Slice quantification method for target positioning error in geophysical inversion results

Abstract

The application discloses a slice quantitative analysis method for positioning error of a target body in geophysical inversion results, and comprises the following steps: a parameter model is established and sampling initialization is performed; position parameters of the target body and model parameters are jointly sampled by combining with geological prior information. An error evaluation mechanism is introduced in the sampling process to guide the sampling results to concentrate in the area with smaller error. The collected multiple position samples are used to construct a three-dimensional uncertainty boundary structure, and a series of error cross-section images are generated by performing geometric slicing in multiple profile directions. Further, the images are weighted and fused according to the importance of different profiles, and finally a three-dimensional positioning error heat map is generated to reflect the uncertainty spatial distribution of the underground target position. The application can express the spatial deviation degree in the inversion results in an intuitive form, and provides a quantitative basis for geological interpretation and resource assessment.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration and imaging technology, and in particular to a method for quantifying the positioning error of target bodies in geophysical inversion results by slicing. Background Technology

[0002] With the continuous development of geophysical exploration technology and inversion algorithms, three-dimensional modeling and imaging of subsurface structures have become key tools in oil and gas exploration, mineral resource location, and geological engineering assessment. Geophysical inversion models, as an important method for deriving subsurface media properties from observational data, directly impact subsequent resource interpretation and decision-making due to their spatial accuracy and target body positioning accuracy. However, in practical applications, due to factors such as observation errors, inversion non-uniqueness, and the geometric complexity of the target body, the spatial positioning of the target body in the inversion results often exhibits significant uncertainty. Therefore, a quantifiable and visualized error analysis method is urgently needed for its systematic evaluation.

[0003] In existing technologies, traditional geophysical inversion error analysis methods mostly rely on single-point confidence interval estimation or global uniform sampling simulation. These methods have several significant shortcomings when dealing with high-dimensional parameter spaces, multi-profile representations, and spatial correlations of target volumes:

[0004] 1. Lack of targeted sampling mechanism: Existing sampling methods often do not consider the anisotropic characteristics of the parameter space, resulting in low efficiency and slow convergence speed of high-dimensional joint sampling, making it difficult to effectively capture the dominant directional characteristics of the target volume space error.

[0005] 2. Error measurement and sampling decoupling: In traditional MCMC or Bayesian inference frameworks, the target localization error index usually does not participate in the sampling process control, lacks the ability to sample reliable regional samples, resulting in insufficient physical interpretability of the generated results.

[0006] 3. Limited Dimensions of Expression: Existing methods usually only provide error estimates from a certain cross-section or overall perspective, and cannot comprehensively express the uncertainty distribution characteristics of the three-dimensional target body on multiple two-dimensional cross-sections, resulting in a lack of hierarchy and detail in the spatial expression of error analysis.

[0007] 4. Fragmented model structure: Error assessment methods and inversion models often operate in a decoupled manner, failing to form a unified structure from parameter sampling to geometric modeling, making it difficult to achieve an integrated uncertainty quantification process.

[0008] Therefore, how to provide a slice-based quantitative analysis method for the positioning error of the target body in the geophysical inversion results is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0009] One objective of this invention is to propose a slice-based quantitative analysis method for target positioning errors in geophysical inversion results. This invention utilizes Markov chain Monte Carlo sampling, adaptive covariance updating, ellipsoidal uncertainty modeling, and multi-profile weighted fusion to describe in detail the entire process from parameter sampling and error measurement to the generation of spatial heat maps. It has the advantages of clear expression, fine distribution, and strong adaptability.

[0010] The method for slice-based quantitative analysis of target body positioning error in geophysical inversion results according to embodiments of the present invention includes the following steps:

[0011] S1. Construct a geophysical inversion model, set the joint prior probability distribution of geophysical model parameters and target body spatial location parameters, and initialize the Markov chain used for parameter sampling.

[0012] S2. Calculate the joint covariance matrix of the model samples in the geophysical inversion model, extract the principal axis direction of the joint covariance matrix, construct anisotropic dynamic proposal distribution based on the principal axis direction, and guide the improved Markov chain Monte Carlo method to jointly sample the geophysical model parameters and the spatial position parameters of the target body.

[0013] S3. For each set of target spatial position parameter samples generated during the joint sampling process, calculate the corresponding target spatial positioning error metric and use the target spatial positioning error metric to adjust the acceptance probability of the current sampling step.

[0014] S4. After joint sampling, summarize all target spatial position parameter samples, perform three-dimensional ellipsoid uncertainty modeling based on target spatial position parameter samples, construct target spatial positioning error ellipsoid structure, and generate target three-dimensional spatial error boundary model.

[0015] S5. Geometrically slice the three-dimensional spatial error boundary model of the target body in multiple preset two-dimensional geological profile directions to obtain two-dimensional cross-sectional images of the three-dimensional ellipsoidal structure model in each two-dimensional geological profile direction.

[0016] S6. All two-dimensional cross-sectional images are weighted and fused according to the corresponding spatial response intensity of the target body to generate a three-dimensional target body positioning error heat map that expresses the spatial positioning error distribution of the target body. This three-dimensional target body positioning error heat map is used to express the spatial uncertainty distribution characteristics of the target body in the geophysical inversion model.

[0017] Optionally, S1 specifically includes:

[0018] S11. Obtain measurement data for geophysical inversion and construct a geophysical measurement model containing geophysical response relationships. The geophysical measurement model is used to define the response mapping structure between subsurface medium parameters and observation data.

[0019] S12. Based on the geophysical measurement model, a geophysical inversion model is constructed. The geophysical inversion model includes geophysical model parameters and target body spatial location parameters. The geophysical model parameters are used to characterize the distribution characteristics of subsurface media properties, and the target body spatial location parameters are used to characterize the geometric spatial properties of the target body.

[0020] S13. Based on the statistical characteristics of geophysical model parameters and target spatial location parameters and geological prior knowledge, a joint prior probability distribution is set. The joint prior probability distribution is used to simultaneously constrain the distribution range and correlation pattern of geophysical model parameters and target spatial location parameters in the joint parameter space.

[0021] S14. Determine the initial state of the Markov chain based on the distribution characteristics of the joint prior probability distribution. The initial state of the Markov chain is jointly composed of the initial values ​​of the geophysical model parameters and the initial values ​​of the target body spatial position parameters, and is mapped to the parameter space of the geophysical inversion model.

[0022] S15. Set the initial control parameters of the Markov chain. The initial control parameters include the maximum number of sampling rounds, the perturbation step size range, the dynamic perturbation strategy, and the initial acceptance rate, which are used to define the sampling stability and update mechanism of the subsequent improved Markov chain Monte Carlo method.

[0023] Optionally, S2 specifically includes:

[0024] S21. Based on the initial state of the Markov chain, start the Markov chain presampling process in the geophysical inversion model to generate a joint parameter sample set containing geophysical model parameter samples and target body spatial location parameter samples.

[0025] S22. Calculate the joint covariance matrix based on the joint parameter sample set. The joint covariance matrix is ​​used to describe the statistical dependence between the geophysical model parameters and the spatial location parameters of the target body in the joint parameter space.

[0026] S23. Perform eigenvalue decomposition on the joint covariance matrix and extract the principal eigenvector representing the direction of maximum covariance. The principal eigenvector is defined as the principal axis direction of the joint distribution of geophysical model parameters and target spatial position parameters.

[0027] S24. Construct an anisotropic dynamic proposal distribution based on the principal axis direction. The anisotropic dynamic proposal distribution is used to generate parameter perturbation vectors in the joint parameter space to control the perturbation amplitude and direction of the sampling points in the principal axis direction.

[0028] S25. Based on the initial control parameters of the Markov chain, the improved Markov chain Monte Carlo method is used to embed the anisotropic dynamic proposal distribution into the geophysical inversion model to perform a joint sampling process of geophysical model parameters and target body spatial location parameters.

[0029] S26. During the joint sampling process, the joint parameter sample set is updated based on the latest round of sampling results, the joint covariance matrix and principal eigenvector are recalculated, the anisotropic dynamic proposal distribution is adjusted, and the improved Markov chain Monte Carlo method is continuously guided to perform adaptive sampling in the geophysical inversion model.

[0030] Optionally, the improved Markov chain Monte Carlo method specifically includes:

[0031] The initial state of the Markov chain is set, which consists of the initial geophysical model parameters and the initial target spatial location parameters. The proposal distribution is initialized as a multidimensional normal distribution, and an initial sample set is established.

[0032] The main sampling loop of the Markov chain is executed. In each round of sampling, when the current round number reaches the adaptive update threshold, the joint covariance matrix is ​​calculated based on the current sample set, and the principal feature vector corresponding to the direction of maximum covariance is extracted to update the principal axis direction and covariance structure of the anisotropic proposal distribution.

[0033] Based on the updated anisotropy proposal distribution, candidate samples of geophysical model parameters and target spatial location parameters are generated from the joint parameter space;

[0034] For candidate samples, a target spatial positioning error metric is calculated. Then, combining the joint posterior probability of the candidate samples with the joint posterior probability of the current state samples, an error-normalized acceptance rate adjustment function is constructed. The sampling acceptance probability α is defined by the following formula:

[0035]

[0036] Wherein, E(x) * ) represents the target spatial positioning error metric in the candidate state. P(x) represents the average positioning error of the sample set in the current round, λ is the error adjustment factor, and P(x) represents the average positioning error of the sample set in the current round. * ) represents candidate sample x * The joint posterior probability density value, P(x t-1 ) represents the current state sample x t-1 The joint posterior probability density value;

[0037] Random numbers are generated for sampling acceptance determination. If a candidate sample meets the acceptance condition, the corresponding candidate sample is used as the current state sample; otherwise, the previous round state sample is retained, and the sampling result is added to the sample set.

[0038] Repeat the above steps until the maximum number of sampling rounds is reached, and output a joint parameter sample set containing geophysical model parameters and target spatial location parameters, which is used for uncertainty modeling and error expression analysis in the geophysical inversion model.

[0039] Optionally, S3 specifically includes:

[0040] S31. During the joint sampling process of the improved Markov chain Monte Carlo method, the corresponding target volume spatial position parameters are extracted from each round of joint parameter samples to construct a target volume spatial position parameter sample set containing multiple target volume spatial position parameter samples.

[0041] S32. For each set of target spatial position parameters in the target spatial position parameter sample set, calculate the spatial offset distance between the target and the reference position in three-dimensional space. The spatial offset distance is calculated based on the difference between the geometric centroid and the boundary range of the target.

[0042] S33. Based on the calculated spatial offset distance, define a target spatial positioning error metric value, which is used to quantitatively characterize the degree of difference between the target spatial position and the reference spatial position in the current sample;

[0043] S34. The target spatial positioning error metric is embedded as an adjustment factor into the acceptance probability function of the improved Markov chain Monte Carlo method, which is used to dynamically adjust the acceptance decision logic of the geophysical model parameters and the target spatial position parameters in each round of joint sampling.

[0044] Optionally, S4 specifically includes:

[0045] S41. After joint sampling of the improved Markov chain Monte Carlo method in the geophysical inversion model is completed, the spatial position parameters of the target body in the joint parameter sample are extracted to construct a target body spatial position parameter sample set. The target body spatial position parameters include the geometric centroid position and boundary structure information of the target body in three-dimensional space.

[0046] S42. Perform statistical processing on the target body spatial position parameter sample set, and calculate the three-dimensional mean vector and three-dimensional covariance matrix of the target body spatial position parameter sample set. The three-dimensional covariance matrix is ​​used to characterize the distribution characteristics and correlation of the target body spatial position in each principal direction.

[0047] S43. A three-dimensional ellipsoid uncertainty modeling method is constructed based on the three-dimensional mean vector and the three-dimensional covariance matrix. The three-dimensional mean vector is used as the center position of the target body spatial positioning error ellipsoid structure. The principal eigenvalues ​​and principal eigenvectors of the three-dimensional covariance matrix are used to calculate the principal axis length and principal axis direction of the ellipsoid structure.

[0048] S44. Using the target body spatial positioning error ellipsoid structure as the spatial positioning uncertainty boundary body of the target body in the geophysical inversion model, a three-dimensional spatial error boundary model of the target body is established to describe the spatial diffusion range and probability distribution characteristics of the target body's spatial position.

[0049] S45. The three-dimensional spatial error boundary model of the target body is used as the input structure for subsequent profile analysis and error visualization of geophysical inversion results, providing basic data support for error boundaries for slice fusion and heat map construction.

[0050] Optionally, S5 specifically includes:

[0051] S51. In the geophysical inversion model, multiple representative two-dimensional geological profile directions are set. The two-dimensional geological profile directions are determined according to the spatial distribution characteristics of the target body, forming a set of two-dimensional geological profile directions.

[0052] S52. For each two-dimensional geological profile direction, construct a corresponding two-dimensional slice plane. The two-dimensional slice plane is used to interact spatially with the three-dimensional spatial error boundary model of the target body in the geophysical inversion model.

[0053] S53. Geometrically cut the target body spatial positioning error ellipsoid structure in the three-dimensional spatial error boundary model of the target body on the two-dimensional slice plane, and extract the two-dimensional projection contour of the target body spatial positioning error ellipsoid structure in the current section direction.

[0054] S54. Convert the two-dimensional projection contour of the target body spatial positioning error ellipsoid structure into structured image data to form a two-dimensional cross-sectional image of the target body positioning error under the corresponding two-dimensional geological profile direction.

[0055] S55. Repeat S52 to S54 for each direction in the set of two-dimensional geological profile directions to obtain a set of two-dimensional cross-sectional images of the target body's three-dimensional spatial error boundary model in multiple two-dimensional geological profile directions, which will be used for subsequent profile fusion and error map construction.

[0056] Optionally, S6 specifically includes:

[0057] S61. Extract the set of two-dimensional cross-sectional images generated by the three-dimensional spatial error boundary model of the target body in multiple two-dimensional geological profile directions, and establish a two-dimensional cross-sectional image index structure corresponding to the spatial positioning error ellipsoid structure of each target body, which is used to organize the correspondence between the two-dimensional images and the geological profile directions.

[0058] S62. Assign a target volume spatial response intensity weight to each two-dimensional cross-sectional image in the set of two-dimensional cross-sectional images. The target volume spatial response intensity weight is calculated based on the geometric extension, inversion parameter gradient or information content of the target volume spatial positioning error ellipsoid structure in the corresponding cross-sectional direction.

[0059] S63. Perform weighted fusion processing on the set of two-dimensional cross-sectional images according to the spatial response intensity weight of the target body. The weighted fusion processing performs spatial alignment in the three-dimensional reference coordinate system and completes the spatial position consistency adjustment of each two-dimensional cross-sectional image through image resampling and spatial registration.

[0060] S64. Based on the weighted fusion result, a three-dimensional target volume positioning error heatmap is generated. The three-dimensional target volume positioning error heatmap expresses the uncertainty distribution value of different spatial positions in the form of voxel color coding, which is used to construct a spatial continuity visual expression structure.

[0061] S65. The three-dimensional target positioning error heat map is used as part of the output of the geophysical inversion model to reflect the spatial positioning uncertainty distribution characteristics of the target in the geophysical inversion process, and to support subsequent visual analysis and interpretation modeling.

[0062] The beneficial effects of this invention are:

[0063] (1) This invention constructs an improved Markov chain Monte Carlo sampling method by introducing an adaptive proposal mechanism guided by the covariance principal axis direction and an acceptance rate adjustment strategy driven by local error. This method achieves efficient joint sampling of geophysical model parameters and target spatial location parameters, effectively improving the stability and spatial representativeness of target location results in high-dimensional space.

[0064] (2) The present invention constructs a three-dimensional ellipsoidal uncertainty model using joint sampling results, and forms a target positioning error heat map with multi-scale spatial resolution by weighted fusion of multi-directional geological profile slices and target spatial response intensity. This realizes a structured visual expression of the uncertainty distribution of underground target bodies and enhances the geological interpretation capability of error assessment results.

[0065] (3) This invention forms a full-process quantitative framework from geophysical inversion model establishment, parameter sampling, error measurement, spatial modeling to multi-profile fusion analysis, which solves the problems of fuzzy error expression, inconsistent scale, and weak profile expression ability of traditional inversion models, and improves the reliability assessment level of model results and the engineering decision support capability of geophysical imaging. Attached Figure Description

[0066] 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:

[0067] Figure 1 This is a flowchart of the slice quantification analysis method for target positioning error in geophysical inversion results proposed in this invention. Detailed Implementation

[0068] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0069] refer to Figure 1 The method for quantifying the target location error in geophysical inversion results by slices includes the following steps:

[0070] S1. Construct a geophysical inversion model, set the joint prior probability distribution of geophysical model parameters and target body spatial location parameters, and initialize the Markov chain used for parameter sampling.

[0071] S2. Calculate the joint covariance matrix of the model samples in the geophysical inversion model, extract the principal axis direction of the joint covariance matrix, construct anisotropic dynamic proposal distribution based on the principal axis direction, and guide the improved Markov chain Monte Carlo method to jointly sample the geophysical model parameters and the spatial position parameters of the target body.

[0072] S3. For each set of target spatial position parameter samples generated during the joint sampling process, calculate the corresponding target spatial positioning error metric and use the target spatial positioning error metric to adjust the acceptance probability of the current sampling step.

[0073] S4. After joint sampling, summarize all target spatial position parameter samples, perform three-dimensional ellipsoid uncertainty modeling based on target spatial position parameter samples, construct target spatial positioning error ellipsoid structure, and generate target three-dimensional spatial error boundary model.

[0074] S5. Geometrically slice the three-dimensional spatial error boundary model of the target body in multiple preset two-dimensional geological profile directions to obtain two-dimensional cross-sectional images of the three-dimensional ellipsoidal structure model in each two-dimensional geological profile direction.

[0075] S6. All two-dimensional cross-sectional images are weighted and fused according to the corresponding spatial response intensity of the target body to generate a three-dimensional target body positioning error heat map that expresses the spatial positioning error distribution of the target body. This three-dimensional target body positioning error heat map is used to express the spatial uncertainty distribution characteristics of the target body in the geophysical inversion model.

[0076] In this embodiment, S1 specifically includes:

[0077] S11. Obtain measurement data for geophysical inversion and construct a geophysical measurement model containing geophysical response relationships. The geophysical measurement model is used to define the response mapping structure between subsurface medium parameters and observation data.

[0078] S12. Based on the geophysical measurement model, a geophysical inversion model is constructed. The geophysical inversion model includes geophysical model parameters and target body spatial location parameters. The geophysical model parameters are used to characterize the distribution characteristics of subsurface media properties, and the target body spatial location parameters are used to characterize the geometric spatial properties of the target body.

[0079] S13. Based on the statistical characteristics of geophysical model parameters and target spatial location parameters and geological prior knowledge, a joint prior probability distribution is set. The joint prior probability distribution is used to simultaneously constrain the distribution range and correlation pattern of geophysical model parameters and target spatial location parameters in the joint parameter space.

[0080] S14. Determine the initial state of the Markov chain based on the distribution characteristics of the joint prior probability distribution. The initial state of the Markov chain is jointly composed of the initial values ​​of the geophysical model parameters and the initial values ​​of the target body spatial position parameters, and is mapped to the parameter space of the geophysical inversion model.

[0081] S15. Set the initial control parameters of the Markov chain. The initial control parameters include the maximum number of sampling rounds, the perturbation step size range, the dynamic perturbation strategy, and the initial acceptance rate, which are used to define the sampling stability and update mechanism of the subsequent improved Markov chain Monte Carlo method.

[0082] This implementation method acquires measurement data for geophysical inversion and establishes a geophysical measurement model, constructing a geophysical inversion model with both physical and spatial attributes. It then sets a joint prior probability distribution based on geological prior knowledge to constrain the rationality of the geophysical model parameters and the spatial location parameters of the target body in the joint space. Furthermore, it determines the initial state of the Markov chain and configures initial control parameters, providing fundamental support for subsequent sampling processes. This process ensures the physical consistency and geological rationality of the model, effectively improves the scientific nature of inversion parameter initialization and sampling convergence efficiency, and provides a stable prior framework for uncertainty analysis.

[0083] In this embodiment, S2 specifically includes:

[0084] S21. Based on the initial state of the Markov chain, start the Markov chain presampling process in the geophysical inversion model to generate a joint parameter sample set containing geophysical model parameter samples and target body spatial location parameter samples.

[0085] S22. Calculate the joint covariance matrix based on the joint parameter sample set. The joint covariance matrix is ​​used to describe the statistical dependence between the geophysical model parameters and the spatial location parameters of the target body in the joint parameter space.

[0086] S23. Perform eigenvalue decomposition on the joint covariance matrix and extract the principal eigenvector representing the direction of maximum covariance. The principal eigenvector is defined as the principal axis direction of the joint distribution of geophysical model parameters and target spatial position parameters.

[0087] S24. Construct an anisotropic dynamic proposal distribution based on the principal axis direction. The anisotropic dynamic proposal distribution is used to generate parameter perturbation vectors in the joint parameter space to control the perturbation amplitude and direction of the sampling points in the principal axis direction.

[0088] S25. Based on the initial control parameters of the Markov chain, the improved Markov chain Monte Carlo method is used to embed the anisotropic dynamic proposal distribution into the geophysical inversion model to perform a joint sampling process of geophysical model parameters and target body spatial location parameters.

[0089] S26. During the joint sampling process, the joint parameter sample set is updated based on the latest round of sampling results, the joint covariance matrix and principal eigenvector are recalculated, the anisotropic dynamic proposal distribution is adjusted, and the improved Markov chain Monte Carlo method is continuously guided to perform adaptive sampling in the geophysical inversion model.

[0090] This implementation introduces an anisotropic dynamic proposal distribution mechanism guided by the principal axis direction into the geophysical inversion model. It generates a joint parameter sample set using the initial state of the Markov chain, dynamically calculates the covariance matrix and extracts the principal eigenvectors, and constructs an adaptive perturbation strategy based on the principal axis direction. This effectively controls the sampling update direction and magnitude, and embeds it into the improved Markov chain Monte Carlo method to construct an adaptive feedback sampling closed loop. This significantly improves the sampling efficiency and stability in the high-dimensional joint parameter space, achieves accurate characterization of the spatial location parameter distribution of the target body, and enhances the spatial representation and error control capabilities of the geophysical inversion model.

[0091] In this embodiment, the improved Markov chain Monte Carlo method specifically includes:

[0092] The initial state of the Markov chain is set, which consists of the initial geophysical model parameters and the initial target spatial location parameters. The proposal distribution is initialized as a multidimensional normal distribution, and an initial sample set is established.

[0093] The main sampling loop of the Markov chain is executed. In each round of sampling, when the current round number reaches the adaptive update threshold, the joint covariance matrix is ​​calculated based on the current sample set, and the principal feature vector corresponding to the direction of maximum covariance is extracted to update the principal axis direction and covariance structure of the anisotropic proposal distribution.

[0094] Based on the updated anisotropy proposal distribution, candidate samples of geophysical model parameters and target spatial location parameters are generated from the joint parameter space;

[0095] For candidate samples, a target spatial positioning error metric is calculated. Then, combining the joint posterior probability of the candidate samples with the joint posterior probability of the current state samples, an error-normalized acceptance rate adjustment function is constructed. The sampling acceptance probability α is defined by the following formula:

[0096]

[0097] Wherein, E(x) * ) represents the target spatial positioning error metric in the candidate state. P(x) represents the average positioning error of the sample set in the current round, λ is the error adjustment factor, and P(x) represents the average positioning error of the sample set in the current round. * ) represents candidate sample x * The joint posterior probability density value, P(x t-1 ) represents the current state sample x t-1 The joint posterior probability density value;

[0098] This formula aims to introduce the moderating effect of target positioning accuracy on the acceptance probability of Markov chain sampling, thereby realizing an error-aware dynamic sampling mechanism. By jointly evaluating the spatial positioning error metric and the posterior probability of the sampled candidate states, the formula makes parameter samples with smaller target positioning errors more likely to be accepted, thus guiding the Markov chain to adaptively converge towards a high-confidence region in the joint parameter space. This acceptance probability function combines Bayesian sampling principles with error control ideas, enhancing the sampling path's ability to identify and constrain spatial uncertainties, and contributing to improved stability of target positioning estimation and the credibility of spatial boundary modeling.

[0099] Random numbers are generated for sampling acceptance determination. If a candidate sample meets the acceptance condition, the corresponding candidate sample is used as the current state sample; otherwise, the previous round state sample is retained, and the sampling result is added to the sample set.

[0100] Repeat the above steps until the maximum number of sampling rounds is reached, and output a joint parameter sample set containing geophysical model parameters and target spatial location parameters, which is used for uncertainty modeling and error expression analysis in the geophysical inversion model.

[0101] This implementation method sets an initial state and constructs a multidimensional normal proposal distribution, initiates an improved Markov chain sampling process, and dynamically adjusts the anisotropic proposal distribution using an adaptive covariance update strategy. This ensures that the sampling direction closely follows the trend of the main axis of the joint parameter distribution. Furthermore, it introduces an acceptance rate adjustment mechanism based on positioning error to effectively balance the exploratory nature and stability of the sampling, ultimately generating a highly representative set of joint parameter samples. This method not only improves the joint sampling efficiency and sample quality of geophysical model parameters and target spatial location parameters, but also enhances the expressive accuracy and convergence performance of target positioning error modeling in geophysical inversion results, providing a solid foundation for subsequent uncertainty modeling and spatial error visualization.

[0102] In this embodiment, S3 specifically includes:

[0103] S31. During the joint sampling process of the improved Markov chain Monte Carlo method, the corresponding target volume spatial position parameters are extracted from each round of joint parameter samples to construct a target volume spatial position parameter sample set containing multiple target volume spatial position parameter samples.

[0104] S32. For each set of target spatial position parameters in the target spatial position parameter sample set, calculate the spatial offset distance between the target and the reference position in three-dimensional space. The spatial offset distance is calculated based on the difference between the geometric centroid and the boundary range of the target.

[0105] S33. Based on the calculated spatial offset distance, define a target spatial positioning error metric value, which is used to quantitatively characterize the degree of difference between the target spatial position and the reference spatial position in the current sample;

[0106] S34. The target spatial positioning error metric is embedded as an adjustment factor into the acceptance probability function of the improved Markov chain Monte Carlo method, which is used to dynamically adjust the acceptance decision logic of the geophysical model parameters and the target spatial position parameters in each round of joint sampling.

[0107] In this implementation, during the joint sampling process of the improved Markov chain Monte Carlo method, the spatial position parameters of the target are extracted in real time. Based on the geometric centroid and boundary structure of the target, the spatial offset distance between each sample and the reference position is calculated to form a target spatial positioning error metric. This error metric is embedded in the sampling acceptance probability function as a dynamic adjustment factor, so that the sampling strategy is adaptively adjusted according to the error feedback in each round of sampling. This improves the discrimination accuracy of sample acceptance and the reliability of target spatial parameter estimation, providing a high-quality sample foundation for subsequent uncertainty modeling and spatial error expression.

[0108] In this embodiment, S4 specifically includes:

[0109] S41. After joint sampling of the improved Markov chain Monte Carlo method in the geophysical inversion model is completed, the spatial position parameters of the target body in the joint parameter sample are extracted to construct a target body spatial position parameter sample set. The target body spatial position parameters include the geometric centroid position and boundary structure information of the target body in three-dimensional space.

[0110] S42. Perform statistical processing on the target body spatial position parameter sample set, and calculate the three-dimensional mean vector and three-dimensional covariance matrix of the target body spatial position parameter sample set. The three-dimensional covariance matrix is ​​used to characterize the distribution characteristics and correlation of the target body spatial position in each principal direction.

[0111] S43. A three-dimensional ellipsoid uncertainty modeling method is constructed based on the three-dimensional mean vector and the three-dimensional covariance matrix. The three-dimensional mean vector is used as the center position of the target body spatial positioning error ellipsoid structure. The principal eigenvalues ​​and principal eigenvectors of the three-dimensional covariance matrix are used to calculate the principal axis length and principal axis direction of the ellipsoid structure.

[0112] S44. Using the target body spatial positioning error ellipsoid structure as the spatial positioning uncertainty boundary body of the target body in the geophysical inversion model, a three-dimensional spatial error boundary model of the target body is established to describe the spatial diffusion range and probability distribution characteristics of the target body's spatial position.

[0113] S45. The three-dimensional spatial error boundary model of the target body is used as the input structure for subsequent profile analysis and error visualization of geophysical inversion results, providing basic data support for error boundaries for slice fusion and heat map construction.

[0114] This implementation statistically processes the sample set of spatial location parameters of the target body obtained by joint sampling using the improved Markov chain Monte Carlo method, calculates the three-dimensional mean vector and the three-dimensional covariance matrix, and constructs a three-dimensional ellipsoidal uncertainty model based on its principal eigenvalues ​​and principal eigenvectors to define the spatial distribution boundary of the target body's positioning error. This error ellipsoid structure not only reflects the discrete trend of the target body's spatial position but also serves as a unified input for subsequent profile slicing and heatmap analysis, significantly improving the structural integrity and visualization effect of the spatial uncertainty expression, and providing a more accurate and interpretable error modeling foundation for geophysical inversion results.

[0115] In this embodiment, S5 specifically includes:

[0116] S51. In the geophysical inversion model, multiple representative two-dimensional geological profile directions are set. The two-dimensional geological profile directions are determined according to the spatial distribution characteristics of the target body, forming a set of two-dimensional geological profile directions.

[0117] S52. For each two-dimensional geological profile direction, construct a corresponding two-dimensional slice plane. The two-dimensional slice plane is used to interact spatially with the three-dimensional spatial error boundary model of the target body in the geophysical inversion model.

[0118] S53. Geometrically cut the target body spatial positioning error ellipsoid structure in the three-dimensional spatial error boundary model of the target body on the two-dimensional slice plane, and extract the two-dimensional projection contour of the target body spatial positioning error ellipsoid structure in the current section direction.

[0119] S54. Convert the two-dimensional projection contour of the target body spatial positioning error ellipsoid structure into structured image data to form a two-dimensional cross-sectional image of the target body positioning error under the corresponding two-dimensional geological profile direction.

[0120] S55. Repeat S52 to S54 for each direction in the set of two-dimensional geological profile directions to obtain a set of two-dimensional cross-sectional images of the target body's three-dimensional spatial error boundary model in multiple two-dimensional geological profile directions, which will be used for subsequent profile fusion and error map construction.

[0121] This implementation method sets multiple representative two-dimensional geological profile directions in the geophysical inversion model and constructs two-dimensional slice planes for each direction. It then geometrically extracts the ellipsoidal structure of the target object's spatial positioning error in the three-dimensional spatial error boundary model, extracts its two-dimensional projection contours in each profile direction, and structures them into image data, ultimately forming a set of two-dimensional cross-sectional images of the target object's positioning error in multiple directions. This method achieves multi-angle slice representation of the spatial error model, enhances the multi-dimensional display and cross-sectional comparison capabilities of the error spatial structure, provides fundamental image support for subsequent error fusion and spatial positioning uncertainty assessment, and improves the spatial perception of geophysical interpretation and the intuitive readability for engineering applications.

[0122] In this embodiment, S6 specifically includes:

[0123] S61. Extract the set of two-dimensional cross-sectional images generated by the three-dimensional spatial error boundary model of the target body in multiple two-dimensional geological profile directions, and establish a two-dimensional cross-sectional image index structure corresponding to the spatial positioning error ellipsoid structure of each target body, which is used to organize the correspondence between the two-dimensional images and the geological profile directions.

[0124] S62. Assign a target volume spatial response intensity weight to each two-dimensional cross-sectional image in the set of two-dimensional cross-sectional images. The target volume spatial response intensity weight is calculated based on the geometric extension, inversion parameter gradient or information content of the target volume spatial positioning error ellipsoid structure in the corresponding cross-sectional direction.

[0125] S63. Perform weighted fusion processing on the set of two-dimensional cross-sectional images according to the spatial response intensity weight of the target body. The weighted fusion processing performs spatial alignment in the three-dimensional reference coordinate system and completes the spatial position consistency adjustment of each two-dimensional cross-sectional image through image resampling and spatial registration.

[0126] S64. Based on the weighted fusion result, a three-dimensional target volume positioning error heatmap is generated. The three-dimensional target volume positioning error heatmap expresses the uncertainty distribution value of different spatial positions in the form of voxel color coding, which is used to construct a spatial continuity visual expression structure.

[0127] S65. The three-dimensional target positioning error heat map is used as part of the output of the geophysical inversion model to reflect the spatial positioning uncertainty distribution characteristics of the target in the geophysical inversion process, and to support subsequent visual analysis and interpretation modeling.

[0128] This implementation method extracts two-dimensional cross-sectional images generated along multiple two-dimensional geological profiles by the three-dimensional spatial error boundary model of the target body, establishes the correspondence between the images and the profile directions, and assigns spatial response intensity weights to each image based on the extension characteristics, inversion gradient, or information content of the target body's spatial positioning error ellipsoidal structure in each profile direction. Then, it performs weighted fusion, spatial registration, and resampling on each image in a three-dimensional coordinate system to generate a three-dimensional heat map that expresses the spatial distribution characteristics of the error. Finally, it serves as the visualization output of the geophysical inversion model, realizing the structured expression and three-dimensional visual support of the target body's positioning uncertainty information, and enhancing the application value and operability of the inversion results in the actual geological modeling and interpretation process.

[0129] Example 1:

[0130] To verify the feasibility of this invention in practice, it was applied to a 3D seismic data inversion project in a shale gas exploration area. This area is characterized by complex geological structures, deep target bodies, and high inversion accuracy requirements. Traditional geophysical inversion methods suffer from significant positioning error propagation in this scenario, making it difficult to accurately describe the spatial boundaries and uncertainties of underground target bodies, leading to increased risks in subsequent drilling site selection and severe resource waste. Therefore, this project introduces the methods of this invention into this geological engineering project to improve the accuracy and representation quality of 3D target body positioning.

[0131] Throughout the implementation process, we first constructed a geophysical inversion model based on the 3D seismic data of the inverted region and set a joint prior probability distribution for the geophysical model parameters and the spatial location parameters of the target body. Then, by initializing the Markov chain control parameters, we initiated the pre-sampling process and completed the extraction of the principal axis directions. During each round of the improved Markov chain Monte Carlo sampling, the joint geophysical parameters and spatial location parameters underwent joint perturbation, updating, and acceptance control in a high-dimensional parameter space. Simultaneously, the acceptance probability was dynamically adjusted by fusing the target body's spatial positioning error metric, thereby constructing a sample distribution set with a statistically dependent structure. After the joint sampling phase, the system statistically analyzed all spatial location sample parameters, constructed a 3D covariance matrix, and generated a spatial positioning error ellipsoid structure based on this matrix, thus establishing the uncertainty boundary volume of the target body.

[0132] To achieve multi-angle profile slicing analysis, we defined multiple typical two-dimensional geological profile directions based on the spatial morphology and structure of the target body. For each direction, we constructed an interactive model between the slicing plane and the three-dimensional error boundary model, extracting its two-dimensional projection contours in each direction and converting them into a structured image format. All two-dimensional images were ultimately assigned response intensity weights, and image fusion was performed within a three-dimensional coordinate framework to generate a three-dimensional target body positioning error heatmap that expresses the spatial uncertainty distribution characteristics of the target body. This heatmap is output to the subsequent analysis system to assist geological engineers in accurately identifying target body boundaries and guiding drilling deployment in complex structural areas.

[0133] To quantitatively verify the performance advantages of this invention in real-world scenarios, we designed a comparative experiment. The experiment selected 3D seismic data from a shale gas block and compared the localization effectiveness and processing efficiency of traditional error expression methods with those of this invention. Key comparative indicators included the average spatial error deviation of the target body, the maximum offset error of the 2D slice, the sampling acceptance rate, the heatmap boundary matching rate, and the time consumed in each processing step.

[0134] Table 1 Comparison of experimental data for different error expression methods

[0135] index Results of traditional methods Results of the method of the present invention Average spatial error deviation of the target body (meters) 15.8 6.3 Maximum projection deviation (meters) of 2D slicing error 22.5 9.7 Sampling acceptance rate (%) 38.2 81.4 Error heatmap boundary matching rate (%) 65.7 91.6 Modeling time (minutes) 93 78 Slicing time (minutes) 47 29 Error plot generation time (minutes) 35 18

[0136] Experimental results show that, supported by the method of this invention, the average spatial error deviation of the target body is reduced from 15.8 meters in the traditional method to 6.3 meters, and the maximum projection deviation in the two-dimensional slice direction is reduced from 22.5 meters to 9.7 meters. The sampling acceptance rate is increased to 81.4%, improving parameter update efficiency. Furthermore, the spatial consistency between the error heatmap boundary and the manually interpreted model reaches 91.6%, an improvement of approximately 26% compared to the traditional method. Simultaneously, the processing time for modeling, slicing, and image fusion is significantly reduced, resulting in a significant improvement in overall analysis efficiency. These achievements fully verify the ability of this invention to achieve high-precision spatial uncertainty expression under complex geological conditions, providing reliable technical support for the refined modeling and visual interpretation of geophysical inversion models.

[0137] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A slice quantification analysis method for target body positioning error in geophysical inversion results, characterized in that, The method comprises the following steps: S1, constructing a geophysical inversion model, setting a joint prior probability distribution of geophysical model parameters and target body spatial position parameters, and initializing a Markov chain for parameter sampling; S2, calculating the joint covariance matrix of the model sample in the geophysical inversion model, extracting the principal axis direction of the joint covariance matrix, and constructing an anisotropic dynamic proposal distribution based on the principal axis direction to guide the joint sampling of the geophysical model parameters and the target body spatial position parameters by the improved Markov chain Monte Carlo method; S3, for each set of target body spatial position parameter samples generated in the joint sampling process, calculating the corresponding target body spatial positioning error measurement value; S4, after the joint sampling is completed, all target body spatial position parameter samples are collected, three-dimensional ellipsoid uncertainty modeling is performed based on the target body spatial position parameter samples, the target body spatial positioning error ellipsoid structure is constructed, and a target body three-dimensional spatial error boundary model is generated; S5, geometrically slicing the target body three-dimensional spatial error boundary model in multiple preset two-dimensional geological profile directions to obtain two-dimensional cross-sectional images of the three-dimensional ellipsoid structure model in each two-dimensional geological profile direction; S6, weighting and fusing all two-dimensional cross-sectional images according to corresponding target body spatial response intensities to generate a three-dimensional target body positioning error heat map for expressing the target body spatial positioning error distribution.

2. The method of claim 1, wherein, The S1 specifically comprises: S11, obtaining measurement data for geophysical inversion, constructing a geophysical measurement model containing geophysical response relationships, and defining the response mapping structure between underground medium parameters and observation data by the geophysical measurement model; S12, constructing a geophysical inversion model based on the geophysical measurement model, wherein the geophysical inversion model comprises geophysical model parameters and target body spatial position parameters, the geophysical model parameters are used to represent the distribution characteristics of underground medium physical properties, and the target body spatial position parameters are used to represent the geometric spatial attributes of the target body; S13, setting a joint prior probability distribution according to the statistical characteristics of the geophysical model parameters and the target body spatial position parameters and the geological prior knowledge, wherein the joint prior probability distribution is used to simultaneously constrain the distribution range and correlation mode of the geophysical model parameters and the target body spatial position parameters in the joint parameter space; S14, determining the initial state of the Markov chain based on the distribution characteristics of the joint prior probability distribution, wherein the initial state of the Markov chain is composed of the initial values of the geophysical model parameters and the initial values of the target body spatial position parameters, and is mapped to the parameter space of the geophysical inversion model; S15, setting the initial control parameters of the Markov chain, wherein the initial control parameters include the maximum sampling round, the perturbation step range, the dynamic perturbation strategy and the initial acceptance rate.

3. The method of claim 1, wherein, The S2 specifically comprises: S21, based on the set initial state of the Markov chain, starting the Markov chain pre-sampling process in the geophysical inversion model to generate a joint parameter sample set containing geophysical model parameter samples and target body spatial position parameter samples; S22, calculate a joint covariance matrix based on the joint parameter sample set, the joint covariance matrix being used to describe a statistical dependence of the geophysical model parameter and the target body spatial position parameter in a joint parameter space; S23, perform eigen-decomposition on the joint covariance matrix, extract a principal eigenvector representing a maximum covariance direction, the principal eigenvector being defined as a principal axis direction of a joint distribution of the geophysical model parameter and the target body spatial position parameter; S24, construct an anisotropic dynamic proposal distribution according to the principal axis direction, the anisotropic dynamic proposal distribution being used to generate a parameter perturbation vector in the joint parameter space, control a perturbation amplitude and direction of a sampling point in the principal axis direction; S25, embed the anisotropic dynamic proposal distribution into the improved Markov chain Monte Carlo method in the geophysical inversion model according to initial control parameters of the Markov chain, and perform a joint sampling process of the geophysical model parameter and the target body spatial position parameter; S26, in the joint sampling process, update the joint parameter sample set according to a latest round of sampling results, recalculate the joint covariance matrix and the principal eigenvector, adjust the anisotropic dynamic proposal distribution, and continuously guide the improved Markov chain Monte Carlo method to perform adaptive sampling in the geophysical inversion model.

4. The slice quantification analysis method of the positioning error of the target body in the geophysical inversion result according to claim 3, characterized in that, The improved Markov chain Monte Carlo method specifically comprises: setting an initial state of the Markov chain, the initial state being composed of an initial geophysical model parameter and an initial target body spatial position parameter, initializing the proposal distribution as a multi-dimensional normal distribution, and establishing an initial sample set; performing a sampling main loop of the Markov chain, in each round of sampling, when a current round number reaches an adaptive update threshold, calculating a joint covariance matrix based on a current sample set, and extracting a principal eigenvector corresponding to a maximum covariance direction; generating a candidate sample of the geophysical model parameter and the target body spatial position parameter from the joint parameter space according to the updated anisotropic proposal distribution; calculating a target body spatial positioning error metric value for the candidate sample, and constructing an error-normalized acceptance rate adjustment function combining a joint posterior probability of the candidate sample and a joint posterior probability of a current state sample, the sampling acceptance probability α being defined by the following formula: wherein E(x * ) represents the target body spatial positioning error metric value under the candidate state, represents the average positioning error of the sample set under the current round, λ is an error adjustment factor, P(x * ) is the joint posterior probability density value of the candidate sample x * , and P(x t-1 ) is the joint posterior probability density value of the current state sample x t-1 . generating a random number for sampling acceptance determination, if the candidate sample satisfies the acceptance condition, the corresponding candidate sample is taken as the current state sample, otherwise, the last round state sample is retained, and the sampling result is added to the sample set; repeating the above steps until a maximum sampling round is reached, and outputting a joint parameter sample set containing the geophysical model parameter and the target body spatial position parameter.

5. The method of claim 1, wherein, The S3 specifically comprises: S31, in the joint sampling process of the improved Markov chain Monte Carlo method, extracting a corresponding target body spatial position parameter from each round of joint parameter samples, and constructing a target body spatial position parameter sample set containing a plurality of target body spatial position parameter samples; S32, for each set of target body spatial position parameters in the target body spatial position parameter sample set, calculate the spatial offset distance between the target body and the reference position in three-dimensional space, the spatial offset distance being obtained based on the difference between the target body geometric centroid and the boundary range; S33, according to the calculated spatial offset distance, define a target body spatial positioning error metric value, the target body spatial positioning error metric value being used to quantitatively represent the difference between the target body spatial position and the reference spatial position in the current sample; S34, embed the target body spatial positioning error metric value as an adjustment factor into the acceptance probability function of the improved Markov chain Monte Carlo method, for dynamically adjusting the acceptance determination logic of the geophysical model parameters and the target body spatial position parameters in each round of joint sampling.

6. The method of claim 1, wherein, The S4 specifically comprises: S41, after the joint sampling of the improved Markov chain Monte Carlo method in the geophysical inversion model is completed, extract the target body spatial position parameters in the joint parameter sample, and construct a target body spatial position parameter sample set, the target body spatial position parameters including the geometric centroid position and the boundary structure information of the target body in three-dimensional space; S42, statistically process the target body spatial position parameter sample set, calculate the three-dimensional mean vector and the three-dimensional covariance matrix of the target body spatial position parameter sample set, and the three-dimensional covariance matrix is used to represent the distribution characteristics and correlation of the target body spatial position in each principal direction; S43, construct a three-dimensional ellipsoid uncertainty modeling method according to the three-dimensional mean vector and the three-dimensional covariance matrix, use the three-dimensional mean vector as the center position of the target body spatial positioning error ellipsoid structure, and use the principal eigenvalues and principal eigenvectors of the three-dimensional covariance matrix to calculate the principal axis length and principal axis direction of the ellipsoid structure; S44, use the target body spatial positioning error ellipsoid structure as the spatial positioning uncertainty boundary body of the target body in the geophysical inversion model, and establish a target body three-dimensional spatial error boundary model.

7. The method of claim 1, wherein, The S5 specifically comprises: S51, set a plurality of representative two-dimensional geological profile directions in the geophysical inversion model, the two-dimensional geological profile directions being determined according to the spatial distribution characteristics of the target body, forming a two-dimensional geological profile direction set; S52, for each two-dimensional geological profile direction, construct a corresponding two-dimensional slice plane, the two-dimensional slice plane being used for spatial interaction with the target body three-dimensional spatial error boundary model in the geophysical inversion model; S53, geometrically intercept the target body spatial positioning error ellipsoid structure in the target body three-dimensional spatial error boundary model on the two-dimensional slice plane, and extract the two-dimensional projection contour of the target body spatial positioning error ellipsoid structure in the current profile direction; S54, convert the two-dimensional projection contour of the target body spatial positioning error ellipsoid structure into structured image data, and form a target body positioning error two-dimensional cross-sectional image in the corresponding two-dimensional geological profile direction; S55, repeat S52 to S54 for each direction in the two-dimensional geological profile direction set to obtain a two-dimensional cross-sectional image set of the target body three-dimensional spatial error boundary model in a plurality of two-dimensional geological profile directions.

8. The method of claim 1, wherein, The S6 specifically includes: S61, extracting a two-dimensional cross-section image set generated by a three-dimensional space error boundary model of a target body in multiple two-dimensional geological profile directions, and establishing a two-dimensional cross-section image index structure corresponding to each target body space positioning error ellipsoid structure; S62, assigning a target body space response intensity weight to each two-dimensional cross-section image in the two-dimensional cross-section image set, the target body space response intensity weight being obtained based on the geometric extension of the target body space positioning error ellipsoid structure in the corresponding profile direction, the inversion parameter gradient, or the information content; S63, performing a weighted fusion process on the two-dimensional cross-section image set according to the target body space response intensity weight, the weighted fusion process being spatially aligned in a three-dimensional reference coordinate system, and the position consistency adjustment of each two-dimensional cross-section image in space being completed through image resampling and spatial registration; S64, generating a three-dimensional target body positioning error heat map based on the weighted fusion result, the three-dimensional target body positioning error heat map expressing the uncertainty distribution values of different spatial positions in the form of voxel color coding.

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