A method and system for adaptive optimization selection of background field conductivity in electromagnetic field forward of horizontal well

Abstract

The application provides a method and system for adaptively and optimally selecting background field conductivity in electromagnetic field forward modeling of a horizontal well, wherein the method comprises the following steps: extracting characteristic parameters from a full-tensor anisotropic conductivity tensor of a target formation, and constructing a candidate background conductivity parameter set; calculating a difference spectral domain field corresponding to the candidate background conductivity parameters; performing convergence quantitative analysis on the difference spectral domain field, comprehensively evaluating and ranking each candidate background conductivity parameter based on a convergence evaluation index, and determining an optimal background conductivity parameter; and performing a background field subtraction operation by using the optimal background conductivity parameter to obtain a final calculation result. The method and system for adaptively and optimally selecting background field conductivity in electromagnetic field forward modeling of a horizontal well can automatically identify the optimal background conductivity parameter in formations with different anisotropic types and intensities, improve the convergence of the difference spectral domain field, and improve the electromagnetic field calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic wave logging data processing technology, and in particular to a method and system for adaptive optimization selection of background field conductivity in forward modeling of electromagnetic fields in horizontal wells. Background Technology

[0002] In forward modeling of electromagnetic fields in horizontal or highly deviated wells, the background field subtraction method is an effective means of solving singularity problems. The core idea of ​​this method is to decompose the electromagnetic field of a fully tensor-anisotropic formation into two parts: a background field and a difference field. The background field uses a simplified uniaxial anisotropic model, which can be calculated quickly or has an analytical solution, while the difference field is solved through numerical integration. However, existing techniques face the following serious challenges: In traditional methods, the selection of background field conductivity parameters typically employs empirical, fixed strategies, such as simply taking the arithmetic mean of the main diagonal elements, lacking systematic selection criteria and optimization methods. The selection of background field conductivity directly affects the convergence speed and integration accuracy of the difference spectral domain field, but the system is essentially blind to different formation characteristics. When encountering formations with different anisotropy types and intensities, the performance of fixed selection strategies varies greatly. Inappropriate selection of background conductivity parameters can lead to slow decay of the difference spectral domain field in the high wavenumber region, easily causing divergence of the integrand or insufficient integration accuracy. Especially in horizontal wells, when the vertical distance between the emission point and the measurement point is zero or less than 0.1 meters, the integrand exhibits slow convergence or even divergence, resulting in non-integrability of the numerical integral, producing singularities, and severely affecting the stability of computational efficiency and the reliability of forward modeling results.

[0003] In view of this, there is an urgent need for an adaptive optimization method and system for selecting the background field conductivity in the forward modeling of electromagnetic fields in horizontal wells, so as to at least solve the above-mentioned shortcomings. Summary of the Invention

[0004] One of the objectives of this invention is to provide an adaptive optimization method and system for selecting background field conductivity in horizontal well electromagnetic field forward modeling. This solves the problems of slow convergence of the integrand, unstable computational efficiency, and insufficient integration accuracy caused by improper selection of background field conductivity parameters in existing horizontal well electromagnetic field forward modeling calculations. Through the adaptive selection mechanism, the optimal background conductivity parameters can be automatically identified in formations with different anisotropy types and intensities, achieving good convergence performance under various formation conditions and further improving the efficiency of electromagnetic field calculation.

[0005] This invention provides an adaptive optimization method for selecting background field conductivity in forward electromagnetic field modeling of a horizontal well, comprising: Characteristic parameters are extracted from the full tensor anisotropic conductivity tensor of the target formation traversed by the horizontal well to obtain conductivity characteristic parameters. Based on the conductivity characteristic parameters, a candidate background conductivity parameter set is constructed; Based on the preset electromagnetic field source parameters, the full tensor anisotropic conductivity tensor, and the candidate background conductivity parameter set, determine the difference spectral field corresponding to each group of candidate background conductivity parameters in the candidate background conductivity parameter set; Convergence quantification analysis was performed on the difference spectral field to determine the convergence evaluation index corresponding to each group of candidate background conductivity parameters; Based on the convergence evaluation index, the candidate background conductivity parameters of each group are comprehensively evaluated and ranked, and the group of candidate background conductivity parameters with the best comprehensive evaluation result is determined as the optimal background conductivity parameters. The background field subtraction operation is performed using the selected optimal background conductivity parameter to obtain the final electromagnetic field calculation result.

[0006] Preferably, the conductivity characteristic parameter is the main diagonal element of the full tensor anisotropic conductivity tensor, and the main diagonal element includes the conductivity in the first horizontal direction, the conductivity in the second horizontal direction, and the conductivity in the vertical direction.

[0007] Preferably, a candidate background conductivity parameter set is constructed based on conductivity characteristic parameters, including: The conductivity characteristic parameters are combined using at least two different statistical combination methods to generate a candidate background conductivity parameter set; the candidate background conductivity parameter set contains multiple sets of candidate background conductivity parameters, and each set of candidate background conductivity parameters corresponds to a uniaxial anisotropic background model; The statistical combination methods include: The arithmetic or geometric mean of the conductivity in the first horizontal direction and the conductivity in the second horizontal direction are taken as the background horizontal conductivity; the conductivity in the vertical direction is taken as the background vertical conductivity; and a transversely isotropic uniaxial anisotropic background model is constructed using the background horizontal conductivity and the background vertical conductivity. or, The arithmetic mean of the conductivity in the first horizontal direction, the conductivity in the second horizontal direction, and the conductivity in the vertical direction is taken and used as the background horizontal conductivity and the background vertical conductivity to construct an isotropic uniaxial anisotropic background model. or, The geometric mean of the conductivity in the first horizontal direction, the second horizontal direction, and the vertical direction is taken and used as the background horizontal conductivity and background vertical conductivity to construct an isotropic uniaxial anisotropic background model. or, The harmonic mean of the conductivity in the first horizontal direction, the second horizontal direction, and the vertical direction is taken and used as the background horizontal conductivity and background vertical conductivity to construct an isotropic uniaxial anisotropic background model.

[0008] Preferably, based on preset electromagnetic field source parameters, the fully tensor anisotropic conductivity tensor, and a candidate background conductivity parameter set, the difference spectral domain field corresponding to each group of candidate background conductivity parameters in the candidate background conductivity parameter set is determined, including: The minimum wavenumber is determined based on the maximum feature scale of the target layer, and the maximum wavenumber is determined based on the preset target integration accuracy. Initial sampling points are generated in a logarithmically evenly spaced range from the minimum wavenumber to the maximum wavenumber. Increase the sampling density of the high wavenumber region relative to the low wavenumber region to obtain the initial set of sampling wavenumber points for the density partition; wherein, the sampling density of the high wavenumber region is set to 2 to 4 times that of the low wavenumber region. On the initial set of sampling wavenumber points, select any set of candidate background conductivity parameters to calculate the estimated difference spectral field. Check the relative change of the amplitude of the estimated difference spectral field of adjacent sampling points one by one. If the relative change exceeds the preset change threshold, insert additional sampling points between the corresponding adjacent sampling points. The set of all encrypted sampling points is used as the sampling wavenumber point set; Based on the preset electromagnetic field source parameters and the full tensor anisotropic conductivity tensor, the spectral domain electromagnetic field under the full tensor anisotropic condition is solved at each wavenumber point of the sampling wavenumber point set to obtain the full tensor anisotropic spectral domain response. Based on the preset electromagnetic field source parameters, the spectral domain electromagnetic field under uniaxial anisotropic conditions corresponding to each set of candidate background conductivity parameters is solved at each wavenumber point of the sampling wavenumber point set, and the uniaxial anisotropic spectral domain response corresponding to each set of candidate background conductivity parameters is obtained. The difference between the full tensor anisotropic spectral domain response and the uniaxial anisotropic spectral domain response corresponding to each group of candidate background conductivity parameters is calculated point by point at each wavenumber point to obtain the difference spectral domain field corresponding to each group of candidate background conductivity parameters.

[0009] Preferably, on the initial set of sampled wavenumber points, any set of candidate background conductivity parameters is selected for the calculation of the estimated difference spectral field. The relative change in the amplitude of the estimated difference spectral field of adjacent sample points is checked one by one. If the relative change exceeds a preset change threshold, additional sample points are inserted between the corresponding adjacent sample points, including: A set of candidate background conductivity parameters is selected from the candidate background conductivity parameter set as the prediction parameters; At each wavenumber point in the initial set of sampling wavenumber points, the full tensor anisotropic spectral domain response is solved based on the preset electromagnetic source parameters and the full tensor anisotropic conductivity tensor, and the corresponding uniaxial anisotropic spectral domain response is solved based on the preset electromagnetic source parameters and the estimated parameters. The difference between the full tensor anisotropic spectral domain response and the single-axis anisotropic spectral domain response corresponding to the predicted parameters is calculated point by point at each wavenumber point, and the amplitude is taken to obtain the predicted difference spectral domain field amplitude sequence. Based on the predicted difference spectral field amplitude sequence, the relative change in amplitude is calculated for each pair of adjacent wavenumber points in ascending order of wavenumber, and a set of relative changes is obtained. Each relative change in the set of relative changes is compared with a preset change threshold to determine the set of intervals to be encrypted corresponding to adjacent wavenumber point pairs whose relative changes exceed the preset change threshold. Insert an extra sampling point at the logarithmic midpoint between two adjacent wavenumber points in each interval to be encrypted, and merge all the extra sampling points into the current sampling wavenumber point set to form an updated sampling wavenumber point set. The process of replacing the initial set of sampled wavenumber points with the updated set of sampled wavenumber points, repeatedly calculating the relative change, determining the interval to be encrypted, and inserting additional sample points continues until the relative change of amplitude of any adjacent wavenumber point pair in the updated set of sampled wavenumber points does not exceed the preset change threshold. The final set of sampled wavenumber points is then used as the adaptively encrypted set of sampled wavenumber points.

[0010] Preferably, a convergence quantization analysis is performed on the difference spectral field to determine the convergence evaluation index corresponding to each group of candidate background conductivity parameters, including: Based on the preset wavenumber boundary threshold, all sampling wavenumber points of the difference spectral field corresponding to each group of candidate background conductivity parameters are divided into low wavenumber regions and high wavenumber regions to obtain the difference spectral field data after partitioning and labeling. Based on the difference spectral field data, the change sequence of the difference spectral field amplitude with increasing wavenumber is extracted in the high wavenumber region. The decay trend of the change sequence is fitted to calculate the decay rate of amplitude with increasing wavenumber, and the amplitude decay rate in the high wavenumber region is obtained. Based on the difference spectral field data, the total spectral field energy of the difference spectral field over the entire wavenumber range and the local spectral field energy within the preset cutoff wavenumber are calculated respectively. The ratio of the local spectral field energy to the total spectral field energy is taken as the energy concentration of the difference spectral field. Based on the difference spectral field data, the change information of positive and negative signs of the real or imaginary part of the difference spectral field between adjacent sampling wavenumber points is extracted, and the number of positive and negative sign flips within a unit wavenumber interval is counted to obtain the oscillation frequency of the difference spectral field. Based on the difference spectral field data, the amplitude attenuation characteristics of the tail of the high wavenumber region are used to extrapolate and estimate the integral contribution from the maximum sampling wavenumber to infinity. The ratio of the integral contribution to the integral estimate of the whole wavenumber range is used as the integral truncation error estimate. The amplitude attenuation rate in the high wavenumber region, the energy concentration in the difference spectral field, the oscillation frequency in the difference spectral field, and the integral truncation error estimation corresponding to each group of candidate background conductivity parameters are used as convergence evaluation indicators for each group of candidate background conductivity parameters.

[0011] Preferably, the set of candidate background conductivity parameters with the best comprehensive evaluation results is determined as the optimal background conductivity parameters, including: Normalize each convergence evaluation index; The comprehensive evaluation function value of each group of candidate background conductivity parameters is obtained by multiplying the normalized index value corresponding to each index weight coefficient by the corresponding index weight coefficient and summing them. The candidate background conductivity parameters with the largest comprehensive evaluation function value are selected as the candidate background conductivity parameters; The convergence of the difference spectral field corresponding to the selected background conductivity parameter is verified. When the absolute value of the amplitude attenuation rate is higher than the preset attenuation threshold and the estimated value of the integral truncation error is lower than the preset accuracy threshold, the corresponding selected background conductivity parameter is taken as the optimal background conductivity parameter. Otherwise, taking the parameters whose comprehensive evaluation function values ​​among the existing candidate background conductivity parameters fall within the preset sorting range as the center, interpolation is performed within the preset percentage range of the corresponding background horizontal conductivity and background vertical conductivity values ​​according to the preset step size to generate new candidate background conductivity parameters. These new parameters are then added to the candidate background conductivity parameter set for re-evaluation until the selected candidate background conductivity parameters pass the convergence verification, thus obtaining the optimal background conductivity parameters.

[0012] Preferably, a background field subtraction operation is performed using the selected optimal background conductivity parameter to obtain the final electromagnetic field calculation result, including: A target uniaxial anisotropic background model is constructed using the background horizontal conductivity and background vertical conductivity parameters from the optimal background conductivity parameters. The background field is obtained by obtaining an analytical solution for the target uniaxial anisotropic background model based on the electromagnetic field source parameters. The difference spectral field corresponding to the optimal background conductivity parameter is integrated by numerical inverse transformation on the set of sampled wavenumber points to transform the spectral data into spatial data, thus obtaining the spatial scattering field. The spatial domain scattered field is superimposed with the background field to obtain the final electromagnetic field calculation result.

[0013] Preferably, the difference spectral field corresponding to the optimal background conductivity parameter is integrated by numerical inverse transform over the set of sampled wavenumber points to transform the spectral data into spatial data, thereby obtaining the spatial scattering field, including: The difference spectral field, the set of sampling wavenumber points, the coordinates of the target space observation points, and the amplitude attenuation rate and integral truncation error estimates in the high wavenumber region obtained by convergence quantization analysis are obtained corresponding to the optimal background conductivity parameters. Inverse transform integral control parameters are generated based on integral truncation error estimation and amplitude attenuation rate in the high wavenumber region. The inverse transform integral control parameters include attenuation model parameters determined based on amplitude attenuation rate in the high wavenumber region and tail compensation accuracy level determined based on integral truncation error estimation. Based on the set of sampled wavenumber points, the coordinates of the target space observation points, and the inverse transform integral control parameters, a numerical inverse transform integral is performed on the difference spectral field to obtain the principal integral result within the range covered by the set of sampled wavenumber points. Based on the attenuation model parameters and the amplitude of the difference spectral field at the maximum sampling wavenumber, the tail integral contribution after the maximum sampling wavenumber is extrapolated and estimated to obtain the tail contribution. The main integral result is combined with the tail contribution to obtain the spatial domain scattering field.

[0014] This invention provides an adaptive optimization system for selecting background field conductivity in forward electromagnetic field modeling of horizontal wells, comprising: The feature extraction module is used to extract feature parameters from the full tensor anisotropic conductivity tensor of the target formation traversed by the horizontal well, and obtain conductivity feature parameters. The candidate parameter acquisition module is used to construct a candidate background conductivity parameter set based on conductivity characteristic parameters; The difference spectral field determination module is used to determine the difference spectral field corresponding to each set of candidate background conductivity parameters in the candidate background conductivity parameter set based on the preset electromagnetic field source parameters, the full tensor anisotropic conductivity tensor, and the candidate background conductivity parameter set. The evaluation index determination module is used to perform convergence quantification analysis on the difference spectral field and determine the convergence evaluation index corresponding to each group of candidate background conductivity parameters. The optimal background conductivity parameter determination module is used to comprehensively evaluate and rank each group of candidate background conductivity parameters based on convergence evaluation index, and determine the group of candidate background conductivity parameters with the best comprehensive evaluation result as the optimal background conductivity parameter. The electromagnetic field calculation module is used to perform background field subtraction operations using the selected optimal background conductivity parameters to obtain the final electromagnetic field calculation results.

[0015] The beneficial effects of this invention are as follows: This invention improves the reliability of background conductivity parameter selection by establishing a quantitative evaluation index system for convergence, transforming the parameter selection process, which originally relied on empirical judgment, into a quantifiable and optimizable mathematical problem. Through an adaptive selection mechanism, it can automatically identify the optimal background conductivity parameter in strata with different anisotropy types and intensities, and achieve good convergence performance under various stratum conditions, further improving the efficiency of electromagnetic field calculation.

[0016] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in this application.

[0017] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a schematic diagram of an adaptive optimization method for selecting background field conductivity in forward modeling of electromagnetic fields in a horizontal well, according to an embodiment of the present invention. Figure 2 This is a schematic diagram of an adaptive optimization system for selecting background field conductivity in forward modeling of electromagnetic fields in a horizontal well, according to an embodiment of the present invention. Detailed Implementation

[0019] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0020] This invention provides an adaptive optimization method for selecting background field conductivity in forward electromagnetic field modeling of horizontal wells, such as... Figure 1 As shown, it includes: Step 1: Extract characteristic parameters from the full tensor anisotropic conductivity tensor of the target formation traversed by the horizontal well to obtain conductivity characteristic parameters.

[0021] In forward modeling of electromagnetic logging in horizontal wells, the electrical conductivity information of the target formation is typically given in the form of a full tensor anisotropic conductivity tensor. The full tensor anisotropic conductivity tensor is a 3x3 symmetric matrix containing 9 components (actually 6 independent components due to symmetry), comprehensively describing the formation's response to electromagnetic wave propagation in all directions. However, to construct a background model with analytical solutions, it is necessary to extract key parameters reflecting the main electromagnetic characteristics of the formation from this complex tensor information.

[0022] In this embodiment, the conductivity characteristic parameter is the main diagonal element of the full-tensor anisotropic conductivity tensor. The main diagonal element includes the conductivity in the first horizontal direction (the conductivity component along the strike of the formation, denoted as...). ), the second horizontal direction conductivity (the conductivity component along the dip direction of the strata, denoted as...) ) and vertical conductivity (the conductivity component along the normal direction of the formation, denoted as ).

[0023] The physical basis for selecting the main diagonal elements as feature parameters lies in the fact that these elements directly reflect the electrical conductivity of the strata along the three principal axes, and are the most important factor controlling the spatial distribution of the electromagnetic field. In contrast, off-diagonal elements reflect the conductivity coupling effect between different directions, which is usually smaller in magnitude and has a secondary impact on the selection of the background field. By extracting the main diagonal elements, the system retains the most critical strata information while reducing the parameter dimension from 9 to 3, laying the foundation for subsequent statistical combination processing and candidate set construction.

[0024] In practical implementation, the system reads the full tensor anisotropic conductivity tensor matrix of the target formation from the input model file of the forward modeling, and directly extracts the values ​​of its first row and first column, second row and second column, and third row and third column, respectively, as... , and The output value. When there is a rotation relationship between the formation coordinate system and the calculation coordinate system, the system first transforms the conductivity tensor to the principal axis coordinate system of the formation through a coordinate rotation matrix, and then extracts the main diagonal elements to ensure that the extracted feature parameters have clear physical meaning.

[0025] Step 2: Construct a candidate background conductivity parameter set based on conductivity characteristic parameters.

[0026] Obtaining the conductivity in the first horizontal direction Horizontal second direction conductivity and vertical conductivity After obtaining these three characteristic parameters, the system combines them using at least two different statistical methods to generate a candidate background conductivity parameter set containing multiple sets of candidate parameters. Each set of candidate background conductivity parameters is defined by a background level. and a background vertical conductivity This constitutes a uniaxial anisotropic background model.

[0027] Different statistical measures have varying sensitivities to outliers and anisotropy intensities. Under different geological conditions, a particular combination may produce background parameters most favorable for convergence. Therefore, a design employing multiple statistical combinations is necessary. Specific statistical combinations include the following: conductivity in the first horizontal direction and horizontal second direction conductivity The arithmetic mean is taken as the background conductivity level. The vertical conductivity is directly taken as the background vertical conductivity, i.e. This allows for the construction of a laterally isotropic, uniaxially anisotropic background model. This approach preserves the anisotropy difference between the horizontal and vertical directions, while simplifying the anisotropy within the horizontal plane through arithmetic averaging. It is suitable for stratigraphic conditions where the anisotropy within the horizontal plane is weak but the anisotropy in the vertical direction is strong.

[0028] Similar to the previous one, but the geometric mean of the horizontal conductivity is taken, i.e. The background vertical conductivity is still taken as Geometric mean exhibits good robustness when dealing with conductivity values ​​that differ by orders of magnitude. When there is a large difference in conductivity between two horizontal directions (e.g., one direction contains cracks while the other does not), geometric mean can provide a more moderate representative value, avoiding the problem that arithmetic mean is easily dominated by large values.

[0029] The arithmetic mean of the conductivity in the three directions is taken, and this value is used as both the background horizontal conductivity and the background vertical conductivity. This approach constructs an isotropic background model (an isotropic model can be considered a special case of a uniaxial anisotropic model, where the horizontal conductivity equals the vertical conductivity). When the conductivity differences in the three directions of the stratum are not significant, the isotropic background model may provide the simplest and most effective background description.

[0030] The geometric mean of the conductivity in the three directions is taken, i.e. Geometric mean is equivalent to arithmetic mean on a logarithmic scale and is particularly suitable for handling conductivity spanning several orders of magnitude. Resistivity (the reciprocal of conductivity) is typically analyzed and displayed on a logarithmic scale, so an isotropic background based on geometric mean has better physical representativeness in certain scenarios.

[0031] The harmonic average of the conductivity in the three directions is taken, i.e. The harmonic mean physically corresponds to the equivalent conductivity in the series resistance model and is more sensitive to low conductivity values ​​(high resistivity values). In formations containing thin interlayers with high resistivity, the harmonic mean can better capture the hindering effect of these thin layers on the propagation of the overall electromagnetic field.

[0032] Through the above combinations, the system generates multiple sets of candidate background conductivity parameters, forming a candidate background conductivity parameter set. In practical applications, the system can also add more combinations as needed, such as weighted average, median, or quantile statistics, to further enrich the candidate parameter set and improve the coverage of the optimization search.

[0033] Step 3: Based on the preset electromagnetic field source parameters, the full tensor anisotropic conductivity tensor, and the candidate background conductivity parameter set, determine the difference spectral domain field corresponding to each group of candidate background conductivity parameters in the candidate background conductivity parameter set.

[0034] The core task of step 3 is to calculate the electromagnetic field response in the spectral domain under both full tensor anisotropy and candidate background model conditions, and then calculate the difference between the two. To minimize computational complexity while maintaining accuracy, this invention designs an adaptive wavenumber sampling strategy.

[0035] First, the system determines the wavenumber sampling range required for spectral domain calculations. Wavenumber is the independent variable in the spectral domain, and its physical meaning corresponds to the frequency components in space. The minimum wavenumber is determined by the reciprocal of the maximum characteristic scale of the target layer (e.g., formation thickness or detection distance), ensuring that the low wavenumber end can cover the overall structural information of the formation; the maximum wavenumber is determined by the preset target integration accuracy, which needs to be large enough to attenuate the difference spectral domain field to a negligible level.

[0036] Within a defined wavenumber range, the system first generates initial sampling points at logarithmic intervals. The reason for using logarithmic intervals instead of nonlinear intervals is that the spectral response of the electromagnetic field typically varies more uniformly on a logarithmic scale of the wavenumber. Linear intervals would result in the low wavenumber region being too dense and the high wavenumber region being too sparse, or vice versa.

[0037] Based on the initial logarithmically spaced distribution, the system further increases the sampling density of the high-wavenumber region relative to the low-wavenumber region. This is because the difference spectral domain field typically exhibits more complex attenuation behavior in the high-wavenumber region, potentially including rapid oscillations or non-monotonic changes, requiring denser sampling for accurate capture. In this embodiment, the sampling density of the high-wavenumber region is set to 2 to 4 times that of the low-wavenumber region. The boundary between the high-wavenumber and low-wavenumber regions can be determined based on physical parameters such as skin depth, for example, taking the reciprocal of the skin depth corresponding to the formation's average conductivity and operating frequency as the boundary wavenumber. It should be noted that the high- and low-wavenumber region boundaries used for sampling density allocation in step 3 can be the same as or different from the high- and low-wavenumber region boundaries used for convergence analysis in subsequent step 4, serving different technical purposes.

[0038] The set of sampled wavenumber points obtained after the above partitioning and encryption is called the initial sampled wavenumber point set. However, due to the diversity of formation conditions, the prior density allocation alone may not be sufficient to fully cover all drastically changing intervals of the difference spectral field. Therefore, the system further performs an adaptive encryption process. The specific steps of the adaptive encryption are as follows: The system selects a set of candidate background conductivity parameters from a candidate background conductivity parameter set as the prediction parameters. The selection can be based on the first set of parameters constructed, or on the set of parameters with the smallest deviation from the three characteristic parameters. These parameters are only used to detect the variation characteristics of the difference spectral field in the wavenumber domain, providing guiding information for adaptive encryption.

[0039] At each wavenumber point in the initial sampling wavenumber set, the system performs two spectral domain solutions: one to solve for the full tensor anisotropic spectral domain response based on preset electromagnetic source parameters and the full tensor anisotropic conductivity tensor; and another to solve for the corresponding uniaxial anisotropic spectral domain response based on preset electromagnetic source parameters and estimated parameters. Then, the difference between the two solutions is calculated point-by-point at each wavenumber point, and the amplitude is taken (i.e., the modulus of the complex difference is calculated) to obtain the estimated difference spectral domain amplitude sequence.

[0040] Based on the predicted difference spectral field amplitude sequence, the system calculates the relative amplitude change for each pair of adjacent wavenumber points in ascending order of wavenumber. The relative amplitude change is defined as the absolute value of the difference between the amplitudes of two adjacent points divided by the larger of the two amplitudes. This definition ensures that small changes in regions with small amplitudes are not misinterpreted as drastic changes.

[0041] The system compares the calculated relative changes in each amplitude with a preset change threshold. The preset change threshold is a value between 5% and 20%, and the specific value can be calibrated according to the target accuracy requirements. When the relative change between a pair of adjacent wavenumber points exceeds the preset change threshold, it indicates that the difference spectral field changes drastically within that range, and the existing sampling density is insufficient to accurately describe its shape.

[0042] For each interval determined to require encryption, the system inserts an additional sampling point at the logarithmic midpoint between the two adjacent wavenumber points corresponding to that interval. The logarithmic midpoint is chosen instead of the nonlinear midpoint to maintain consistency with the overall logarithmically spaced sampling strategy.

[0043] After incorporating all newly inserted additional sampling points into the current sampled wavenumber point set, the system replaces the initial set with the updated set, repeating the process of calculating relative changes, determining the interval to be encrypted, and inserting additional sampling points. This iterative process continues until the relative change in amplitude of any pair of adjacent wavenumber points in the updated sampled wavenumber point set does not exceed a preset change threshold. The final sampled wavenumber point set is the adaptively encrypted sampled wavenumber point set.

[0044] The key advantage of the adaptive encryption strategy is that it intelligently concentrates sampling resources in the region where the difference spectral field changes most drastically, while maintaining sparser sampling in the region where the changes are gradual, thus achieving optimal sampling efficiency with a limited number of total sampling points.

[0045] After the set of sampled wavenumber points with adaptive encryption is determined, the system performs a formal spectral domain electromagnetic field solution at each wavenumber point in the set.

[0046] When calculating the full tensor anisotropic spectral response, the system solves for the projected form of Maxwell's equations in the spectral domain at each wavenumber point based on preset electromagnetic source parameters (including source type, frequency, location, and direction) and the full tensor anisotropic conductivity tensor. The spectral domain equations under full tensor anisotropy conditions are a set of coupled ordinary differential equations, typically solved by applying continuity conditions at each stratigraphic interface using the propagation matrix method or the global matrix method. This yields the spectral domain values ​​of each electromagnetic field component at each wavenumber point, constituting the full tensor anisotropic spectral response.

[0047] When calculating the uniaxial anisotropic spectral response, the system, based on preset electromagnetic source parameters, solves for the spectral electromagnetic field under uniaxial anisotropic conditions at each wavenumber point of the same sampling wavenumber point set, for each set of candidate background conductivity parameters (including one background horizontal conductivity and one background vertical conductivity). The symmetry of the uniaxial anisotropic background model allows the spectral equations to be decoupled into two independent polarization modes, resulting in significantly higher solution efficiency than the full tensor case. After solving for each set of candidate parameters separately, the uniaxial anisotropic spectral response corresponding to each set of candidate background conductivity parameters is obtained.

[0048] Finally, the system calculates the difference (complex subtraction) point-by-point between the full tensor anisotropic spectral domain response and the uniaxial anisotropic spectral domain response corresponding to each set of candidate background conductivity parameters at each wavenumber point, obtaining the difference spectral domain field corresponding to each set of candidate background conductivity parameters. The difference spectral domain field is a set of complex numerical sequences that vary with wavenumber, and its amplitude and attenuation characteristics directly reflect the degree of matching between the corresponding candidate background conductivity parameters and the full tensor anisotropic formation.

[0049] It is worth noting that the calculation of the full tensor anisotropic spectral domain response only needs to be performed once, and its result is shared by all candidate parameters. Different candidate parameters only differ in the solution of the uniaxial anisotropic spectral domain response, and the computational cost of the uniaxial anisotropic solution is much less than that of the full tensor solution. Therefore, the computational cost of the entire process mainly comes from one full tensor solution and multiple uniaxial solutions, and the overall computational cost is controllable.

[0050] Step 4: Perform convergence quantization analysis on the difference spectral field to determine the convergence evaluation index corresponding to each group of candidate background conductivity parameters.

[0051] This invention designs four convergence evaluation indices (amplitude attenuation rate in the high wavenumber region, energy concentration in the difference spectral field, oscillation frequency in the difference spectral field, and integral truncation error estimation). Each index reflects the convergence characteristics of the difference spectral field from different physical and numerical perspectives: The system first divides all sampled wavenumber points of the difference spectral field into low-wavenumber and high-wavenumber regions based on a preset wavenumber boundary threshold. The wavenumber boundary threshold can be set with reference to the characteristic wavenumber corresponding to the skin depth of the formation, for example, it can be taken as two to five times the reciprocal of the skin depth. The low-wavenumber region mainly contains the main information of the difference spectral field, while the behavior of the high-wavenumber region directly determines the convergence of the numerical integration.

[0052] Within the high wavenumber region, the system extracts the variation sequence of the difference spectral field amplitude as the wavenumber increases. For a well-converged difference spectral field, its amplitude in the high wavenumber region should exhibit a monotonically decreasing decay trend with increasing wavenumber. The system fits this variation sequence to the decay trend, typically using a power-law decay or exponential decay model. The resulting decay exponent or decay constant is the amplitude decay rate in the high wavenumber region.

[0053] The larger the absolute value of the attenuation rate, the more rapidly the difference spectral field attenuates in the high wavenumber region, the better the convergence of the numerical integral, and the smaller the truncation error. This is the most direct and core indicator for evaluating convergence.

[0054] The energy concentration of the difference spectral field measures the degree of energy concentration of the difference spectral field in the wavenumber domain. The system calculates the total spectral energy of the difference spectral field over the entire wavenumber range (i.e., the integral or summation of the square of the difference spectral field amplitude over the entire wavenumber range) and the local spectral energy within the preset cutoff wavenumber.

[0055] The preset cutoff wavenumber is usually taken as a certain percentage of the maximum wavenumber actually sampled (e.g., 50% to 80%), representing the range of wavenumbers that can be reliably covered by numerical integration.

[0056] The ratio of local spectral energy to total spectral energy is the energy concentration of the difference spectral field. The closer this ratio is to 1, the more concentrated the energy of the difference spectral field is in the lower wavenumber range, and the smaller the energy contribution in the high wavenumber region. This means that even if the integration is terminated at a lower cutoff wavenumber, not much information will be lost, and the convergence will be better.

[0057] The oscillation frequency of the difference spectral domain field is used to evaluate the quality of the difference spectral domain field from the perspective of numerical stability. The system extracts the sign change information of the real part (or imaginary part, depending on the specific electromagnetic field component) of the difference spectral domain field between adjacent sampling wavenumber points. When the real or imaginary part of the difference spectral domain field has opposite signs at a pair of adjacent sampling points, it is recorded as a sign flip.

[0058] The system counts the number of sign flips per unit wavenumber interval across the entire wavenumber range (or within a high wavenumber region) to obtain the difference spectral field oscillation frequency.

[0059] A lower oscillation frequency indicates a smoother change in the difference spectral field within the spectral domain, making numerical integration easier to control accuracy. Conversely, a higher oscillation frequency indicates drastic alternation between positive and negative values ​​in the difference spectral field. In such cases, numerical integration is prone to significant discretization errors due to insufficient sampling, and even with rapid amplitude decay, the actual integration accuracy may still be unsatisfactory. Therefore, a low oscillation frequency is an important supplementary indicator for good convergence.

[0060] In numerical inverse transform integration, since computers cannot directly integrate over an infinite interval, it is necessary to truncate the integral at a certain maximum sampling wavenumber. The integral contribution over the range from the truncated wavenumber to infinity constitutes the truncation error.

[0061] The system utilizes the amplitude attenuation characteristics at the tail of the high wavenumber region to establish an attenuation model (such as a power-law attenuation model or an exponential attenuation model). The fitted attenuation parameters are substituted into the integral expression of the attenuation model to extrapolate and estimate the integral contribution from the maximum sampling wavenumber to infinity.

[0062] The ratio of the estimated integral contribution to the full wavenumber range integral estimate (i.e., the numerical integral result from the minimum to the maximum wavenumber range plus the extrapolated tail contribution) is the integral truncation error estimate.

[0063] The smaller the integral truncation error estimate, the smaller the error introduced by truncation at the current maximum sampling wavenumber, and the more reliable the calculation result. The integral truncation error estimate directly quantifies the accuracy level of the current integration scheme.

[0064] At this point, the system has calculated and stored a complete four-dimensional convergence evaluation index for each group of candidate background conductivity parameters: amplitude attenuation rate in the high wavenumber region, energy concentration in the difference spectral domain field, oscillation frequency in the difference spectral domain field, and integral truncation error estimation.

[0065] Step 5: Based on the convergence evaluation index, perform a comprehensive evaluation and ranking of the candidate background conductivity parameters in each group, and determine the group of candidate background conductivity parameters with the best comprehensive evaluation result as the optimal background conductivity parameters.

[0066] Since the four convergence evaluation indicators reflect convergence from different dimensions, and the dimensions and numerical ranges of each indicator are different, it is necessary to integrate the multidimensional evaluation information into a unified evaluation standard through normalization and weighted synthesis.

[0067] First, the system normalizes each convergence evaluation index. The purpose of normalization is to eliminate differences in units and numerical ranges between different indices, making them comparable. Specifically, for each index, the system finds the maximum and minimum values ​​corresponding to that index among all candidate parameters, and then normalizes the index value of each candidate parameter to the range of 0 to 1 through a linear mapping.

[0068] For positive indices (i.e., indices with larger values ​​indicating better convergence, such as the absolute value of amplitude decay rate and energy concentration in the high wavenumber region), the normalization formula is the index value minus the minimum value, divided by the difference between the maximum and minimum values. For negative indices (i.e., indices with smaller values ​​indicating better convergence, such as oscillation frequency and integral truncation error estimation), the inverse mapping is used during normalization to ensure that a larger normalized value indicates better convergence.

[0069] Then, the system multiplies each normalized index value corresponding to each group of candidate background conductivity parameters by the corresponding index weight coefficient and sums them to obtain the comprehensive evaluation function value of each group of candidate background conductivity parameters.

[0070] The weighting coefficients of the indicators reflect the relative importance of each indicator to the overall convergence evaluation. In this preferred embodiment, the amplitude attenuation rate in the high wavenumber region, as the most crucial convergence indicator, is assigned the highest weight (e.g., 40%); the integral truncation error estimation, as an indicator of direct quantization accuracy, is assigned the second highest weight (e.g., 30%); energy concentration is assigned a medium weight (e.g., 20%); and oscillation frequency, as an auxiliary indicator, is assigned a low weight (e.g., 10%). These weight values ​​can be adjusted and calibrated according to different application scenarios and accuracy requirements.

[0071] After obtaining the comprehensive evaluation function values ​​of all candidate parameters, the system sorts them from largest to smallest and selects the group of candidate background conductivity parameters with the largest comprehensive evaluation function values ​​as the candidate background conductivity parameters.

[0072] However, simply ranking the comprehensive evaluation function is insufficient to confirm that the parameter truly meets the engineering accuracy requirements. Therefore, the system performs convergence verification on the difference spectral field corresponding to the selected background conductivity parameter. The convergence verification criteria include two conditions: first, the absolute value of the amplitude attenuation rate is higher than a preset attenuation threshold, ensuring that the difference spectral field attenuates sufficiently quickly in the high wavenumber region; second, the estimated value of the integral truncation error is lower than a preset accuracy threshold, ensuring that the truncation error of the numerical integration is within an acceptable range.

[0073] The typical value of the preset attenuation threshold depends on the specific attenuation model. If a power-law attenuation model is used, the absolute value of the attenuation exponent usually needs to be greater than 2-3 to ensure integral convergence; if an exponential attenuation model is used, the attenuation constant needs to be large enough to ensure the tail approaches zero quickly. The preset accuracy threshold is typically set between 0.1% and 1%, depending on the accuracy requirements of the application.

[0074] When both conditions are met, the system will confirm the corresponding candidate background conductivity parameter as the optimal background conductivity parameter, and the optimization selection process will end.

[0075] When the convergence verification fails, it indicates that the current candidate parameter set does not contain sufficiently good background conductivity parameters, and further refinement of the search is required. At this time, the system starts an adaptive local densification search strategy: taking the parameters whose comprehensive evaluation function values ​​are ranked within a preset ranking range (e.g., the top 3 to top 5) among the existing candidate background conductivity parameters as the center, and performing two-dimensional grid interpolation within a preset percentage range (e.g., ±10% to ±20%) of the corresponding background horizontal conductivity and background vertical conductivity values, at a preset step size (e.g., 5%), to generate several new sets of candidate background conductivity parameters.

[0076] The newly generated candidate parameters are added to the candidate background conductivity parameter set. The system then re-executes the complete process of difference spectral field calculation, convergence quantification analysis, and comprehensive evaluation and ranking for these new parameters. This iterative process continues until the selected candidate background conductivity parameters pass convergence verification, thus obtaining the optimal background conductivity parameters.

[0077] This progressive local encryption search strategy is both efficient and robust. Instead of exhaustively searching the entire parameter space, it intelligently performs a refined search in the most promising regions based on existing information, significantly reducing the number of computational iterations required.

[0078] Step 6: Perform background field subtraction using the selected optimal background conductivity parameter to obtain the final electromagnetic field calculation results.

[0079] After determining the optimal background conductivity parameters, the system constructs a target uniaxial anisotropic background model using the background horizontal conductivity and background vertical conductivity. This model has uniform background horizontal conductivity in the horizontal direction and uniform background vertical conductivity in the vertical direction, and is an idealized model with analytical solutions.

[0080] The system obtains the background field by calculating the analytical solution of the target uniaxial anisotropic background model based on the electromagnetic field source parameters (including source type, frequency, location, direction, and intensity). The analytical solution of the electromagnetic field in a uniaxial anisotropic homogeneous medium can be derived through the theory of dyadic Green's functions, which has a closed analytical expression, high computational accuracy, and fast speed.

[0081] Subsequently, the system performs a numerical inverse transform integration on the sampled wavenumber point set for the difference spectral field corresponding to the optimal background conductivity parameter, transforming the spectral data into spatial data to obtain the spatial scattering field.

[0082] The numerical inverse transform integral is a crucial step in restoring the difference field information from the spectral domain back to the spatial domain. This invention fully utilizes prior information obtained during the convergence quantization analysis phase to guide the integration process, thereby improving integration accuracy. The specific implementation method is as follows: The system acquires the difference spectral field corresponding to the optimal background conductivity parameter, the set of sampled wavenumber points, the coordinates of the target space observation points, and the amplitude attenuation rate and integral truncation error estimates in the high wavenumber region obtained by convergence quantization analysis.

[0083] The system generates inverse transform integral control parameters based on integral truncation error estimation and amplitude attenuation rate in the high wavenumber region. The inverse transform integral control parameters include at least two items: attenuation model parameters determined based on the amplitude attenuation rate in the high wavenumber region, used to describe the attenuation law of the difference spectral field in the high wavenumber region, such as the attenuation exponent and coefficient in a power-law attenuation model, or the attenuation constant and coefficient in an exponential attenuation model; and a tail compensation accuracy level determined based on integral truncation error estimation, used to control the accuracy requirements of the tail extrapolation compensation calculation.

[0084] During the numerical inverse transform integration, the system performs numerical integration on the difference spectral domain field based on the sampled wavenumber point set and the coordinates of the target spatial observation points. In forward modeling of electromagnetic fields in horizontal wells, the inverse transform typically involves a one-dimensional or two-dimensional inverse Fourier transform (or inverse Hankel transform), the specific form of which depends on the spectral domain decomposition method used. The system employs a high-precision numerical integration method (such as Gauss-Legend quadrature or adaptive Simpson's rule) to calculate the integral over the wavenumber range covered by the sampled wavenumber point set, obtaining the main integral result.

[0085] Since the integral is truncated at the maximum sampling wavenumber, a tail integral contribution still exists from the maximum sampling wavenumber to infinity. The system extrapolates and estimates this tail contribution using the analytical integral expression of the attenuation model, based on the attenuation model parameters and the actual amplitude of the difference spectral field at the maximum sampling wavenumber. For example, if the attenuation model is in power-law form, the tail integral can be directly calculated using the analytical integral formula of the power-law function from the maximum wavenumber to infinity; if the attenuation model is in exponential form, the incomplete integral formula of the exponential function is used. This yields the tail contribution.

[0086] Finally, the system synthesizes the main integral result with the tail contribution to obtain the complete spatial domain scattering field.

[0087] By superimposing the spatially scattered field with the previously obtained background field point by point in the spatial domain, the final electromagnetic field calculation result can be obtained. This result contains complete information on the response of the fully tensor anisotropic strata to electromagnetic waves, and benefits from the selection of the optimal background conductivity parameter, exhibiting good computational accuracy and efficiency.

[0088] This invention provides an adaptive optimization system for selecting background field conductivity in forward electromagnetic field modeling of horizontal wells, such as... Figure 2 As shown, it includes: Feature extraction module 1 is used to extract feature parameters from the full tensor anisotropic conductivity tensor of the target formation traversed by the horizontal well, and obtain conductivity feature parameters. Candidate parameter acquisition module 2 is used to construct a candidate background conductivity parameter set based on conductivity characteristic parameters; The difference spectral field determination module 3 is used to determine the difference spectral field corresponding to each set of candidate background conductivity parameters in the candidate background conductivity parameter set based on the preset electromagnetic field source parameters, the full tensor anisotropic conductivity tensor and the candidate background conductivity parameter set. The evaluation index determination module 4 is used to perform convergence quantification analysis on the difference spectral field and determine the convergence evaluation index corresponding to each group of candidate background conductivity parameters. The optimal background conductivity parameter determination module 5 is used to comprehensively evaluate and rank each group of candidate background conductivity parameters based on convergence evaluation index, and determine the group of candidate background conductivity parameters with the best comprehensive evaluation result as the optimal background conductivity parameter. Electromagnetic field calculation module 6 is used to perform background field subtraction operation using the selected optimal background conductivity parameter to obtain the final electromagnetic field calculation result.

[0089] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for adaptive optimization selection of background field conductivity in forward electromagnetic field modeling of horizontal wells, characterized in that, include: Characteristic parameters are extracted from the full tensor anisotropic conductivity tensor of the target formation traversed by the horizontal well to obtain conductivity characteristic parameters. Based on the conductivity characteristic parameters, a candidate background conductivity parameter set is constructed; Based on the preset electromagnetic field source parameters, the full tensor anisotropic conductivity tensor, and the candidate background conductivity parameter set, determine the difference spectral field corresponding to each group of candidate background conductivity parameters in the candidate background conductivity parameter set; Convergence quantification analysis was performed on the difference spectral field to determine the convergence evaluation index corresponding to each group of candidate background conductivity parameters; Based on the convergence evaluation index, the candidate background conductivity parameters of each group are comprehensively evaluated and ranked, and the group of candidate background conductivity parameters with the best comprehensive evaluation result is determined as the optimal background conductivity parameters. The background field subtraction operation is performed using the selected optimal background conductivity parameter to obtain the final electromagnetic field calculation result.

2. The adaptive optimization method for selecting background field conductivity in forward modeling of electromagnetic fields in a horizontal well as described in claim 1, characterized in that, The conductivity characteristic parameters are the main diagonal elements of the full-tensor anisotropic conductivity tensor, which include the conductivity in the first horizontal direction, the conductivity in the second horizontal direction, and the conductivity in the vertical direction.

3. The adaptive optimization method for selecting background field conductivity in forward modeling of electromagnetic fields in horizontal wells as described in claim 2, characterized in that, Based on the conductivity characteristic parameters, a candidate background conductivity parameter set is constructed, including: The conductivity characteristic parameters are combined using at least two different statistical combination methods to generate a candidate background conductivity parameter set; the candidate background conductivity parameter set contains multiple sets of candidate background conductivity parameters, and each set of candidate background conductivity parameters corresponds to a uniaxial anisotropic background model; The statistical combination methods include: The arithmetic or geometric mean of the conductivity in the first horizontal direction and the conductivity in the second horizontal direction are taken as the background horizontal conductivity; the conductivity in the vertical direction is taken as the background vertical conductivity; and a transversely isotropic uniaxial anisotropic background model is constructed using the background horizontal conductivity and the background vertical conductivity. or, The arithmetic mean of the conductivity in the first horizontal direction, the conductivity in the second horizontal direction, and the conductivity in the vertical direction is taken and used as the background horizontal conductivity and the background vertical conductivity to construct an isotropic uniaxial anisotropic background model. or, The geometric mean of the conductivity in the first horizontal direction, the second horizontal direction, and the vertical direction is taken and used as the background horizontal conductivity and background vertical conductivity to construct an isotropic uniaxial anisotropic background model. or, The harmonic mean of the conductivity in the first horizontal direction, the second horizontal direction, and the vertical direction is taken and used as the background horizontal conductivity and background vertical conductivity to construct an isotropic uniaxial anisotropic background model.

4. The adaptive optimization method for selecting background field conductivity in forward modeling of electromagnetic fields in a horizontal well as described in claim 1, characterized in that, Based on the preset electromagnetic field source parameters, the fully tensor anisotropic conductivity tensor, and the candidate background conductivity parameter set, the difference spectral domain field corresponding to each group of candidate background conductivity parameters in the candidate background conductivity parameter set is determined, including: The minimum wavenumber is determined based on the maximum feature scale of the target layer, and the maximum wavenumber is determined based on the preset target integration accuracy. Initial sampling points are generated in a logarithmically evenly spaced range from the minimum wavenumber to the maximum wavenumber. Increase the sampling density of the high wavenumber region relative to the low wavenumber region to obtain the initial set of sampling wavenumber points for the density partition; wherein, the sampling density of the high wavenumber region is set to 2 to 4 times that of the low wavenumber region. On the initial set of sampling wavenumber points, select any set of candidate background conductivity parameters to calculate the estimated difference spectral field. Check the relative change of the amplitude of the estimated difference spectral field of adjacent sampling points one by one. If the relative change exceeds the preset change threshold, insert additional sampling points between the corresponding adjacent sampling points. The set of all encrypted sampling points is used as the sampling wavenumber point set; Based on the preset electromagnetic field source parameters and the full tensor anisotropic conductivity tensor, the spectral domain electromagnetic field under the full tensor anisotropic condition is solved at each wavenumber point of the sampling wavenumber point set to obtain the full tensor anisotropic spectral domain response. Based on the preset electromagnetic field source parameters, the spectral domain electromagnetic field under uniaxial anisotropic conditions corresponding to each set of candidate background conductivity parameters is solved at each wavenumber point of the sampling wavenumber point set, and the uniaxial anisotropic spectral domain response corresponding to each set of candidate background conductivity parameters is obtained. The difference between the full tensor anisotropic spectral domain response and the uniaxial anisotropic spectral domain response corresponding to each group of candidate background conductivity parameters is calculated point by point at each wavenumber point to obtain the difference spectral domain field corresponding to each group of candidate background conductivity parameters.

5. The adaptive optimization method for selecting background field conductivity in forward modeling of electromagnetic fields in a horizontal well, as described in claim 4, is characterized in that... On the initial set of sampled wavenumber points, any set of candidate background conductivity parameters is selected for the calculation of the estimated difference spectral field. The relative change in the amplitude of the estimated difference spectral field of adjacent sample points is checked one by one. If the relative change exceeds a preset change threshold, additional sample points are inserted between the corresponding adjacent sample points, including: A set of candidate background conductivity parameters is selected from the candidate background conductivity parameter set as the prediction parameters; At each wavenumber point in the initial set of sampling wavenumber points, the full tensor anisotropic spectral domain response is solved based on the preset electromagnetic source parameters and the full tensor anisotropic conductivity tensor, and the corresponding uniaxial anisotropic spectral domain response is solved based on the preset electromagnetic source parameters and the estimated parameters. The difference between the full tensor anisotropic spectral domain response and the single-axis anisotropic spectral domain response corresponding to the predicted parameters is calculated point by point at each wavenumber point, and the amplitude is taken to obtain the predicted difference spectral domain field amplitude sequence. Based on the predicted difference spectral field amplitude sequence, the relative change in amplitude is calculated for each pair of adjacent wavenumber points in ascending order of wavenumber, and a set of relative changes is obtained. Each relative change in the set of relative changes is compared with a preset change threshold to determine the set of intervals to be encrypted corresponding to adjacent wavenumber point pairs whose relative changes exceed the preset change threshold. Insert an extra sampling point at the logarithmic midpoint between two adjacent wavenumber points in each interval to be encrypted, and merge all the extra sampling points into the current sampling wavenumber point set to form an updated sampling wavenumber point set. The process of replacing the initial set of sampled wavenumber points with the updated set of sampled wavenumber points, repeatedly calculating the relative change, determining the interval to be encrypted, and inserting additional sample points continues until the relative change of amplitude of any adjacent wavenumber point pair in the updated set of sampled wavenumber points does not exceed the preset change threshold. The final set of sampled wavenumber points is then used as the adaptively encrypted set of sampled wavenumber points.

6. The adaptive optimization method for selecting background field conductivity in forward modeling of electromagnetic fields in a horizontal well as described in claim 1, characterized in that, Convergence quantification analysis was performed on the difference spectral field to determine the convergence evaluation index corresponding to each group of candidate background conductivity parameters, including: Based on the preset wavenumber boundary threshold, all sampling wavenumber points of the difference spectral field corresponding to each group of candidate background conductivity parameters are divided into low wavenumber regions and high wavenumber regions to obtain the difference spectral field data after partitioning and labeling. Based on the difference spectral field data, the change sequence of the difference spectral field amplitude with increasing wavenumber is extracted in the high wavenumber region. The decay trend of the change sequence is fitted to calculate the decay rate of amplitude with increasing wavenumber, and the amplitude decay rate in the high wavenumber region is obtained. Based on the difference spectral field data, the total spectral field energy of the difference spectral field over the entire wavenumber range and the local spectral field energy within the preset cutoff wavenumber are calculated respectively. The ratio of the local spectral field energy to the total spectral field energy is taken as the energy concentration of the difference spectral field. Based on the difference spectral field data, the change information of positive and negative signs of the real or imaginary part of the difference spectral field between adjacent sampling wavenumber points is extracted, and the number of positive and negative sign flips within a unit wavenumber interval is counted to obtain the oscillation frequency of the difference spectral field. Based on the difference spectral field data, the amplitude attenuation characteristics of the tail of the high wavenumber region are used to extrapolate and estimate the integral contribution from the maximum sampling wavenumber to infinity. The ratio of the integral contribution to the integral estimate of the whole wavenumber range is used as the integral truncation error estimate. The amplitude attenuation rate in the high wavenumber region, the energy concentration in the difference spectral field, the oscillation frequency in the difference spectral field, and the integral truncation error estimation corresponding to each group of candidate background conductivity parameters are used as convergence evaluation indicators for each group of candidate background conductivity parameters.

7. The adaptive optimization method for selecting background field conductivity in forward modeling of electromagnetic fields in a horizontal well as described in claim 1, characterized in that, Based on convergence evaluation metrics, the candidate background conductivity parameters are comprehensively evaluated and ranked. The candidate background conductivity parameters with the best comprehensive evaluation results are determined as the optimal background conductivity parameters, including: Normalize each convergence evaluation index; The comprehensive evaluation function value of each group of candidate background conductivity parameters is obtained by multiplying the normalized index value corresponding to each index weight coefficient by the corresponding index weight coefficient and summing them. The candidate background conductivity parameters with the largest comprehensive evaluation function value are selected as the candidate background conductivity parameters; The convergence of the difference spectral field corresponding to the selected background conductivity parameter is verified. When the absolute value of the amplitude attenuation rate is higher than the preset attenuation threshold and the estimated value of the integral truncation error is lower than the preset accuracy threshold, the corresponding selected background conductivity parameter is taken as the optimal background conductivity parameter. Otherwise, taking the parameters whose comprehensive evaluation function values ​​among the existing candidate background conductivity parameters fall within the preset sorting range as the center, interpolation is performed within the preset percentage range of the corresponding background horizontal conductivity and background vertical conductivity values ​​according to the preset step size to generate new candidate background conductivity parameters. These new parameters are then added to the candidate background conductivity parameter set for re-evaluation until the selected candidate background conductivity parameters pass the convergence verification, thus obtaining the optimal background conductivity parameters.

8. The adaptive optimization method for selecting background field conductivity in forward modeling of electromagnetic fields in a horizontal well as described in claim 1, characterized in that, The background field is subtracted using the selected optimal background conductivity parameter to obtain the final electromagnetic field calculation results, including: A target uniaxial anisotropic background model is constructed using the background horizontal conductivity and background vertical conductivity parameters from the optimal background conductivity parameters. The background field is obtained by obtaining an analytical solution for the target uniaxial anisotropic background model based on the electromagnetic field source parameters. The difference spectral field corresponding to the optimal background conductivity parameter is integrated by numerical inverse transformation on the set of sampled wavenumber points to transform the spectral data into spatial data, thus obtaining the spatial scattering field. The spatial domain scattered field is superimposed with the background field to obtain the final electromagnetic field calculation result.

9. The adaptive optimization method for selecting background field conductivity in forward modeling of electromagnetic fields in a horizontal well, as described in claim 8, is characterized in that... The difference spectral field corresponding to the optimal background conductivity parameter is integrated by performing a numerical inverse transform on the set of sampled wavenumber points, transforming the spectral data into spatial data, and obtaining the spatial scattering field, including: The difference spectral field, the set of sampling wavenumber points, the coordinates of the target space observation points, and the amplitude attenuation rate and integral truncation error estimates in the high wavenumber region obtained by convergence quantization analysis are obtained corresponding to the optimal background conductivity parameters. Inverse transform integral control parameters are generated based on integral truncation error estimation and amplitude attenuation rate in the high wavenumber region. The inverse transform integral control parameters include attenuation model parameters determined based on amplitude attenuation rate in the high wavenumber region and tail compensation accuracy level determined based on integral truncation error estimation. Based on the set of sampled wavenumber points, the coordinates of the target space observation points, and the inverse transform integral control parameters, a numerical inverse transform integral is performed on the difference spectral field to obtain the principal integral result within the range covered by the set of sampled wavenumber points. Based on the attenuation model parameters and the amplitude of the difference spectral field at the maximum sampling wavenumber, the tail integral contribution after the maximum sampling wavenumber is extrapolated and estimated to obtain the tail contribution. The main integral result is combined with the tail contribution to obtain the spatial domain scattering field.

10. A system for adaptive optimization selection of background field conductivity in forward modeling of electromagnetic fields in horizontal wells, characterized in that, include: The feature extraction module is used to extract feature parameters from the full tensor anisotropic conductivity tensor of the target formation traversed by the horizontal well, and obtain conductivity feature parameters. The candidate parameter acquisition module is used to construct a candidate background conductivity parameter set based on conductivity characteristic parameters; The difference spectral field determination module is used to determine the difference spectral field corresponding to each set of candidate background conductivity parameters in the candidate background conductivity parameter set based on the preset electromagnetic field source parameters, the full tensor anisotropic conductivity tensor, and the candidate background conductivity parameter set. The evaluation index determination module is used to perform convergence quantification analysis on the difference spectral field and determine the convergence evaluation index corresponding to each group of candidate background conductivity parameters. The optimal background conductivity parameter determination module is used to comprehensively evaluate and rank each group of candidate background conductivity parameters based on convergence evaluation index, and determine the group of candidate background conductivity parameters with the best comprehensive evaluation result as the optimal background conductivity parameter. The electromagnetic field calculation module is used to perform background field subtraction operations using the selected optimal background conductivity parameters to obtain the final electromagnetic field calculation results.

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