructured tetrahedral grids to obtain a three-dimensional grid geoelectric model;

[0035] A three-dimensional forward modeling module, which obtains the electric field linear equations according to the three-dimensional forward modeling algorithm;

[0036] A calculation module, which calculates the initial electric field, and then solves the electric field linear equations to calculate the electric field response value with terrain and the electric field response value without terrain;

[0037] A terrain correction module, which calculates the electric field response result after terrain correction according to the measured electric field response value, the electric field response value with terrain and the electric field response value without terrain.

[0038] As a specific implementation manner of the embodiment of the present disclosure, obtaining the electric field linear equations according to the three-dimensional forward modeling algorithm includes:

[0039] According to the 3D forward algorithm, calculate the electric field response at any arbitrary point in space in the 3D grid geoelectric model;

[0040] Based on the electric field response, determine the electric field equation according to the Galerkin weighted residual method;

[0041] Discretize time using the second-order backward Euler difference scheme to obtain a discrete equation;

[0042] Substitute the discrete equation into the electric field equation to obtain a linear system of electric field equations.

[0043] As a specific implementation manner of an embodiment of the present disclosure, the electric field response at any arbitrary point in space in the 3D grid geoelectric model is:

[0044]

[0045] where E(r, t) is the electric field vector at position r at time t, E j (t) is the tangential electric field value on the j-th edge of the tetrahedral element, which is the degree of freedom; N j (r) is the vector interpolation basis function.

[0046] As a specific implementation manner of an embodiment of the present disclosure, the electric field equation is:

[0047]

[0048] where S and M are the global stiffness matrix and mass matrix, and J is the source term,

[0049] As a specific implementation manner of an embodiment of the present disclosure, the discrete equation is:

[0050]

[0051] where Δt is the time step of the previous two time steps at the i-th moment.

[0052] As a specific implementation manner of an embodiment of the present disclosure, the linear system of electric field equations is:

[0053]

[0054] As a specific implementation manner of an embodiment of the present disclosure, according to the measured electric field response value, the electric field response value with topography, and the electric field response value without topography, calculate the electric field response result after topography correction as:

[0055]

[0056] where r(t) is the correction coefficient, and E 1 ′(t) is the measured electric field response value, and E 1 (t) is the electric field response value with topography, and E 0 (t) is the electric field response value without topography, and E 0 ′(t) is the electric field response result after terrain correction.

[0057] In a third aspect, an embodiment of the present disclosure further provides an electronic device, which includes:

[0058] a memory storing executable instructions;

[0059] a processor that runs the executable instructions in the memory to implement the terrain correction method based on three-dimensional forward modeling of the electric field.

[0060] In a fourth aspect, an embodiment of the present disclosure further provides a computer-readable storage medium, which stores a computer program that, when executed by a processor, implements the terrain correction method based on three-dimensional forward modeling of the electric field.

[0061] The method and apparatus of the present invention have other characteristics and advantages, which will be apparent from or will be described in detail in the accompanying drawings and the following detailed description incorporated herein. These drawings and the detailed description together are used to explain the specific principles of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] By describing the exemplary embodiments of the present invention in more detail in conjunction with the accompanying drawings, the above and other objects, features, and advantages of the present invention will become more apparent, wherein, in the exemplary embodiments of the present invention, the same reference numerals generally represent the same components.

[0063] Figure 1 shows a flowchart of the steps of a terrain correction method based on three-dimensional forward modeling of the electric field according to an embodiment of the present invention.

[0064] Figure 2 shows a schematic diagram of a three-dimensional geoelectric model combining logging information and elevation data according to an embodiment of the present invention.

[0065] Figure 3 shows a schematic diagram of a three-dimensional grid geoelectric model according to an embodiment of the present invention.

[0066] Figure 4 shows a flowchart of three-dimensional forward modeling of topography according to an embodiment of the present invention.

[0067] Figure 5a and Figure 5bSchematic diagrams of the electric field profiles before and after terrain correction according to an embodiment of the present invention are respectively shown.

[0068] Figure 6 A block diagram of a terrain correction device based on three-dimensional forward modeling of the electric field according to an embodiment of the present invention is shown.

[0069] Description of reference numerals:

[0070] 201, model construction module; 202, mesh generation module; 203, three-dimensional forward modeling module; 204, calculation module; 205, terrain correction module. Detailed implementation manners

[0071] 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 by the embodiments set forth herein.

[0072] To facilitate understanding of the solutions and effects of the embodiments of the present invention, six specific application examples are given below. Those skilled in the art should understand that this example is only for facilitating the understanding of the present invention, and any specific details are not intended to limit the present invention in any way.

[0073] Example 1

[0074] Figure 1 A flowchart of the steps of a terrain correction method based on three-dimensional forward modeling of the electric field according to an embodiment of the present invention is shown.

[0075] As Figure 1 shown, the terrain correction method based on three-dimensional forward modeling of the electric field includes: Step 101, constructing a three-dimensional geoelectric model according to the existing well logging information and elevation data in the survey area; Step 102, performing mesh generation on the three-dimensional geoelectric model using unstructured tetrahedral meshes to obtain a three-dimensional meshed geoelectric model; Step 103, obtaining a linear system of electric field equations according to the three-dimensional forward modeling algorithm; Step 104, calculating the initial electric field, and then solving the linear system of electric field equations to calculate the electric field response values with and without terrain; Step 105, calculating the electric field response result after terrain correction according to the measured electric field response value, the electric field response value with terrain, and the electric field response value without terrain.

[0076] In one example, obtaining the linear system of electric field equations according to the three-dimensional forward modeling algorithm includes:

[0077] Calculating the electric field response at any arbitrary point in space in the three-dimensional meshed geoelectric model according to the three-dimensional forward modeling algorithm;

[0078] Determining the electric field equation based on the electric field response according to the Galerkin weighted residual method;

[0079] The time is discretized using the second - order backward Euler difference scheme to obtain a discrete equation;

[0080] The discrete equation is substituted into the electric - field equation to obtain a linear system of electric - field equations.

[0081] In one example, the electric - field response at any arbitrary point in space in a three - dimensional grid geoelectric model is:

[0082]

[0083] where \(E(\mathbf{r},t)\) is the electric - field vector at position \(\mathbf{r}\) at time \(t\), \(E_j(t)\) is the tangential electric - field value on the \(j\) - th edge of the tetrahedral element, which is the degree of freedom; \(N_j(\mathbf{r})\) is the vector interpolation basis function. j (t) is the tangential electric - field value on the \(j\) - th edge of the tetrahedral element, which is the degree of freedom; \(N\) j (r) is the vector interpolation basis function.

[0084] In one example, the electric - field equation is:

[0085]

[0086] where \(S\) and \(M\) are the global stiffness matrix and mass matrix, respectively, and \(J\) is the source term,

[0087] In one example, the discrete equation is:

[0088]

[0089] where \(\Delta t\) is the time step between the previous two time steps at the \(i\) - th moment.

[0090] In one example, the linear system of electric - field equations is:

[0091]

[0092] In one example, according to the measured electric - field response value, the electric - field response value with topography, and the electric - field response value without topography, the electric - field response result after terrain correction is calculated as:

[0093]

[0094] where \(r(t)\) is the correction coefficient, \(E_j^{\prime}(t)\) is the measured electric - field response value, \(E_j(t)\) is the electric - field response value with topography, \(E_j^0(t)\) is the electric - field response value without topography, and \(E_j^{\prime\prime}(t)\) is the electric - field response result after terrain correction. 1 ′(t) is the measured electric - field response value, \(E\) 1 (t) is the electric - field response value with topography, \(E\) 0 (t) is the electric - field response value without topography, \(E\) 0 ′(t) is the electric - field response result after terrain correction.

[0095] Specifically, select the GDEMV3 30M resolution digital elevation data, input the corresponding longitude and latitude coordinates of the survey area to obtain elevation data, and construct a high-precision three-dimensional geoelectric model in combination with well logging data.

[0096] Use unstructured tetrahedral meshes for mesh division, and locally refine the meshes near the emission sources and measurement points to obtain a three-dimensional meshed geoelectric model.

[0097] Based on Maxwell's equations, eliminating the magnetic field variables can obtain the electric field diffusion equation in the time domain:

[0098]

[0099] Among them, E(r, t) is the electric field vector at position r at time t, J s (r, t) is the current density of the emission source, μ is the magnetic permeability of the medium, σ is the conductivity. When induced polarization exists, the induced polarization model in the time domain can be used to obtain the time-varying conductivity.

[0100] Use unstructured tetrahedral meshes to discretize the calculation area, and adopt the Nédélec vector interpolation basis function that automatically satisfies the continuity of the tangential component of the electric field and is divergence-free to approximate the linear distribution of the electric field within the element. The electric field at any position within each tetrahedral element can be expressed as:

[0101]

[0102] In the formula, E j (t) is the tangential electric field value on the j-th edge of the tetrahedral element, which can be called the degree of freedom; N j (r) is the vector interpolation basis function. Based on the Galerkin weighted residual method, using the vector interpolation basis function N(r) as the weighting function, the surface integrals on both sides of the inner boundary surface cancel each other out. The outer boundary is far enough from the emission source to satisfy the sommerfeld boundary condition, ignoring the surface integral, and combining with the electric field formula, the following form of the electric field equation can be finally obtained:

[0103]

[0104] In the formula, S and M are the global stiffness matrix and mass matrix, J is the source term,

[0105] To improve the numerical accuracy, use the second-order backward Euler difference scheme to discretize time and obtain the discrete equation:

[0106]

[0107] Δt is the time step of the first two time steps before the i-th moment. Substituting the discrete equation into the electric field equation gives

[0108] (3S+2ΔtM)E i (t)=S[4E i-1 (t)-E i-2 (t)]-2ΔtJ i

[0109] Finally, the electric field linear equations are formed, which can be expressed as

[0110] KE=b.

[0111] To solve the electric field linear equations, the initial electric field E at time 0 needs to be given 0 .

[0112] For a grounded long wire source, a series of current sources with zero initial current, such as square wave, triangle wave, sine wave, trapezoidal wave, etc., the initial electric field E 0 =0, and the initial electric field of the next step waveform is composed of two parts: the spatial electric field distribution caused by the long wire source and the stable DC electric field formed by the positive and negative electrode power supply

[0113]

[0114] It can be calculated according to Ohm's law, It can be calculated by the negative gradient of the potential φ

[0115]

[0116] Assume that the current intensity of the point source is I, located at r=(x s ,y s ,z s ), using the differential form of Ohm's law j = σE, according to the continuity of the electric field, we get:

[0117]

[0118] Where δ is the pulse function, the above equations can be combined to obtain the three-dimensional Poisson equation satisfied by the point source field

[0119]

[0120] The same grid is used for DC electric field and time domain electromagnetic field problems to ensure the consistency of the DC electric field and vector electric field boundaries, and the DC field problem and the time domain electromagnetic problem are solved using the total field method. Due to the large solution area, the Dirichlet boundary condition φ| is applied to the external boundary Γ during the calculation process. Γ =0, (n×E)| Γ =0.

[0121] The electric field linear equations can also be written in the following format:

[0122] ​​​​

[0123] For the solution of large-scale linear equations, there are mainly two methods: iterative method and direct method. Since the matrix condition number formed by the unstructured finite element method is too large, the iterative algorithm has a long solution time and may not converge. That is, by using the PARDISO solver of Inter MKL to perform LU decomposition and fast back substitution on the above equations, the tangential electric field of all the edges of the tetrahedrons is obtained, and the electric field response at any point in space is linearly interpolated by using the basis functions. The magnetic field component response is obtained through Faraday's law of electromagnetic induction. That is, the terrain response value E 1 (t) with terrain and the terrain-free response value E 0 (t).

[0124] According to the correction coefficient formula:

[0125]

[0126] Calculate the correction coefficient r(t), where E 1 (t) and E 0 (t) are the terrain response value with terrain and the terrain-free response value obtained from 3D forward simulation respectively, and the terrain-corrected response result E 1 ′(t) can be obtained by calculating with the measured electric field response value E 0 ′(t), which provides strong help for the subsequent inversion.

[0127] This method combines the existing well logging information in the survey area and the obtained high-precision elevation data to establish a high-precision 3D geoelectric model, uses unstructured tetrahedral meshes for mesh division, and uses the unstructured mesh vector finite element method to perform 3D forward simulation on the 3D complex geoelectric model, calculates the electric field responses under the terrain conditions and terrain-free conditions in the survey area, obtains the correction coefficient r(t) through the following formula, and then can obtain the electric field response value after eliminating the terrain influence under the measured data.

[0128] Example 2

[0129] The present invention also provides a terrain correction device based on 3D forward simulation of electric fields, including:

[0130] A model construction module, which constructs a 3D geoelectric model according to the existing well logging information and elevation data in the survey area;

[0131] A mesh division module, which uses unstructured tetrahedral meshes to perform mesh division on the 3D geoelectric model to obtain a 3D mesh geoelectric model;

[0132] A 3D forward module, which obtains a linear equation system of electric fields according to the 3D forward algorithm;

[0133] A calculation module that calculates the initial electric field, then solves the linear electric field equations, and calculates the electric field response values with and without topography.

[0134] A topography correction module that calculates the topographically corrected electric field response results based on the measured electric field response values, the electric field response values with topography, and the electric field response values without topography.

[0135] In one example, according to the 3D forward modeling algorithm, the linear electric field equations include:

[0136] According to the 3D forward modeling algorithm, calculate the electric field response at any point in space in the 3D grid geoelectric model.

[0137] Based on the electric field response, determine the electric field equation according to the Galerkin weighted residual method.

[0138] Discretize time using the second-order backward Euler difference scheme to obtain the discrete equation.

[0139] Substitute the discrete equation into the electric field equation to obtain the linear electric field equations.

[0140] In one example, the electric field response at any point in space in the 3D grid geoelectric model is:

[0141]

[0142] where E(r, t) is the electric field vector at position r at time t, E j (t) is the tangential electric field value on the j-th edge of the tetrahedral element, which is the degree of freedom; N j (r) is the vector interpolation basis function.

[0143] In one example, the electric field equation is:

[0144]

[0145] where S and M are the global stiffness matrix and mass matrix, and J is the source term.

[0146] In one example, the discrete equation is:

[0147]

[0148] where Δt is the time step between the previous two time steps at the i-th moment.

[0149] In one example, the linear electric field equations are:

[0150]

[0151] In one example, based on the measured electric field response value, the electric field response value with topography, and the electric field response value without topography, the calculated electric field response result after topography correction is as follows:

[0152]

[0153] where r(t) is the correction coefficient, E 1 ′(t) is the measured electric field response value, E 1 (t) is the electric field response value with topography, E 0 (t) is the electric field response value without topography, E 0 ′(t) is the electric field response result after topography correction.

[0154] Specifically, select the GDEMV3 30M resolution digital elevation data, input the corresponding longitude and latitude coordinates of the survey area to obtain elevation data, and construct a high-precision three-dimensional geoelectric model in combination with well logging data.

[0155] Use unstructured tetrahedral meshes for mesh division, and locally refine the meshes near the emission source and measurement points to obtain a three-dimensional meshed geoelectric model.

[0156] Based on Maxwell's equations, eliminating the magnetic field variable can obtain the electric field diffusion equation in the time domain:

[0157]

[0158] where E(r, t) is the electric field vector at position r at time t, J s (r, t) is the current density of the emission source, μ is the magnetic permeability of the medium, σ is the conductivity, and when induced polarization exists, a time-domain induced polarization model can be used to obtain the time-varying conductivity.

[0159] Use unstructured tetrahedral meshes to discretize the calculation region, and adopt the Nédélec vector interpolation basis function that automatically satisfies the continuity of the tangential component of the electric field and is divergence-free to approximate the linear distribution of the electric field within the element. For the electric field at any position within each tetrahedral element, it can be expressed as:

[0160]

[0161] In the formula, E j (t) is the tangential electric field value on the j-th edge of the tetrahedral element, which can be called the degree of freedom; N j (r) is the vector interpolation basis function. Based on the Galerkin weighted residual method, using the vector interpolation basis function N(r) as the weighting function, the surface integrals on both sides of the internal boundary surface cancel each other out, the outer boundary is far enough from the emission source to satisfy the sommerfeld boundary condition, the surface integral is ignored, and combined with the electric field formula, the following form of the electric field equation can be finally obtained:

[0162]

[0163] where \(S\) and \(M\) are the global stiffness matrix and mass matrix, and \(J\) is the source term.

[0164] To improve the numerical accuracy, the second-order backward Euler difference scheme is used to discretize time, and the discrete equation is obtained:

[0165]

[0166] \(\Delta t\) is the previous two time steps at the \(i\)-th moment. Substituting the discrete equation into the electric field equation gives

[0167] (3S + 2\(\Delta t\)M)E i (t) = S[4E i-1 (t) - E i-2 (t)] - 2\(\Delta t\)J i

[0168] Finally, a linear system of equations for the electric field is formed, which can be expressed as

[0169] KE = b.

[0170] To solve the linear system of equations for the electric field, the initial electric field \(E\) at time \(t = 0\) needs to be given. 0 .

[0171] For a grounded long-wire source, a series of current sources with an initial current of zero, such as square waves, triangular waves, sine waves, trapezoidal waves, etc., their initial electric field \(E\) 0 = 0, while the initial electric field of the step-down waveform consists of two parts: the spatial electric field distribution caused by the long-wire source and the stable DC electric field formed by the positive and negative electrode power supplies.

[0172]

[0173] It can be calculated according to Ohm's law. It can be calculated through the negative gradient of the electric potential \(\varphi\).

[0174]

[0175] Suppose the point-source current intensity is \(I\), located at \(r=(x\) s , \(y\) s , \(z\) s ). Using the differential form of Ohm's law \(j = \sigma E\), according to the electric field continuity, we get:

[0176]

[0177] where \(\delta\) is the impulse function. Combining the above equations, the three-dimensional Poisson equation satisfied by the point-source field can be obtained.

[0178]

[0179] The same grid is used for DC electric field and time-domain electromagnetic field problems to ensure the consistency of the boundaries between the DC electric field and the vector electric field. Both the DC field problem and the time-domain electromagnetic problem are solved using the total field method. Due to the large solution region, Dirichlet boundary conditions are applied to the outer boundary Γ during the calculation process

[0180] φ| Γ =0, (n×E)| Γ =0.

[0181] The linear system of equations for the electric field can also be written in the following form:

[0182]

[0183] For the solution of large linear systems of equations, there are mainly two methods: the iterative method and the direct method. Since the condition number of the matrix formed by the unstructured finite element method is too large, the iterative algorithm has a long solution time and may not converge. That is, by using the PARDISO solver of Inter MKL to perform LU decomposition and fast back substitution on the above equations, the tangential electric field of all the edges of the tetrahedrons is obtained, and the electric field response at any point in space is linearly interpolated using the basis functions. The magnetic field component response is obtained through Faraday's law of electromagnetic induction. That is, the terrain response value E 1 (t) with terrain and the terrain-free response value E 0 (t) can be calculated through the linear system of equations for the electric field.

[0184] According to the correction coefficient formula:

[0185]

[0186] Calculate the correction coefficient r(t), where E 1 (t) and E 0 (t) are the terrain response value with terrain and the terrain-free response value obtained from 3D forward modeling respectively, and the terrain-corrected response result E 1 ′(t) can be obtained by calculating with the measured electric field response value E 0 ′(t), which provides strong help for subsequent inversion.

[0187] Example 3

[0188] Taking a certain oil and gas resource exploration area in Sichuan, southwestern China as an example, the terrain correction for 3D forward modeling of the electrical source transient electromagnetic method is carried out using this method.

[0189] Figure 2 The schematic diagram of a 3D geoelectric model combining well logging information and elevation data according to an embodiment of the present invention is shown.

[0190] Collect the logging data of the survey area to obtain high-precision elevation data of the survey area and construct a high-precision three-dimensional geoelectric model, such as Figure 2 shown.

[0191] Figure 3 Fig. shows a schematic diagram of a three-dimensional grid geoelectric model according to an embodiment of the present invention.

[0192] Use an unstructured tetrahedral grid for grid meshing, locally refine the grid near the emission source and measurement points, and obtain a three-dimensional grid geoelectric model, such as Figure 3 shown.

[0193] Figure 4 Fig. shows a flow chart of three-dimensional forward modeling of topography according to an embodiment of the present invention.

[0194] Based on Maxwell's equations, eliminating the magnetic field variable can obtain the electric field diffusion equation in the time domain:

[0195]

[0196] When induced polarization exists, an induced polarization model in the time domain can be used to obtain the time-varying conductivity.

[0197] Use an unstructured tetrahedral grid to discretize the calculation area, and adopt the Nédélec vector interpolation basis function that automatically satisfies the continuity of the tangential component of the electric field and is divergence-free to approximate the linear distribution of the electric field within the element. The electric field equation at any position within each tetrahedral element can be expressed as:

[0198]

[0199] where E j (t) is the tangential electric field value on the j-th edge of the tetrahedral element, which can be called the degree of freedom; N j (r) is the vector interpolation basis function. Based on the Galerkin weighted residual method, the following form of the electric field equation can be finally obtained:

[0200]

[0201] where S and M are the global stiffness matrix and mass matrix, J is the source term,

[0202] To improve the numerical accuracy, use the second-order backward Euler difference scheme to discretize time and obtain the discrete equation:

[0203]

[0204] Δt is the time step of the first two time steps before the i-th moment. Substituting the discrete equation into the electric field equation gives

[0205] (3S+2ΔtM)E i (t)=S[4E i-1 (t)-E i-2 (t)]-2ΔtJ i

[0206] Finally, the electric field linear equations are formed, which can be expressed as

[0207] KE=b.

[0208] For a grounded long wire source, a series of current sources with zero initial current, such as square wave, triangle wave, sine wave, trapezoidal wave, etc., the initial electric field E 0 =0, and the initial electric field of the next step waveform is composed of two parts: the spatial electric field distribution caused by the long wire source and the stable DC electric field formed by the positive and negative electrode power supply

[0209]

[0210] It can be calculated according to Ohm's law, It can be calculated by the negative gradient of the potential φ

[0211]

[0212] Assume that the current intensity of the point source is I, located at r=(x s ,y s ,z s ), using the differential form of Ohm's law j = σE, according to the continuity of the electric field, we get:

[0213]

[0214] Where δ is the pulse function, the above equations can be combined to obtain the three-dimensional Poisson equation satisfied by the point source field

[0215]

[0216] The same grid is used for DC electric field and time domain electromagnetic field problems to ensure the consistency of the DC electric field and vector electric field boundaries, and the DC field problem and the time domain electromagnetic problem are solved using the total field method. Due to the large solution area, the Dirichlet boundary condition φ| is applied to the external boundary Γ during the calculation process. Γ =0, (n×E)| Γ =0

[0217] The electric field linear equations can also be written in the following format:

[0218]

[0219] ​​​​By using the PARDISO solver of Inter MKL to perform LU decomposition and fast back substitution on the above equations, the tangential electric field of all the edges of the tetrahedrons is obtained. The electric field response at any point in space is linearly interpolated using the basis functions, and the magnetic field component response is obtained through Faraday's law of electromagnetic induction.

[0220] Figure 5a 、 Figure 5b Schematically show the electric field profiles before and after topographic correction according to an embodiment of the present invention.

[0221] According to the correction coefficient formula:

[0222]

[0223] Calculate the correction coefficient r(t), and calculate it with the measured electric field response value E 1 ′(t) to obtain the response result E 0 ′(t) of the topographic correction, which provides strong help for subsequent inversion. The electric field profiles before and after topographic correction are as Figure 5a 、 Figure 5b shown.

[0224] Example 4

[0225] Figure 6 Shows a block diagram of a topographic correction device based on three-dimensional forward modeling of electric fields according to an embodiment of the present invention.

[0226] As Figure 6 shown, the topographic correction device based on three-dimensional forward modeling of electric fields includes:

[0227] A model construction module 201, which constructs a three-dimensional geoelectric model according to the existing logging information and elevation data in the survey area;

[0228] A grid meshing module 202, which meshes the three-dimensional geoelectric model using unstructured tetrahedral grids to obtain a three-dimensional grid geoelectric model;

[0229] A three-dimensional forward modeling module 203, which obtains a system of linear equations of the electric field according to the three-dimensional forward modeling algorithm;

[0230] A calculation module 204, which calculates the initial electric field, then solves the system of linear equations of the electric field, and calculates the electric field response values with and without topography;

[0231] A topographic correction module 205, which calculates the electric field response result after topographic correction according to the measured electric field response value, the electric field response value with topography, and the electric field response value without topography.

[0232] As an optional solution, obtaining a system of linear equations of the electric field according to the three-dimensional forward modeling algorithm includes:

[0233] According to the 3D forward algorithm, calculate the electric field response at any point in space in the 3D grid geoelectric model;

[0234] Based on the electric field response, determine the electric field equation according to the Galerkin weighted residual method;

[0235] Discretize time using the second-order backward Euler difference scheme to obtain the discrete equation;

[0236] Substitute the discrete equation into the electric field equation to obtain the electric field linear equations.

[0237] As an alternative, the electric field response at any point in space in the 3D grid geoelectric model is:

[0238]

[0239] where E(r, t) is the electric field vector at position r at time t, and E j (t) is the tangential electric field value on the j-th edge of the tetrahedral element, which is the degree of freedom; N j (r) is the vector interpolation basis function.

[0240] As an alternative, the electric field equation is:

[0241]

[0242] where S and M are the global stiffness matrix and mass matrix, J is the source term,

[0243] As an alternative, the discrete equation is:

[0244]

[0245] where Δt is the time step of the previous two time steps at the i-th moment.

[0246] As an alternative, the electric field linear equations are:

[0247]

[0248] As an alternative, according to the measured electric field response value, the electric field response value with topography, and the electric field response value without topography, calculate the electric field response result after terrain correction as:

[0249]

[0250] where r(t) is the correction coefficient, E 1 ′(t) is the measured electric field response value, E 1 (t) is the electric field response value with topography, E 0(t) is the terrain - free electric - field response value, E 0 ′(t) is the electric - field response result after terrain correction.

[0251] Example 5

[0252] The present disclosure provides an electronic device, which includes: a memory storing executable instructions; and a processor that runs the executable instructions in the memory to implement the above - mentioned terrain correction method based on three - dimensional forward modeling of the electric field.

[0253] The electronic device according to an embodiment of the present disclosure includes a memory and a processor.

[0254] The memory is used to store non - transient computer - readable instructions. Specifically, the memory may include one or more computer program products, and the computer program products may include various forms of computer - readable storage media, such as volatile memory and / or non - volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory, etc. The non - volatile memory may include, for example, read - only memory (ROM), hard disk, flash memory, etc.

[0255] The processor may be a central processing unit (CPU) or other forms of processing units with data - processing capabilities and / or instruction - execution capabilities, and may control other components in the electronic device to perform desired functions. In an embodiment of the present disclosure, the processor is used to run the computer - readable instructions stored in the memory.

[0256] Those skilled in the art should understand that, in order to solve the technical problem of how to obtain a good user - experience effect, this embodiment may also include well - known structures such as communication buses, interfaces, etc., and these well - known structures should also be included in the protection scope of the present disclosure.

[0257] For the detailed description of this embodiment, reference may be made to the corresponding descriptions in the foregoing embodiments, and details will not be repeated here.

[0258] Example 6

[0259] The embodiment of the present disclosure provides a computer - readable storage medium, which stores a computer program, and when the computer program is executed by a processor, it implements the terrain correction method based on three - dimensional forward modeling of the electric field.

[0260] The computer - readable storage medium according to an embodiment of the present disclosure stores non - transient computer - readable instructions. When the non - transient computer - readable instructions are run by a processor, all or part of the steps of the methods of the foregoing embodiments of the present disclosure are executed.

[0261] The above 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 removable hard disk), media with built-in rewritable non-volatile memory (e.g., memory card), and media with built-in ROM (e.g., ROM cartridge).

[0262] 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 of the examples given.

[0263] The embodiments of the present invention have been described above. The above description is exemplary and not exhaustive, and is also not limited to the disclosed embodiments. Many modifications and variations are obvious to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A terrain correction method based on three-dimensional electric field forward modeling, characterized in that: include: Construct a three-dimensional geoelectric model based on the existing well logging information and elevation data in the survey area; Using an unstructured tetrahedral grid to perform grid division on the three-dimensional geoelectric model to obtain a three-dimensional grid geoelectric model; According to the three-dimensional forward algorithm, the electric field linear equations are obtained; Calculating the initial electric field, and then solving the electric field linear equations to calculate the electric field response value with terrain and the electric field response value without terrain; The electric field response result after terrain correction is calculated according to the measured electric field response value, the electric field response value with terrain and the electric field response value without terrain.

2. The terrain correction method based on electric field three-dimensional forward modeling according to claim 1, wherein: According to the three-dimensional forward algorithm, the electric field linear equations include: Calculating the electric field response of any point in the three-dimensional grid geoelectric model according to a three-dimensional forward algorithm; Based on the electric field response, the electric field equation is determined according to the Galerkin weighted residual method; The time is discretized using the second-order backward Euler difference scheme to obtain the discrete equation; Substituting the discrete equation into the electric field equation, a set of linear electric field equations is obtained.

3. The terrain correction method based on electric field three-dimensional forward modeling according to claim 2, wherein: The electric field response of any point in the space of the three-dimensional grid geoelectric model is: Where E(r,t) is the electric field vector at position r at time t, E j (t) is the tangential electric field value on the jth edge of the tetrahedron unit, which is the degree of freedom; N j (r) is the vector interpolation basis function.

4. The terrain correction method based on electric field three-dimensional forward modeling according to claim 2, wherein: The electric field equation is: Among them, S and M are the overall stiffness matrix and mass matrix, J is the source term, 5. The terrain correction method based on electric field three-dimensional forward modeling according to claim 2, wherein: The discrete equation is: Among them, Δt is the time step length of the first two tracks before the i-th moment.

6. The terrain correction method based on electric field three-dimensional forward modeling according to claim 2, wherein: The electric field linear equations are:

7. The terrain correction method based on electric field three-dimensional forward modeling according to claim 1, wherein: According to the measured electric field response value, the electric field response value with terrain and the electric field response value without terrain, the electric field response result after terrain correction is calculated as: Among them, r(t) is the correction coefficient, E1′(t) is the measured electric field response value, E1(t) is the electric field response value with terrain, E0(t) is the electric field response value without terrain, and E0 ′ (t) is the electric field response result after terrain correction.

8. A terrain correction device based on three-dimensional electric field forward modeling, characterized in that: include: Model building module, which builds a three-dimensional geoelectric model based on the existing well logging information and elevation data in the survey area; A mesh generation module, which uses an unstructured tetrahedral mesh to perform mesh generation on the three-dimensional geoelectric model to obtain a three-dimensional mesh geoelectric model; The three-dimensional forward modeling module obtains the electric field linear equations according to the three-dimensional forward modeling algorithm; A calculation module calculates the initial electric field, and then solves the electric field linear equations to calculate the electric field response value with terrain and the electric field response value without terrain; The terrain correction module calculates the electric field response result after terrain correction according to the measured electric field response value, the electric field response value with terrain and the electric field response value without terrain.

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 terrain correction method based on electric field three-dimensional forward modeling according to any one of claims 1 to 8.

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 terrain correction method based on three-dimensional electric field forward modeling described in any one of claims 1 to 8 is implemented.

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