Differential enhancement and multi-constraint combined stratum dispersion high-precision and high-resolution electromagnetic imaging method

Abstract

The invention discloses a differential enhancement and multi-constraint combined stratigraphic dispersion high-precision high-resolution electromagnetic imaging method, which comprises the following steps of: S1, carrying out differential operation on acquired three-component data of a magnetic field, and highlighting the change characteristics of the magnetic field by calculating the difference values of the magnetic field components of adjacent measurement points and different moments so as to obtain a difference value of the three-component data of the magnetic field; the influence of the smoothing effect is reduced, so that the deep information resolution is improved; step S2, introducing a tipper parameter and performing calculation: calculating the tipper parameter according to the three-component data of the magnetic field, correcting and verifying the tipper parameter obtained by calculation, removing abnormal data points, enriching constraint conditions of inversion, and improving the accuracy and resolution of an inversion result; and S3, performing multi-constraint inversion imaging in combination with the drilling core parameters and the signal phase constraint. According to the method, the influence of the smoothing effect can be reduced, the deep information resolution and the inversion result accuracy are improved, the electrical property distribution of the underground geologic body is obtained more accurately, and the electromagnetic data processing precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of artificial source electromagnetic detection, and relates to an electromagnetic imaging method, in particular to a high-precision and high-resolution electromagnetic imaging method for formation dispersion combining differential enhancement and multiple constraints. Background Art

[0002] The electromagnetic method is an important branch of geophysical exploration. It extracts the information of the geoelectric structure by observing the electromagnetic response excited by natural field sources or artificial field sources. The semi-airborne electromagnetic method usually uses a high-power transmitting device to transmit on the ground, and the receiving end is carried on a flying platform. The semi-airborne time-frequency electromagnetic detection method combines the advantages of high-power transmission of the time-frequency electromagnetic method and the flexibility of semi-airborne detection, and can adapt to areas with relatively complex geological and topographical conditions such as high-altitude mountainous areas, deserts, gobi, forest-covered areas, and karst-developed areas, and can carry out long-term detection tasks, with a wide range of applications.

[0003] In the field of geophysical exploration, due to the extremely complex underground geological structure, the electrical properties of each layer and geological bodies such as resistivity and polarizability are significantly different. However, due to the smoothing effect, the resistivity image obtained by traditional inversion is blurred and the true distribution of the electrical properties of underground geological bodies cannot be accurately obtained, which brings great obstacles to work such as mineral resource exploration and geological disaster assessment. At the same time, the complex topographical conditions also pose a huge challenge to traditional inversion methods. In areas with high mountains and steep ridges and severe terrain cutting, the data obtained by traditional resistivity methods are severely distorted by the terrain, which makes it difficult for traditional inversion methods based on signal amplitude to distinguish the terrain influence from the true change of the electrical properties of underground geological bodies, and thus leads to deviation or even error in the inversion results.

[0004] With the continuous development of geophysical exploration technology and the continuous expansion of application fields, whether it is to determine the location and scale of ore bodies in mineral resource exploration or to identify potential hazards in geological disaster assessment, the requirements for the accuracy of inversion results and imaging resolution are increasing. Therefore, there is an urgent need for a high-precision and high-resolution electromagnetic inversion imaging method that can overcome the limitations of traditional methods and improve the accuracy of inversion results. Summary of the Invention

[0005] In order to reduce the influence of the smoothing effect and overcome the deficiencies of traditional inversion methods, the present invention provides a high-precision and high-resolution electromagnetic imaging method for formation dispersion combining differential enhancement and multiple constraints. This method can reduce the influence of the smoothing effect, improve the resolution of deep information and the accuracy of inversion results, more accurately obtain the distribution of the electrical properties of underground geological bodies, and improve the accuracy of electromagnetic data processing.

[0006] The object of the present invention is achieved by the following technical solutions:

[0007] A high-precision and high-resolution electromagnetic imaging method for formation dispersion combining differential enhancement and multi-constraints, comprising the following steps:

[0008] Step S1: Process the three-component magnetic field data using differential technology:

[0009] First, collect the three-component magnetic field data in the field, and then perform differential operations on the collected three-component magnetic field data. By calculating the differences in magnetic field components at adjacent measurement points and at different times, the variation characteristics of the magnetic field are highlighted, the influence of the smoothing effect is reduced, and thus the resolution of deep information is improved;

[0010] Step S2: Introduce the dip parameter and perform calculations:

[0011] Calculate the dip parameter based on the three-component magnetic field data, correct and verify the calculated dip parameter, remove abnormal data points, enrich the constraints for inversion, and improve the accuracy and resolution of the inversion results;

[0012] Step S3: Perform multi-constraint inversion imaging by combining borehole core parameters and signal phase constraints:

[0013] According to the laboratory measurement results of borehole core samples, obtain the actual distribution of formation resistivity, introduce it as prior information into the inversion process to constrain the inversion results; based on the formation dispersion effect, analyze the variation characteristics of signal phase, extract information related to the electrical properties of the formation, and further constrain the inversion process; establish a layered medium model, determine the initial parameters of the model, perform forward simulation using the finite element method, perform non-linear inversion using the particle swarm optimization algorithm, update the inversion model parameters, and find the optimal inversion model parameters to achieve fine inversion of resistivity.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] The present invention processes the three-component magnetic field data using differential technology, effectively reducing the smoothing effect of traditional signal amplitude inversion, improving the resolution of deep information, and being able to more clearly reveal the electrical structure of underground geological bodies. At the same time, introducing multi-constraint conditions such as dip parameters, borehole core physical property parameters constraints, and signal phase constraints, making full use of geological information from different sources, reducing the non-uniqueness of inversion, and improving the accuracy and reliability of inversion results, providing more powerful technical support for work such as mineral resource exploration and geological disaster assessment. Description of the Drawings

[0016] Figure 1 It is a flowchart of the high-precision and high-resolution electromagnetic imaging method for formation dispersion combining differential enhancement and multi-constraints. Detailed Embodiment

[0017] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings, but it is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention shall be covered by the protection scope of the present invention.

[0018] The present invention provides a high-precision and high-resolution electromagnetic imaging method for formation dispersion combining differential enhancement and multiple constraints, as Figure 1 shown. The method includes the following steps:

[0019] Step S1: Process the three-component magnetic field data using differential technology:

[0020] First, collect the three-component magnetic field data in the field, and then perform differential operations on the collected three-component magnetic field data. By calculating the differences in magnetic field components at adjacent measurement points and different times, the variation characteristics of the magnetic field are highlighted, and the influence of the smoothing effect is reduced, thereby improving the resolution of deep information. The specific steps are as follows:

[0021] Step S11: Use a semi-aerial time-frequency electromagnetic system to collect the three-component magnetic field data according to a certain measurement grid in the research area to ensure the accuracy and integrity of the data.

[0022] In this step, the specific requirements of the measurement grid are usually closely related to geological conditions, exploration targets, and topography. For example, if the measurement target is small, a small grid needs to be used. When the geological structure is complex or the lithology changes greatly, the grid needs to be encrypted. In addition, for areas with large topographic undulations, the measurement grid needs to be adjusted according to the topographic changes. At locations with drastic topographic changes, the survey lines and measurement points should be appropriately encrypted, and irregular grids can be used. In flat areas, the measurement grid can be relatively regular and uniform.

[0023] Step S12: Input the collected three-component magnetic field data B x 、B y 、B z into the differential calculation program, and use the central difference format to calculate the differences of each component in space and time respectively.

[0024] Step S13: Filter the differential data, select a wavelet filter according to the spectral characteristics of the data, and remove the high-frequency noise introduced during the differential process to obtain the processed three-component magnetic field differential data.

[0025] For spatial differences, taking the x direction as an example, the first-order difference of the magnetic field B x can be expressed as:

[0026]

[0027] In the formula, (x, y, z) represents the spatial grid point coordinates, and Δx is the spatial sampling interval; for the time difference, similarly, it can be calculated based on the magnetic field values at adjacent time points.

[0028] Step S2: Introduce the dipole parameter and perform calculations:

[0029] Calculate the dipole parameter based on the three-component magnetic field data, correct and verify the calculated dipole parameter, remove abnormal data points, enrich the constraints for inversion, and improve the accuracy and resolution of the inversion results. The specific steps are as follows:

[0030] Step S21: When performing semi-aerial time-frequency electromagnetic system measurements, in addition to measuring the three-component magnetic field, simultaneously measure the horizontal electric field components E x 、E y , and calculate the dipole values T z at different frequency points and different measurement points.

[0031] The calculation formula for the dipole value T z is:

[0032]

[0033] In the formula, is the imaginary unit, ω is the angular frequency, μ 0 is the vacuum magnetic permeability, and E y is the electric field component in the y direction.

[0034] Step S22: Adopt the multi-frequency point measurement technology, measure at multiple different frequency points, each frequency point corresponding to a different detection depth, so as to obtain the dipole information of the strata at different depths underground. At the same time, conduct error analysis and correction on the measurement data, remove abnormal data points, and improve the accuracy and reliability of the dipole parameter.

[0035] Step S3: Conduct multi-constraint inversion imaging by combining borehole core parameters and signal phase constraints:

[0036] Use the combination of the borehole core parameter constraints reflecting the formation resistivity distribution and the signal phase constraints based on the formation dispersion effect to conduct multi-constraint inversion imaging. On the one hand, according to the laboratory measurement results of the borehole core samples, obtain the actual distribution of the formation resistivity, introduce it as prior information into the inversion process, and constrain the inversion results; on the other hand, based on the formation dispersion effect, analyze the change characteristics of the signal phase, extract the information related to the formation electrical properties, and further constrain the inversion process; finally, establish a layered medium model, determine the initial parameters of the model, use the finite element method for forward simulation, use the particle swarm optimization algorithm for non-linear inversion, update the inversion model parameters, and find the optimal inversion model parameters to achieve the fine inversion of the resistivity. The specific steps are as follows:

[0037] Step S31. Constraint of borehole core parameters based on formation resistivity distribution:

[0038] Step S311. Through laboratory measurement of borehole cores at representative locations in the study area, obtain the resistivity of the cores and the physical parameters of the rock (mineral composition, porosity, density, and water saturation).

[0039] Step S312. Use Archie's formula to establish a quantitative relationship model between borehole core parameters and formation resistivity distribution. Determine the empirical constants in the model through core measurement data, thereby realizing the conversion from core parameters to formation resistivity. During the inversion process, input the borehole core parameters and their corresponding formation resistivity distribution as constraint conditions into the inversion algorithm.

[0040] Archie's formula is calculated as follows:

[0041]

[0042] In the formula, ρ is the formation resistivity, ν is the porosity, S w is the water saturation, and a, m, n are empirical constants.

[0043] Step S32. Constraint of signal phase based on formation dispersion effect:

[0044] Step S321. Using spectral analysis technology, perform a fast Fourier transform on the measured electromagnetic signals to obtain the signal amplitude and phase information at different frequencies.

[0045] Step S322. According to the geological characteristics of the formation and known electrical parameters, select the Cole-Cole model to establish a theoretical model between formation resistivity and signal phase. Through the dielectric constant and resistivity measurement results of borehole cores, obtain the functional relationship between the two. At the same time, calculate the signal phase from the imaginary and real parts of the complex dielectric constant ε * (ω), and then calculate the relationship between the signal phase and formation resistivity at different frequencies.

[0046] The formation dispersion effect refers to the phenomenon that when electromagnetic waves propagate in underground formations, their phase velocity (the velocity at which the electromagnetic wave equiphase surface propagates) changes with frequency. That is, when electromagnetic waves of different frequencies propagate in underground media, their propagation velocities are different, causing electromagnetic waves of different frequencies to separate, resulting in signal dispersion.

[0047] The calculation formula of the Cole-Cole model is as follows:

[0048]

[0049] In the formula, ε *($\omega$) is the complex permittivity, $\varepsilon$ ∞ is the high-frequency permittivity, $\varepsilon$ s is the static permittivity, $\omega$ is the angular frequency, $\tau$ is the relaxation time, and $\alpha$ is the Cole-Cole parameter.

[0050] Signal phase The relationship with the complex permittivity is as follows:

[0051]

[0052] In the formula, Im($\varepsilon$ * ($\omega$)) is the imaginary part of the complex permittivity, and Re($\varepsilon$ * ($\omega$)) is the real part of the complex permittivity.

[0053] Step S33: Achieve fine resistivity inversion:

[0054] Step S331: Based on the geological background and prior information of the study area, establish a layered medium model, determine the initial parameters of the model, such as the number of strata and the initial resistivity of each layer, perform forward simulation using the finite element method, and calculate the three components of the magnetic field, the dipole parameter, and the signal phase according to the current model parameters.

[0055] Step S332: Construct a regularized objective function based on the differential data of the three components of the magnetic field, the dipole parameter, the constraints of borehole core parameters, and the constraints of the signal phase.

[0056] Step S333: Compare the forward simulation data corresponding to the borehole core parameters and the signal phase with the actual measurement data, and calculate the objective function value.

[0057] Step S334: Use the particle swarm optimization algorithm for nonlinear inversion, continuously iterate and optimize the regularized inversion objective function, update the inversion model parameters, and repeat the forward simulation and the calculation and optimization process of the regularized inversion objective function until the regularized inversion objective function converges or reaches the preset number of iterations, and then find the optimal inversion model parameters.

[0058] The calculation formula of the regularized inversion objective function is as follows:

[0059]

[0060] In the formula, F(k) is the regularized inversion objective function, $\varphi$ ρ is the model stability function of the resistivity, $\lambda$ ρ is the regularization factor of the resistivity stability function, k is the inversion model parameter, $\delta$ 1 , $\delta$ 2 ,... $\delta$ N is the assumed variance of the observed data, T zThe observed dipoles data is \(D(k)\), the forward simulation data is \(G(k)\), and \(\lambda\) 1 and \(\lambda\) 2 are constraint weight coefficients. \(C\) 1 (k) and \(C\) 2 (k) are the constraint terms of borehole core parameters and signal phase constraint terms respectively. Among them, \(C\) 1 (k) is constructed based on the prior physical property constraints of rock anisotropy, and the calculation formula is as follows:

[0061]

[0062] In the formula, \(P\) is the number of inversion units, \(Q\) is the number of clustering centers, \(f\) p is the physical property parameter of the \(p\)-th unit, \(f\) q is the measured value of the reference physical property of the \(q\)-th rock, and \(\sigma\) q is the variance of the \(q\)-th reference physical property.

[0063] \(C\) 2 (k) is constructed based on the least squares method, and the calculation formula is as follows:

[0064]

[0065] In the formula, is the actually measured signal phase, \(h\) is different measurement points or frequency points, \(H\) is the total number of measurement points, and \(\beta\) h is the weight coefficient.

[0066] Step S335: Calculate two statistical indicators, namely the root mean square error and the correlation coefficient, to evaluate the quality of the resistivity results obtained by inversion, and achieve fine inversion of resistivity.

Claims

1. A high-precision and high-resolution electromagnetic imaging method for formation dispersion combining differential enhancement and multi-constraints, characterized in that The method comprises the following steps: Step S1: Process the three-component data of the magnetic field using differential technology: First, the three-component magnetic field data are collected in the field. Then, the three-component magnetic field data are differentially calculated. By calculating the difference of magnetic field components at adjacent measurement points and at different times, the variation characteristics of the magnetic field are highlighted and the influence of the smoothing effect is reduced, thereby improving the resolution of deep information. Step S2: Introduce the tilting sub-parameters and perform calculations: Calculate the dipole parameters based on the three-component magnetic field data, calibrate and verify the calculated dipole parameters, remove abnormal data points, enrich the inversion constraints, and improve the accuracy and resolution of the inversion results; Step S3, combining the drilling core parameters and the signal phase constraints to perform multi-constrained inversion imaging: Based on the laboratory measurement results of the drill core samples, the actual distribution of the formation resistivity is obtained and introduced into the inversion process as prior information to constrain the inversion results. Based on the formation dispersion effect, the change characteristics of the signal phase are analyzed to extract information related to the electrical properties of the formation to further constrain the inversion process. A layered medium model is established, the initial parameters of the model are determined, the finite element method is used for forward simulation, the particle swarm optimization algorithm is used for nonlinear inversion, the inversion model parameters are updated, the optimal inversion model parameters are found, and the fine inversion of resistivity is achieved.

2. The method for high-precision and high-resolution electromagnetic imaging of formation dispersion by combining differential enhancement and multiple constraints according to claim 1 is characterized in that The specific steps of step S1 are as follows: Step S11, using a semi-aeronautical time-frequency electromagnetic system to collect three-component magnetic field data according to a measurement grid in the study area to ensure the accuracy and integrity of the data; Step S12: collect the three-component magnetic field data B x , B y , B z Input into the difference calculation program, and use the central difference format to calculate the difference of each component in space and time; Step S13, filtering the differential data, selecting a wavelet filter according to the frequency spectrum characteristics of the data, removing the high-frequency noise introduced in the differential process, and obtaining the processed three-component differential data of the magnetic field.

3. The method for high-precision and high-resolution electromagnetic imaging of formation dispersion by combining differential enhancement and multiple constraints according to claim 1 is characterized in that The specific steps of step S2 are as follows: Step S21: When performing semi-aerospace time-frequency electromagnetic system measurement, in addition to measuring the three components of the magnetic field, the horizontal electric field component E is also measured. x 、E y , calculate the inclination value T at different frequency points and different measurement points z ; Step S22, using multi-frequency measurement technology, measurement is performed at multiple different frequency points, each frequency point corresponds to a different detection depth, so as to obtain the inclination information of strata at different depths underground, and at the same time perform error analysis and correction on the measurement data, remove abnormal data points, and improve the accuracy and reliability of the inclination parameters.

4. The method for high-precision and high-resolution electromagnetic imaging of formation dispersion by combining differential enhancement and multiple constraints according to claim 3 is characterized in that The tilt value T z The calculation formula is: In the formula, is the imaginary unit, ω is the angular frequency, μ0 is the vacuum permeability, E y is the electric field component in the y direction.

5. The method for high-precision and high-resolution electromagnetic imaging of formation dispersion by combining differential enhancement and multiple constraints according to claim 1 is characterized in that The specific steps of step S3 are as follows: Step S31, drilling core parameter constraints based on formation resistivity distribution: Step S311, obtaining the resistivity of the core and the physical parameters of the rock by conducting laboratory measurements on the drill cores at representative locations in the study area; Step S312: using Archie's formula to establish a quantitative relationship model between the borehole core parameters and the formation resistivity distribution, and determining the empirical constants in the model through the core measurement data, thereby realizing the conversion from the core parameters to the formation resistivity; Step S32: Signal phase constraint based on formation dispersion effect: Step S321: Using spectrum analysis technology, perform fast Fourier transform on the measured electromagnetic signal to obtain signal amplitude and phase information at different frequencies; Step S322: According to the geological characteristics of the formation and the known electrical parameters, the Cole-Cole model is selected to establish a theoretical model of formation resistivity and signal phase. The functional relationship between the dielectric constant and resistivity of the drilled core is obtained. At the same time, the complex dielectric constant ε * The imaginary and real parts of (ω) are used to calculate the signal phase Then the relationship between the signal phase and the formation resistivity at different frequencies is calculated; Step S33, realizing fine resistivity inversion: Step S331: According to the geological background and prior information of the study area, a layered medium model is established, the initial parameters of the model are determined, the finite element method is used for forward simulation, and the three components of the magnetic field, the dipole parameters, and the signal phase are calculated according to the current model parameters; Step S332, constructing a regularized objective function based on the three-component differential data of the magnetic field, the tilt parameter, the drilling core parameter constraint and the signal phase constraint; Step S333, comparing the forward modeling data corresponding to the drilling core parameters and the signal phase with the actual measurement data, and calculating the objective function value; Step S334, using a particle swarm optimization algorithm to perform nonlinear inversion, optimizing the regularized inversion objective function through continuous iteration, updating the inversion model parameters, repeating the forward simulation and regularized inversion objective function calculation and optimization process until the regularized inversion objective function converges or reaches a preset number of iterations, thereby finding the optimal inversion model parameters; Step S335, calculate the two statistical indicators of root mean square error and correlation coefficient, conduct quality assessment on the resistivity results obtained by inversion, and realize fine inversion of resistivity.

6. The method for high-precision and high-resolution electromagnetic imaging of formation dispersion by combining differential enhancement and multiple constraints according to claim 5 is characterized in that The Archie formula is calculated as follows: Where ρ is the formation resistivity, ν is the porosity, S w is water saturation, a, m, n are empirical constants.

7. The method for high-precision and high-resolution electromagnetic imaging of formation dispersion by combining differential enhancement and multiple constraints according to claim 5 is characterized in that The Cole-Cole model calculation formula is as follows: In the formula, ε * (ω) is the complex dielectric constant, ε ∞ is the high frequency dielectric constant, ε s is the static dielectric constant, ω is the angular frequency, τ is the relaxation time, and α is the Cole-Cole parameter.

8. The method for high-precision and high-resolution electromagnetic imaging of formation dispersion by combining differential enhancement and multiple constraints according to claim 5 is characterized in that The signal phase The relationship with the complex dielectric constant is as follows: In the formula, Im(ε * (ω)) is the imaginary part of the complex dielectric constant, Re(ε * (ω)) is the real part of the complex dielectric constant.

9. The method for high-precision and high-resolution electromagnetic imaging of formation dispersion by combining differential enhancement and multiple constraints according to claim 5, characterized in that The calculation formula of the regularized inversion objective function is as follows: Where F(k) is the regularized inversion objective function, φ ρ is the model stability function of resistivity, λ ρ is the regularization factor of the resistivity stability function, k is the inversion model parameter, δ1,δ2,...δ N is the assumed variance of the observed data, T z is the observed dipole data, G(k) is the forward simulation data, λ1 and λ2 are the constraint weight coefficients, C1(k) and C2(k) are the borehole core parameter constraint terms and signal phase constraint terms, respectively.

10. The method for high-precision and high-resolution electromagnetic imaging of formation dispersion by combining differential enhancement and multiple constraints according to claim 9, characterized in that The C1(k) is constructed based on the prior physical property constraints of rock heterogeneity, and the calculation formula is as follows: In the formula, P is the number of inversion units, Q is the number of cluster centers, and f p is the physical property parameter of the pth unit, f q is the measured value of the qth rock reference property, σ q is the variance of the qth reference property. The C2(k) is constructed based on the least squares method, and the calculation formula is as follows: In the formula, is the actual measured signal phase, h is the different measurement points or frequency points, H is the total number of measurement points, β h is the weight coefficient.

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