Basin construction parameter inversion method and system based on proxy model optimization, and medium

Abstract

The invention provides a basin structure parameter inversion method and system based on proxy model optimization and a medium, and the method comprises the steps: obtaining the structure-stratigraphic section observation data of a target basin, and building a geometry-equilibrium-rheology coupled flexural cantilever forward modeling model; initial sampling is carried out in the parameter space, an initial training set is constructed, and a mapping relation between parameters and target function values is established by utilizing Gaussian process regression; based on a Bayesian optimization framework, selecting a to-be-evaluated parameter combination through an expected improved acquisition function, calling a forward modeling model to calculate and update a training set, and iterating until convergence; and finally, importance resampling is carried out based on the trained proxy model, and uncertainty quantification and confidence interval output of inversion parameters are realized. The problems that a traditional method is high in calculation cost, slow in convergence, unable to quantify multiplicity and insufficient in forward modeling physical coupling are solved, and the efficiency and the result reliability of extended basin construction parameter inversion are remarkably improved.

Description

Technical Field

[0001] This invention relates to the fields of computational geophysics and geological exploration technology, specifically providing a method, system, and medium for inverting basin tectonic parameters based on surrogate model optimization. Background Technology

[0002] The formation of extensional basins is closely related to the stretching and thinning of the lithosphere under regional tensile stress. The flexural cantilever beam model is a classic forward modeling model of basin dynamics to simulate the formation process of extensional basins. Unlike the McKenzie model, which assumes uniform stretching, the flexural cantilever beam model simplifies the lithosphere into elastic plates, with brittle fracture of the upper crust and viscous flow of the lower crust and lithospheric mantle. By establishing the kinematic relationship between the rigid rotation of the brittle upper crustal block and the ductile deformation of the lower crust, the model simulates tectonic subsidence during rifting and the warping and uplift of the basin flank.

[0003] The core parameters of this model include the horizontal extension of the controlling fault, the dip angle, the brittle-ductile transition depth of the crust, and the effective elastic thickness of the lithosphere. Currently, the common practice is to manually adjust the parameters or use exhaustive grid search for parameter calibration. However, these parameters are strongly coupled. For example, a large extension combined with a steep dip angle can produce a settlement effect with very similar geometry to that produced by a small extension combined with a gentle dip angle. Traditional algorithms are prone to getting trapped in local optima and exhibit strong ambiguity. Furthermore, the forward modeling of the cantilever beam model itself involves solving the variable stiffness deflection equation, requiring several seconds to tens of seconds for a single calculation. When the inversion object involves a multi-fault system, the parameter dimensionality increases dramatically, and the computational load of grid search or Monte Carlo simulation grows exponentially, making it difficult to complete within a feasible timeframe. Moreover, existing tools often treat fault geometry and deflection isostatics as independent modules in series, ignoring their real-time coupling relationship in geological processes, which affects the physical rationality of the model. In recent years, Bayesian inversion methods have been applied in basin evolution simulations (e.g., Chandra & Müller, 2020), but they still suffer from shortcomings such as a lack of uncertainty quantification capabilities, high computational cost of the MCMC algorithm, and imperfect physical coupling mechanisms. Therefore, there is an urgent need for a method that can simultaneously improve the physical realism of forward models and the computational efficiency of inversion. Summary of the Invention

[0004] To address the aforementioned problems, in a first aspect, this invention provides a basin tectonic parameter inversion method based on surrogate model optimization, comprising: S1. Based on the obtained structural-stratigraphic profile observation data of the target basin, a forward model of a geometric-equilibrium-rheological coupled flexural cantilever beam is constructed, including: using a finite difference scheme to discretize and solve the fourth-order differential equations controlling the flexural equilibrium of the lithosphere; for multi-fault systems, calculating the total extension factor by linearly superimposing the crustal thinning distribution of each fault; and processing the effective elastic thickness as a function of time decay based on a viscoelastic rheological model to dynamically update the bending stiffness; and defining the parameters to be inverted and their prior constraints. S2. Initial sampling is performed in the parameter space of the forward model of the flexural cantilever beam. The corresponding objective function value is calculated through the forward model of the flexural cantilever beam. An initial training set is constructed and set as the current training set. The objective function value is the negative mean square error between the observed data and the model prediction. S3. Train a Gaussian process regression surrogate model based on the current training set to establish a mapping relationship from geological parameters to objective function values ​​and obtain the predicted mean and predicted variance. S4. Calculate the acquisition function based on the Gaussian process regression surrogate model according to the predicted mean and predicted variance, and determine the next set of parameter combinations to be evaluated by maximizing the acquisition function. S5. Call the forward model of the flexural cantilever beam to calculate the true objective function value of the parameter combination and add it to the current training set to update the data; S6. Repeat steps S3 to S5 for iteration until the preset convergence condition is met. S7. Based on the finally trained surrogate model, perform uncertainty quantification, generate an approximate posterior sample set by resampling based on the importance of the predicted distribution, and output the statistical characteristics and confidence intervals of the inversion parameters.

[0005] Preferably, S2, initial sampling is performed in the parameter space of the forward model of the flexural cantilever beam, and the corresponding objective function value is calculated through the forward model of the flexural cantilever beam. The construction of the initial training set includes: Within a parameter space comprised of fault extension, dip angle, and initial effective elastic thickness of the lithosphere, a Latin hypercube sampling method is used to generate... Initial parameter sample set ,; The forward model of the flexural cantilever beam is used to calculate the objective function value corresponding to each set of parameters. This constitutes the initial training set. ; The objective function is a measure of the fit between the observed data and the model predictions. The method further includes: constructing the objective function and setting physical constraints: constructing a robust objective function. The optimization objective is defined as maximizing the log-likelihood function that best fits the model predictions to the observed data. The main body of the likelihood function is modeled using Student's t-distribution instead of a standard Gaussian distribution. ; in, and The first Observation data points and their parameters The model predictions are as follows. For the corresponding data error estimation, represents the degrees of freedom parameter of the t-distribution; Apply at least one of the following geophysical constraints: fault cut-off depth constraint, effective elastic thickness range constraint, and fault dip angle prior distribution constraint.

[0006] Preferably, S1, based on the acquired structural-stratigraphic profile observation data of the target basin, constructing a forward model for the flexural cantilever beam includes: Step S11: Numerical solution of geometric-equilibrium coupling The fourth-order differential equations governing the flexural equilibrium of the lithosphere are discretized and solved using a five-point finite difference scheme: ; ; Step S12, Linear superposition of loads in a multi-fault system for systems with A complex system of faults, with overall crustal thinning distribution. It is composed of the linear superposition of contributions from each fault: ; in, For the first The amount of crustal thinning caused by fault activity; Calculate the total stretch factor of the entire profile. ,in For the initial crustal thickness, this It will be used simultaneously for driving thermal settling calculations and load equalization. Update; Step S13, Time-domain correction of viscoelastic rheology To simulate long-term stress relaxation in the lithosphere, the effective elastic thickness is... Processed as over time decay function The rheological characteristics are described using Maxwell's or the standard linear solid (SLS) rheological model: Maxwell model: ; SLS model: ; in, To the viscosity of the mantle The relevant relaxation time; In forward simulation, based on the evolution time after the constructed event... Dynamic updates The value was adjusted, and the bending stiffness was recalculated. .

[0007] Preferably, during step S1 or the optimization iteration, multi-dimensional geophysical constraints are forcibly applied to ensure the geological rationality of the inversion results, wherein the geophysical constraints include at least one of the following: Geometric kinematic constraints: The maximum cutting depth of the controlling fault must not exceed the preset regional crustal thickness. ,Right now This is a hard boundary constraint; Lithosphere rheological constraint: Effective elastic thickness of the lithosphere It must be a non-negative value, and its range must conform to the background range given by the regional geophysical study, that is... ; Prior constraints on fault structure: To suppress the ambiguity caused by parameter trade-offs, the fault dip angle is... Apply a reasonable prior probability distribution, limiting its range to... to In between, this prior information will be incorporated into the objective function as an additional term, guiding the optimization process toward a geologically more credible solution.

[0008] Preferably, S3, training a Gaussian process regression surrogate model based on the current training set includes: Based on the current training set The maximum likelihood estimation method is used to optimize the hyperparameters of the Matern5 / 2 kernel function, which is defined as follows: ; in, The distance in the parameter space is the hyperparameter to be optimized, which includes the signal variance. With feature length scale ; After training, the Gaussian process regression surrogate model is applied to any parameter point. Give the predicted mean with standard deviation .

[0009] Preferably, S4, calculating the acquisition function based on the predicted mean and predicted variance using the Gaussian process regression surrogate model, and determining the next set of parameter combinations to be evaluated by maximizing the acquisition function includes: Using the expected improvement criterion as the acquisition function Balanced exploration and development:

[0010] in, This is the current optimal observation value. To adjust the parameters, , and These are the cumulative distribution function and probability density function of the standard normal distribution, respectively. Global maximization using the L-BFGS-B optimization algorithm Determine the next set of parameter combinations to be evaluated. .

[0011] Preferably, step S5, calling the forward model of the flexural cantilever beam to calculate the true objective function value of the parameter combination and adding it to the current training set to update the data, includes: Call forward model to calculate The true objective function value , to put the new data Add to training set .

[0012] Preferably, in step S7, uncertainty quantification is performed based on the finally trained surrogate model. An approximate posterior sample set is generated by resampling based on the importance of the predicted distribution. The statistical characteristics and confidence intervals of the output inversion parameters include: Generate a large number of candidate samples in the parameter space. The Gaussian process model is used to quickly predict the approximate nonnormalized log-likelihood value for each sample. ; Calculate the importance weight of each candidate sample And normalize it: ; Based on this weight distribution, the candidate sample set is resampled according to importance to generate a sample set that approximates the true posterior distribution. ; Based on the posterior sample set Calculate the marginal probability distribution, median, mean, and confidence interval of specified quantiles for each inversion parameter to quantitatively characterize the uncertainty of the inversion results.

[0013] Secondly, this invention provides a basin tectonic parameter inversion system based on a surrogate model optimization, comprising: a data acquisition and modeling module, used to acquire tectonic-stratigraphic profile observation data of the target basin and construct a geometric-equilibrium-rheological coupled flexural cantilever beam forward model, including: using a finite difference scheme to discretize and solve the fourth-order differential equations controlling the flexural equilibrium of the lithosphere; for multi-fault systems, calculating the total extension factor by linearly superimposing the crustal thinning distribution of each fault; and processing the effective elastic thickness as a function of time decay based on a viscoelastic rheological model to dynamically update the bending stiffness; and defining the parameters to be inverted and their prior constraints; and defining the parameters to be inverted and their prior constraints. The sampling and initialization module is used to perform initial sampling in the parameter space of the forward model of the flexural cantilever beam, calculate the corresponding objective function value through the forward model, construct an initial training set and set it as the current training set; the objective function value is the negative mean square error between the observed data and the model prediction. The surrogate model construction module is used to train a Gaussian process regression surrogate model based on the current training set to establish a mapping relationship from geological parameters to objective function values ​​and obtain the predicted mean and predicted variance. The decision module calculates the acquisition function based on the predicted mean and predicted variance of the Gaussian process regression surrogate model, and determines the next set of parameter combinations to be evaluated by maximizing the acquisition function. The forward modeling and update module is used to call the forward modeling model of the flexural cantilever beam to calculate the true objective function value of the parameter combination and add it to the current training set to update the data. The iterative control module is used to control the repeated execution of the agent model construction module, decision module, and forward and update module until the preset convergence condition is met. The uncertainty quantification and output module is used to perform uncertainty quantification based on the finally trained surrogate model. It generates an approximate posterior sample set by resampling based on the importance of the predicted distribution and outputs the statistical characteristics and confidence intervals of the inversion parameters.

[0014] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the basin tectonic parameter inversion method based on surrogate model optimization.

[0015] The beneficial effects of this invention are as follows: 1. Improved Inversion Efficiency: By constructing a Gaussian process regression surrogate model to replace the computationally expensive physical forward model, and employing a Bayesian optimization framework to guide parameter sampling, the number of forward model calls required for the inversion process is significantly reduced. Compared to traditional grid search or Monte Carlo methods, this method reduces the inversion computation time by several orders of magnitude while maintaining accuracy, making it particularly suitable for inversion scenarios involving high-dimensional parameter spaces and multi-fault systems.

[0016] 2. Quantifying the uncertainty of inversion results: Traditional inversion methods typically output only a single "optimal solution," failing to assess the pluralism and reliability of parameters. This invention, after the surrogate model converges, performs importance resampling based on the predicted distribution to generate an approximate posterior sample set, outputting the confidence intervals (e.g., P10 / P90) and probability distributions of each inversion parameter. This provides a clear probabilistic basis for result interpretation, improving the scientific rigor and interpretability of geological decision-making.

[0017] 3. Enhanced intelligence and adaptability of the inversion process: By employing an acquisition function incorporating the Expected Improvement (EI) criterion, the system can automatically balance "exploration" and "development," dynamically selecting the most informative parameter combination for verification during iteration. Combined with adaptively optimized kernel function hyperparameters, the surrogate model can better fit nonlinear and non-smooth response surfaces, improving the efficiency of the optimization path and global convergence capability.

[0018] 4. Enhancing the physical realism and coupling of the forward model: The constructed flexural cantilever beam forward model not only achieves complete coupling between fault geometric motion, equilibrium response, and lithospheric rheological behavior, but also supports linear superposition of multiple fault systems and viscoelastic time-domain correction. This gives the parameter set obtained from the inversion a clear physical meaning, enabling it to be directly and reliably used for basin thermal history simulation and hydrocarbon maturity prediction, thus extending the geological application chain of the inversion results.

[0019] 5. Demonstrates strong robustness and practicality: By introducing a robust likelihood function based on Student's t-distribution, the system enhances its tolerance for outliers in the observed data. Simultaneously, geophysical constraints (such as fault cut-off depth and elastic thickness range) are applied during optimization to ensure that the inversion results conform to geological laws. The system adopts a modular design, supporting full automation from data input and inversion calculation to result visualization and uncertainty analysis, lowering the barrier to entry and enhancing the method's engineering practical value. Attached Figure Description

[0020] The disclosure of this invention will become more readily understood with reference to the accompanying drawings. It will be readily understood by those skilled in the art that these drawings are for illustrative purposes only and are not intended to limit the scope of protection of this invention. Furthermore, similar numbers in the drawings are used to denote similar components, wherein: Figure 1 This is a flowchart illustrating a basin tectonic parameter inversion method based on surrogate model optimization according to an embodiment of the present invention. Detailed Implementation

[0021] Some embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0022] Example 1 like Figure 1 As shown, this invention provides a basin tectonic parameter inversion method based on surrogate model optimization, comprising: S1. Based on the obtained structural-stratigraphic profile observation data of the target basin, a forward model of a flexural cantilever beam with geometric-equilibrium-rheological coupling is constructed.

[0023] In this embodiment, the actual geological data of the basin obtained through geological exploration, seismic profiling, drilling measurements, etc., includes real observation information such as stratum thickness, structural morphology, basement subsidence, and rock layer distribution.

[0024] In one embodiment, S1, based on the acquired tectonic-stratigraphic profile observation data of the target basin, constructing a geometric-equilibrium-rheological coupled forward model of the flexural cantilever beam includes: Step S11: Numerical solution of geometric-equilibrium coupling The fourth-order differential equations governing the flexural equilibrium of the lithosphere are discretized and solved using a five-point finite difference scheme: ; ; in, For bending stiffness, For settlement, To balance the load.

[0025] Step S12, Linear superposition of loads in a multi-fault system for systems with A complex system of faults, with overall crustal thinning distribution. It is composed of the linear superposition of contributions from each fault: ; in, For the first The amount of crustal thinning caused by fault activity. Based on this, the total extension factor of the entire profile is calculated. ,in This represents the initial crustal thickness. It will be used simultaneously for driving thermal settling calculations and load equalization. Update; Step S13, Time-domain correction of viscoelastic rheology To simulate long-term stress relaxation in the lithosphere, the effective elastic thickness is... Processed as over time decay function The rheological characteristics are described using Maxwell's or the standard linear solid (SLS) rheological model: Maxwell model: ; SLS model: ; in, For instantaneous elastic thickness, For long-term steady-state elastic thickness, To the viscosity of the mantle The relevant relaxation time; In forward simulation, based on the evolution time after the constructed event... Dynamic updates The value was adjusted, and the bending stiffness was recalculated. .

[0026] S2. Initial sampling is performed in the parameter space of the forward model of the flexural cantilever beam. The corresponding objective function value is calculated through the forward model of the flexural cantilever beam, and an initial training set is constructed and set as the current training set.

[0027] In one embodiment, S2 involves initial sampling within the parameter space of the forward model of the flexural cantilever beam, calculating the corresponding objective function value using the forward model of the flexural cantilever beam, and constructing an initial training set, including: Within a parameter space comprised of fault extension, dip angle, and initial effective elastic thickness of the lithosphere, a Latin hypercube sampling method is used to generate... Initial parameter sample set ,; The forward model of the flexural cantilever beam is used to calculate the objective function value corresponding to each set of parameters. This constitutes the initial training set. .

[0028] In one embodiment, the objective function value is the negative mean square error between the observed data and the model prediction.

[0029] Furthermore, the construction of the objective function and the setting of physical constraints include the following steps: Constructing a robust objective function: The optimization objective is defined as maximizing the log-likelihood function that best fits the model predictions to the observed data. To enhance the robustness of the inversion algorithm to outliers in the observed data, the main body of the likelihood function is modeled using Student's t-distribution instead of a standard Gaussian distribution. ; in, and The first Observation data points and their parameters The model predictions are as follows. For the corresponding data error estimation, These are the degrees of freedom parameters of the t-distribution (controlling the degree of heavy tails of the distribution). The optimization process aims to find these parameters. To maximize .

[0030] Applying multi-dimensional geophysical constraints: To ensure the geological validity of the inversion results, the following physical constraints are enforced during the optimization process: Geometric kinematic constraints: The maximum cutting depth of the controlling fault must not exceed the preset regional crustal thickness. ,Right now This is a hard boundary constraint.

[0031] Lithosphere rheological constraint: Effective elastic thickness of the lithosphere It must be a non-negative value, and its range must conform to the background range given by the regional geophysical study, that is... (For example, 5km to 100km).

[0032] Prior constraints on fault structure: To suppress the ambiguity caused by parameter trade-offs, the fault dip angle is... Apply a reasonable prior probability distribution (such as...) Centered on, with standard deviation of The truncated Gaussian distribution), limiting its range of values ​​to to This prior information will be incorporated into the objective function as an additional term, guiding the optimization process toward a geologically more plausible solution.

[0033] S3. Train a Gaussian process regression surrogate model based on the current training set to establish a mapping relationship from geological parameters to objective function values ​​and obtain the predicted mean and predicted variance.

[0034] In one embodiment, training a Gaussian process regression surrogate model based on the current training set includes: Based on the current training set The maximum likelihood estimation method is used to optimize the hyperparameters of the Matern5 / 2 kernel function, which is defined as follows: ; in, The distance in the parameter space is the hyperparameter to be optimized, which includes the signal variance. With feature length scale After training, the model can operate on any parameter points. Give the predicted mean with standard deviation .

[0035] Furthermore, the kernel function hyperparameter adaptive optimization process includes the following steps: The maximum likelihood estimation (MLE) method is used to adaptively optimize the hyperparameters.

[0036] The kernel function uses a combination of a Matern5 / 2 kernel and a white noise kernel: ; in: ; ; The hyperparameters to be optimized include: :: Signal variance, the overall variation range of the control function value; Feature scale (length scale) controls the smoothness of the function; Observational noise variance is used to absorb random errors in the training data.

[0037] The goal of hyperparameter optimization is to maximize the marginal log-likelihood: ; Where (=(_f^2,l,_n^2)) is the set of hyperparameters. The optimization process uses the L-BFGS-B algorithm, combined with a multiple random restart strategy to avoid getting trapped in local optima.

[0038] S4. Construct and optimize the acquisition function based on the Gaussian process regression surrogate model, and determine the next set of parameter combinations to be evaluated.

[0039] In one embodiment, S4, constructing and optimizing the acquisition function based on the Gaussian process regression surrogate model, and determining the next set of parameter combinations to be evaluated includes: Using the expected improvement criterion as the acquisition function to balance exploration and development: ; in, This is the current optimal observation value. To adjust the parameters, , and These are the cumulative distribution function and probability density function of the standard normal distribution, respectively. Global maximization using the L-BFGS-B optimization algorithm Determine the next set of parameter combinations to be evaluated. .

[0040] S5. Call the forward model of the flexural cantilever beam to calculate the true objective function value of the parameter combination and add it to the current training set to update the data.

[0041] In one embodiment, S5, calling the forward model of the flexural cantilever beam to calculate the true objective function value of the parameter combination and adding it to the current training set to update the data includes: Call forward model to calculate The true objective function value , to put the new data Add to training set .

[0042] S6. Repeat steps S3 to S5 for iteration until the preset convergence condition is met.

[0043] S7. Based on the finally trained surrogate model, perform uncertainty quantification, generate an approximate posterior sample set by resampling based on the importance of the predicted distribution, and output the statistical characteristics and confidence intervals of the inversion parameters.

[0044] In one embodiment, S7, uncertainty quantification is performed based on the finally trained surrogate model, and an approximate posterior sample set is generated by importance resampling based on the predicted distribution. The statistical characteristics and confidence intervals of the output inversion parameters include: Generate a large number of candidate samples in the parameter space. The Gaussian process model is used to quickly predict the approximate nonnormalized log-likelihood value for each sample. ; Calculate the importance weight of each candidate sample And normalize it: ; Based on this weight distribution, the candidate sample set is resampled according to importance to generate a sample set that approximates the true posterior distribution. ; Based on the posterior sample set Calculate the marginal probability distribution, median, mean, and confidence interval of specified quantiles for each inversion parameter to quantitatively characterize the uncertainty of the inversion results.

[0045] In one possible implementation, the cantilever beam inversion workflow includes the following steps: Step S1: Forward model construction and inversion parameter definition Users set the physical value range of the inversion parameters based on their understanding of the regional geology. For typical extensional basins, the core parameter range is typically set as follows: fault horizontal extension (Heave) 0.5 to 30 km, fault dip (Dip) 20 to 70 degrees, and effective elastic thickness of the lithosphere (Te) 5 to 100 km. For multi-fault systems, the Heave and Diip parameters can be defined independently for each fault.

[0046] Step S2: Initial Training Set Construction The system employs the Latin hypercube sampling method to generate 12 to 18 sets of initial parameter samples within the aforementioned multidimensional parameter space, ensuring uniform distribution across all dimensions. Subsequently, for each set of samples, the cantilever beam forward modeling engine is invoked to calculate the fitting residual between the predicted settlement profile and the observed data, which is then converted into initial log-likelihood values ​​to form the training set required for initiating optimization.

[0047] Steps S3-S6: Iterative Bayesian Optimization This stage involves iterative iterations to approximate the optimal solution. Two-level iteration termination conditions are set: (hard) the total number of forward calls reaches a preset upper limit (e.g., 60 times for a single fault, 100 times for a double fault); (soft) the improvement in the optimal objective function value is less than a threshold (e.g., 0.01) in multiple consecutive iterations (e.g., 8 times).

[0048] Hard termination: When the total number of forward modeling calls reaches the preset limit (e.g., 60 times for single fault inversion, 100 times for double fault inversion), it will be forcibly stopped.

[0049] Soft convergence: When the improvement of the optimal likelihood value is less than a preset threshold (e.g., 0.01) in multiple consecutive iterations (e.g., 8 times), it is determined to be converged and terminated early.

[0050] Step S3, surrogate model construction and update: Based on the current sample training set, construct a Gaussian process regression surrogate model. This model uses the Matern5 / 2 kernel function by default and automatically optimizes its hyperparameters by maximizing the marginal likelihood function.

[0051] Step S4, Acquisition Function Optimization and Sample Point Selection: In each iteration, the distribution of the acquisition function to be improved across the entire parameter space is calculated and optimized. To efficiently find the global maximum point of the EI function and avoid getting trapped in local maxima, the L-BFGS-B algorithm is used in conjunction with a multiple (e.g., 3) random restart strategy for optimization. The found optimal point is determined as the next set of parameter combinations to be evaluated.

[0052] Step S5, Forward Modeling Verification and Iterative Control: Perform a complete forward modeling calculation of the cantilever beam for the selected parameter combination to obtain its true likelihood value, and add the new data point to the training set to update the surrogate model.

[0053] During the optimization process, if a set of parameters causes the numerical solution of the forward model to fail (such as a singularity in the flexure equation), the system marks the sample as invalid and assigns it an extremely low objective function value. This mechanism ensures the robustness of the optimization process and prevents it from being interrupted by a few invalid samples.

[0054] Step 6: Iteration Judgment: Check if the preset convergence condition is met. If it is met, exit the loop and proceed to step S7; otherwise, return to step S3 to continue iteration.

[0055] Step S7: Quantification of Posterior Uncertainty and Output of Results Step S71, Posterior Sample Generation: Generate a large number (e.g., 20,000) of candidate points uniformly in the parameter space, and quickly predict the approximate log-likelihood value of each point using a well-trained Gaussian process surrogate model. Subsequently, through importance resampling, samples are extracted from the candidate points according to the probability weights of the likelihood transformation to generate a sample set that approximates the posterior distribution of the parameters.

[0056] Step S72, Statistics and Correlation Analysis: Based on the posterior sample set, calculate the marginal probability distribution and key quantiles (e.g., P10, P50, P90) of each inversion parameter. Simultaneously, by plotting correlation scatter plots (e.g., Heave-Dip, Dip-Te) between parameters, the trade-offs between parameters are visually revealed, providing quantitative evidence for geological interpretation.

[0057] Example 2 This invention discloses a basin tectonic parameter inversion system based on surrogate model optimization. The basin tectonic parameter inversion system based on surrogate model optimization in this embodiment mainly includes a data acquisition and modeling module, a sampling and initialization module, a surrogate model construction module, a decision module, a forward modeling and updating module, an iterative control module, and an uncertainty quantification and output module. In some embodiments, one or more of the data acquisition and modeling module, sampling and initialization module, surrogate model construction module, decision module, forward modeling and updating module, iterative control module, and uncertainty quantification and output module can be combined into a single module. In some embodiments, the data acquisition and modeling module can be configured to execute step S1. The sampling and initialization module can be configured to execute step S2. The surrogate model construction module can be configured to execute step S3. The decision module can be configured to execute step S4. The forward modeling and updating module can be configured to execute step S5. The iterative control module can be configured to execute step S6. The uncertainty quantification and output module can be configured to execute step S7. In one embodiment, a description of the specific functions can be found in steps S1-S7.

[0058] The above-described basin tectonic parameter inversion system based on surrogate model optimization is used to implement the basin tectonic parameter inversion method based on surrogate model optimization. The technical principles, technical problems solved, and technical effects of the two are similar. Those skilled in the art can clearly understand that, for the sake of convenience and brevity, the specific working process and related descriptions of the basin tectonic parameter inversion system based on surrogate model optimization can be found in the description of the basin tectonic parameter inversion method based on surrogate model optimization, and will not be repeated here.

[0059] Furthermore, it should be understood that since the various modules are only provided to illustrate the functional units of the device of the present invention, the physical devices corresponding to these modules may be the processor itself, or a part of the software, a part of the hardware, or a combination of software and hardware within the processor. Therefore, the number of modules shown in the figures is merely illustrative.

[0060] Those skilled in the art will understand that the various modules in the device can be adaptively split or combined. Such splitting or combining of specific modules will not cause the technical solution to deviate from the principles of the present invention; therefore, the technical solutions after splitting or combining will fall within the protection scope of the present invention.

[0061] Example 3 The present invention also provides a computer-readable storage medium. In one embodiment of the present invention, the computer-readable storage medium can be configured to store a program for executing the basin tectonic parameter inversion method based on surrogate model optimization described in the above-described method embodiments. This program can be loaded and run by a processor to implement the above-described basin tectonic parameter inversion method based on surrogate model optimization. For ease of explanation, only the parts related to the embodiments of the present invention are shown; for specific technical details not disclosed, please refer to the method section of the embodiments of the present invention. The computer-readable storage medium can be a storage device comprising various electronic devices. Optionally, in the embodiments of the present invention, the computer-readable storage medium is a non-transitory computer-readable storage medium.

[0062] The technical solution of the present invention has been described above with reference to the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the original technical features, and the technical solutions resulting from these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A basin tectonic parameter inversion method based on surrogate model optimization, characterized in that, Includes the following steps: S1. Based on the obtained structural-stratigraphic profile observation data of the target basin, a forward model of a geometric-equilibrium-rheological coupled flexural cantilever beam is constructed, including: using a finite difference scheme to discretize and solve the fourth-order differential equations controlling the flexural equilibrium of the lithosphere; for multi-fault systems, calculating the total extension factor by linearly superimposing the crustal thinning distribution of each fault; and processing the effective elastic thickness as a function of time decay based on a viscoelastic rheological model to dynamically update the bending stiffness; and defining the parameters to be inverted and their prior constraints. S2. Initial sampling is performed in the parameter space of the forward model of the flexural cantilever beam. The corresponding objective function value is calculated through the forward model of the flexural cantilever beam. An initial training set is constructed and set as the current training set. The objective function value is the negative mean square error between the observed data and the model prediction. S3. Train a Gaussian process regression surrogate model based on the current training set to establish a mapping relationship from geological parameters to objective function values ​​and obtain the predicted mean and predicted variance. S4. Calculate the acquisition function based on the Gaussian process regression surrogate model according to the predicted mean and predicted variance, and determine the next set of parameter combinations to be evaluated by maximizing the acquisition function. S5. Call the forward model of the flexural cantilever beam to calculate the true objective function value of the parameter combination and add it to the current training set to update the data; S6. Repeat steps S3 to S5 for iteration until the preset convergence condition is met. S7. Based on the finally trained surrogate model, perform uncertainty quantification, generate an approximate posterior sample set by resampling based on the importance of the predicted distribution, and output the statistical characteristics and confidence intervals of the inversion parameters.

2. The method according to claim 1, characterized in that, S2. Initial sampling is performed in the parameter space of the forward model of the flexural cantilever beam. The corresponding objective function value is calculated through the forward model of the flexural cantilever beam, and the initial training set is constructed, including: Within a parameter space comprised of fault extension, dip angle, and initial effective elastic thickness of the lithosphere, a Latin hypercube sampling method is used to generate... Initial parameter sample set ,; The forward model of the flexural cantilever beam is used to calculate the objective function value corresponding to each set of parameters. This constitutes the initial training set. ; The objective function is a measure of the fit between the observed data and the model predictions. The method further includes: constructing the objective function and setting physical constraints: constructing a robust objective function. The optimization objective is defined as maximizing the log-likelihood function that best fits the model predictions to the observed data. The main body of the likelihood function is modeled using Student's t-distribution instead of a standard Gaussian distribution. ； in, and The first Observation data points and their parameters The model predictions are as follows. For the corresponding data error estimation, represents the degrees of freedom parameter of the t-distribution; Apply at least one of the following geophysical constraints: fault cut-off depth constraint, effective elastic thickness range constraint, and fault dip angle prior distribution constraint.

3. The method according to claim 1, characterized in that, S1. Based on the obtained structural-stratigraphic profile observation data of the target basin, a forward model of a geometrically-equilibrium-rheologically coupled flexural cantilever beam is constructed, including: Step S11: Numerical solution of geometric-equilibrium coupling The fourth-order differential equations governing the flexural equilibrium of the lithosphere are discretized and solved using a five-point finite difference scheme: ； ； Step S12, Linear superposition of loads in a multi-fault system for systems with A complex system of faults, with overall crustal thinning distribution. It is composed of the linear superposition of contributions from each fault: ； in, For the first The amount of crustal thinning caused by fault activity; Calculate the total stretch factor of the entire profile. ,in For the initial crustal thickness, this It will be used simultaneously for driving thermal settling calculations and load equalization. Update; Step S13, Time-domain correction of viscoelastic rheology To simulate long-term stress relaxation in the lithosphere, the effective elastic thickness is... Processed as over time decay function The rheological characteristics are described using Maxwell's or the standard linear solid (SLS) rheological model: Maxwell model: ; SLS model: ; in, To the viscosity of the mantle The relevant relaxation time; In forward simulation, based on the evolution time after the constructed event... Dynamic updates The value was adjusted, and the bending stiffness was recalculated. .

4. The method according to claim 1, characterized in that, In step S1 or during the optimization iteration, multi-dimensional geophysical constraints are forcibly applied to ensure the geological rationality of the inversion results. These geophysical constraints include at least one of the following: Geometric kinematic constraints: The maximum cutting depth of the controlling fault must not exceed the preset regional crustal thickness. ,Right now This is a hard boundary constraint; Lithosphere rheological constraint: Effective elastic thickness of the lithosphere It must be a non-negative value, and its range must conform to the background range given by the regional geophysical study, that is... ; Prior constraints on fault structure: To suppress the ambiguity caused by parameter trade-offs, the fault dip angle is... Apply a reasonable prior probability distribution, limiting its range to... to In between, this prior information will be incorporated into the objective function as an additional term, guiding the optimization process toward a geologically more credible solution.

5. The method according to claim 1, characterized in that, S3. Training a Gaussian process regression surrogate model based on the current training set includes: Based on the current training set The maximum likelihood estimation method is used to optimize the hyperparameters of the Matern5 / 2 kernel function, which is defined as follows: ； in, The distance in the parameter space is the hyperparameter to be optimized, which includes the signal variance. With feature length scale ; After training, the Gaussian process regression surrogate model is applied to any parameter point. Give the predicted mean with standard deviation .

6. The method according to claim 1, characterized in that, S4. Calculate the acquisition function based on the predicted mean and predicted variance using the Gaussian process regression surrogate model. Determine the next set of parameter combinations to be evaluated by maximizing the acquisition function, including: Using the expected improvement criterion as the acquisition function Balanced exploration and development: ； in, This is the current optimal observation value. To adjust the parameters, , and These are the cumulative distribution function and probability density function of the standard normal distribution, respectively. Global maximization using the L-BFGS-B optimization algorithm Determine the next set of parameter combinations to be evaluated. .

7. The method according to claim 1, characterized in that, S5. Calculate the true objective function value of the parameter combination using the forward model of the flexural cantilever beam, and add it to the current training set to update the data, including: Call forward model to calculate The true objective function value , to put the new data Add to training set .

8. The method according to claim 1, characterized in that, S7. Based on the finally trained surrogate model, uncertainty quantification is performed. An approximate posterior sample set is generated by resampling based on the importance of the predicted distribution. The statistical characteristics and confidence intervals of the output inversion parameters include: Generate a large number of candidate samples in the parameter space. The Gaussian process model is used to quickly predict the approximate nonnormalized log-likelihood value for each sample. ; Calculate the importance weight of each candidate sample And normalize it: ； Based on this weight distribution, the candidate sample set is resampled according to importance to generate a sample set that approximates the true posterior distribution. ; Based on the posterior sample set Calculate the marginal probability distribution, median, mean, and confidence interval of specified quantiles for each inversion parameter to quantitatively characterize the uncertainty of the inversion results.

9. A basin tectonic parameter inversion system based on surrogate model optimization, characterized in that, include: The data acquisition and modeling module is used to acquire structural-stratigraphic profile observation data of the target basin, construct a geometric-equilibrium-rheological coupled forward model of a flexural cantilever beam, including: using a finite difference scheme to discretize and solve the fourth-order differential equations controlling the flexural equilibrium of the lithosphere; for multi-fault systems, calculating the total extension factor by linearly superimposing the crustal thinning distribution of each fault; and processing the effective elastic thickness as a function of time decay based on a viscoelastic rheological model to dynamically update the bending stiffness; and defining the parameters to be inverted and their prior constraints. The sampling and initialization module is used to perform initial sampling in the parameter space of the forward model of the flexural cantilever beam, calculate the corresponding objective function value through the forward model, construct an initial training set and set it as the current training set; the objective function value is the negative mean square error between the observed data and the model prediction. The surrogate model construction module is used to train a Gaussian process regression surrogate model based on the current training set to establish a mapping relationship from geological parameters to objective function values ​​and obtain the predicted mean and predicted variance. The decision module calculates the acquisition function based on the predicted mean and predicted variance of the Gaussian process regression surrogate model, and determines the next set of parameter combinations to be evaluated by maximizing the acquisition function. The forward modeling and update module is used to call the forward modeling model of the flexural cantilever beam to calculate the true objective function value of the parameter combination and add it to the current training set to update the data. The iterative control module is used to control the repeated execution of the agent model construction module, decision module, and forward and update module until the preset convergence condition is met. The uncertainty quantification and output module is used to perform uncertainty quantification based on the finally trained surrogate model. It generates an approximate posterior sample set by resampling based on the importance of the predicted distribution and outputs the statistical characteristics and confidence intervals of the inversion parameters.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the basin tectonic parameter inversion method based on surrogate model optimization as described in any one of claims 1 to 8.

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