A Physics- and Data-Driven Receiver Function Inversion Method

Abstract

This invention provides a physics- and data-driven receiver function inversion method. By determining the model parameters to be optimized, an objective function for the inversion problem is constructed. This objective function includes a data fitting term, a model regularization term, and a coupling term combining data-driven and physics-driven approaches. During inversion, iterative optimization is performed by introducing the objective function and the coupling term combining data-driven and physics-driven approaches to determine the inversion model. By combining the advantages of the BFGS optimization algorithm and the UNet deep learning algorithm, a more robust receiver function inversion is achieved, outperforming single physics-driven or data-driven inversion methods. Compared to receiver function linearization inversion methods, it no longer relies on the initial model, reducing the possibility of the inversion solution getting trapped in local minima. Compared to deep learning inversion methods, it can better fit observational data and more closely approximate the true inversion solution.

Description

Technical Field

[0001] This invention relates to the field of Earth observation technology, and more specifically, to a physics- and data-driven receiver function inversion method. Background Technology

[0002] Receiver function inversion is a technique similar to reflection seismology used to probe the crust and upper mantle structure beneath seismic stations. Traditional receiver function inversion imaging methods, by linearizing the objective function, search for the best model that fits the observed data based on existing physical processes, starting from an initial model. Because it is based on fundamental physical criteria, it is considered a physics-driven inversion method. Well-known inversion methods include the conjugate gradient method, the Gauss-Newton method, the damped least squares method, and the quasi-Newton method. These methods are highly efficient, and the models can interpret the observational data well. However, gradient-based inversion methods based on regularization exhibit strong non-uniqueness when applied to receiver function inversion, and are prone to getting trapped in local minima without good prior constraints. Nevertheless, this receiver function inversion technique is widely used for crustal structure detection.

[0003] Deep learning inversion frameworks build inversion operators from data without needing to understand the forward modeling process, making them a completely data-driven approach. By minimizing labels and the prediction model, iterative updates build the weight model of the neural network. This approach belongs to the fully data-driven "complete learning reconstruction" method, requiring a large number of representative training samples to build a robust neural network model that can be successfully used to predict models never seen in the training set. The core challenge of deep learning is establishing excellent model generalization ability to prevent overfitting and the failure of predictions from unfamiliar models; good generalization ability requires an even wider training set. Its greatest advantage is the ability to establish arbitrarily complex nonlinear relationships between data and models, avoiding local minima problems found in linearization methods. However, the fit between most deep learning inversion models and observed data obtained through forward modeling is generally inferior to that of physically driven inversion results.

[0004] A new trend in deep learning inversion is incorporating physical processes into it. This is because pseudo-inverse operators, which rely entirely on statistical meaning, may exhibit limitations in many practical situations and may require further adjustments to ensure the results satisfy physical properties. Meanwhile, data-driven methods, random sampling of models and data spaces, and the nonlinearity of connecting data and models are key advantages of machine learning for inversion applications. Combining data-driven and physics-driven methods can help improve inversion performance. For example, the paper "Xiong X, F De la Torre. 2013. Supervised descent method and its application to facealignment. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, 532–539." integrates a DNN module into the inversion iteration for fast gradient direction estimation, improving gradient computation efficiency. The paper "Adler J, O 2017. Solving ill-posed inverse problems using iterative deep neural networks: Inverse Problems, 33, 124007, doi:10.1088 / 1361-6420 / aa9581. This paper trains convolutional neural networks based on the theoretical forward modeling process, while the inverse modeling process is the decoding process of the neural network. The paper "Colombo D, Turkoglu E, Li W, et al. 2021. Physics-driven deep-learning inversion with application to transient..." "electromagnets. Geophysics, 86(3), E209-E224." This further develops the above scheme, proposing to embed physics-driven inversion into data-driven inversion through an iterative process. Unlike previous proposals that integrated forward modeling into the DNN framework, Colombo's scheme essentially combines the results of physics-driven inversion and data-driven inversion (PhyDLI). This structure provides great flexibility for automated dual-driven hybrid inversion procedures, combining the advantages of pseudo-random sampling in deep learning and (physics-based) traditional gradient-based optimization algorithms to achieve mutual complementarity. Through DL retraining, the algorithm repeatedly optimizes the prior model during the gradient-based algorithm iteration process, making the objective function escape local minima as much as possible and obtain the optimal solution. This scheme has been successfully applied to synthetic and measured data of transient electromagnetics.

[0005] Inversion of the receiver function is a complex, nonlinear problem with many solutions. While deep learning can yield a reasonable velocity model for receiver function inversion, its data fit is significantly insufficient; and purely physical-driven methods heavily rely on the initial model. Summary of the Invention

[0006] In view of this, the purpose of this invention is to improve and transfer the algorithm to receiver function inversion based on the scheme proposed in the literature "Colombo D, Turkoglu E, Li W, et al. 2021. Physics-driven deep-learning inversion with application to transient electromagnetics. Geophysics, 86(3), E209-E224.", aiming to approximate the global optimal solution, reduce the non-uniqueness of the receiver function, and reduce the dependence of receiver function inversion on the initial model; at the same time, establish a more stable and reliable receiver function inversion mode.

[0007] A first aspect of the present invention provides a physics- and data-driven receiver function inversion method, the method comprising:

[0008] S1, determine the model parameters that need to be optimized and construct the objective function of the inversion problem; the objective function of the inversion problem includes a data fitting term, a model regularization term, and a coupling term of joint data-driven and physical-driven; wherein, the coupling term of joint data-driven and physical-driven is a coupling operator of deep learning inversion and BFGS inversion models;

[0009] S2, during inversion, the inversion model is determined by performing iterative optimization on the objective function and the coupling terms of the joint data-driven and physics-driven functions.

[0010] Preferably, the objective function of the inversion problem is expressed as:

[0011]

[0012] Where m represents the model parameters to be optimized, and μ1 and μ2 are the weight coefficients for adjusting different objective functions. For data fitting terms:

[0013]

[0014] Where, d obs For the observed data, G is the forward modeling operator, and W is the forward modeling operator. dThis is the data weight matrix or data covariance matrix. This matrix allows observations with large variances to have a smaller weight in the calculation of the objective function, ensuring that the inversion can proceed stably when the quality of the observation data is poor. In the testing of synthetic data, since the data is error-free, the identity matrix is ​​used.

[0015] Model regularization term This is used to adjust the weights between the data fitting term and the model smoothing term, thereby improving the stability of the inversion, and is expressed as:

[0016]

[0017] Where L is the roughness matrix, which is usually a first-order or second-order difference operator;

[0018] The coupling term of the objective function, which combines data-driven and physical-driven approaches, is expressed as follows:

[0019]

[0020] Where, m l =H θ d obs H θ W is a pseudo-inverse operator obtained by training the UNet network, which maps the data space to the model space. m The weight matrix is ​​used to control the constraint parameters.

[0021] Preferably, S1 further includes:

[0022] Using the data in the training set t and model m t For H θ To optimize, the loss function is determined as follows:

[0023]

[0024] By minimizing the loss function The optimized network parameters θ are obtained; the trained network parameters are used to predict new model parameters.

[0025] m l =H θ d obs (6).

[0026] Preferably, in step S2, during the inversion, the optimal result of the objective function is determined by performing iterative optimization on the objective function and the coupling terms of the joint data-driven and physical-driven functions, including:

[0027] The objective function of the inversion problem is obtained through the following iterative method:

[0028]

[0029] at this time m l For neural network prediction models, prior information is used to constrain the model, transforming the objective function into a single-variable optimization problem. Since the objective function of formula (7) is continuously differentiable, it is easy to use gradient-based optimization algorithms to find the minimum. The optimal solution under the given conditions. This invention uses the quasi-Newton method (BFGS) to solve for this.

[0030] After obtaining the inversion model, the network weights need to be updated to predict the new m in the next iteration. l The update method is as follows:

[0031]

[0032] The specific process of inversion can be described as follows: First, establish a training set m for the receiving function. t d t A training network was built using synthetic receptive function data and a one-dimensional layered crustal model as the training set; the deep learning network used the UNet framework. The network was then trained, with parameters updated to θ, and the observed receptive function data was input. The trained network was then used to make a prediction on the target model. The prediction result was used as the prior model m. l Entering the physics-driven objective function Then use BFGS on the objective function Optimization is performed to obtain the inversion model m at the end of the first iteration. inv Simultaneously, the orthogonal m inv Get the receiving function d inv Next, based on the new data m inv and d inv The UNet model is retrained (Equation (8)), the weight parameters θ are updated, and then the prior model m is re-predicted. l And so on, usually a convergent inversion result can be obtained within 10 iterations.

[0033] Preferably, the UNet network applies the ELU activation function to the output of the convolutional layer; after the convolution operation, the data is standardized based on Batch_normilization.

[0034] Furthermore, a second aspect of the present invention provides a physics- and data-driven receiver function inversion apparatus, the apparatus comprising:

[0035] The module for determining and constructing the model parameters to be optimized is defined, and the objective function for the inversion problem is constructed. The objective function for the inversion problem includes a data fitting term, a model regularization term, and a coupling term that combines data-driven and physics-driven approaches. The coupling term that combines data-driven and physics-driven approaches is a coupling operator of the deep learning inversion and BFGS inversion models.

[0036] The inversion module determines the inversion model by performing iterative optimization on the objective function and the coupling terms of the joint data-driven and physics-driven functions during the inversion process.

[0037] Furthermore, a third aspect of the present invention provides an electronic device comprising: one or more processors, and a memory for storing one or more computer programs; the computer programs being configured to be executed by the one or more processors, the programs including steps for performing the physics- and data-driven receiver function inversion method as described above.

[0038] Furthermore, a fourth aspect of the present invention provides a storage medium storing a computer program; the program is loaded and executed by a processor to implement the steps of the physical and data-driven receiver function inversion method as described above.

[0039] In this invention, the objective function for the inversion problem is constructed by determining the model parameters to be optimized. This objective function includes a data fitting term, a model regularization term, and a coupling term combining data-driven and physics-driven approaches. During inversion, iterative optimization is performed on the objective function and the coupling term combining data-driven and physics-driven approaches to determine the inversion model. By combining the advantages of the BFGS optimization algorithm and the UNet deep learning algorithm, a more robust receiver function inversion is achieved, outperforming single physics-driven or data-driven inversion methods. Compared to receiver function linearization inversion methods, it no longer relies on the initial model, reducing the possibility of the inversion solution getting trapped in local minima. Compared to deep learning inversion methods, this invention can better fit observational data and more closely approximate the true inversion solution. Attached Figure Description

[0040] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0041] Figure 1This is a flowchart illustrating the physical and data-driven receiver function inversion method disclosed in this embodiment of the invention.

[0042] Figure 2 The UNet architecture for receiving function inversion disclosed in this invention embodiment;

[0043] Figure 3 A schematic diagram of the inversion results of the simple layered model PhyDLI disclosed in this embodiment of the invention.

[0044] Figure 4 A schematic diagram of the inversion results of the PhyDLI model with low-speed anomalies disclosed in this embodiment of the invention. Detailed Implementation

[0045] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided to make this application more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art.

[0046] Furthermore, the described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a thorough understanding of embodiments of this application. However, those skilled in the art will recognize that the technical solutions of this application can be practiced without one or more of the specific details, or other methods, components, apparatuses, steps, etc., can be employed. In other instances, well-known methods, apparatuses, implementations, or operations are not shown or described in detail to avoid obscuring various aspects of this application.

[0047] The block diagrams shown in the accompanying drawings are merely functional entities and do not necessarily correspond to physically independent entities. That is, these functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0048] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily need to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0049] It should be noted that "multiple" in this embodiment refers to two or more.

[0050] The implementation details of the technical solutions in the embodiments of this application are described in detail below.

[0051] This embodiment is based on the scheme proposed by Colombo et al., 2021 (Colombo D, Turkoglu E, Li W, et al. 2021. Physics-driven deep-learning inversion with application to transient electromagnetics. Geophysics, 86(3), E209-E224). The algorithm is improved and transferred to receiver function inversion, aiming to approximate the global optimum, reduce the non-uniqueness of the receiver function, and reduce the dependence of receiver function inversion on the initial model. At the same time, a more stable and reliable receiver function inversion mode is established.

[0052] Please see Figure 1 , Figure 1 This is a flowchart illustrating a physics- and data-driven receiver function inversion method disclosed in an embodiment of the present invention. Figure 1 As shown in the figure, an embodiment of the present invention provides a physical and data-driven receiver function inversion method, the method comprising:

[0053] S1, determine the model parameters that need to be optimized and construct the objective function of the inversion problem; the objective function of the inversion problem includes a data fitting term, a model regularization term, and a coupling term of joint data-driven and physical-driven; wherein, the coupling term of joint data-driven and physical-driven is a coupling operator of deep learning inversion and BFGS inversion models.

[0054] The essence of receiver function forward modeling is to calculate the Green's function in a layered medium, then add a plane-incident P-wave (or S-wave) as the source term in the bottom layer (i.e., semi-infinite space), and finally calculate the spectral ratio of the radial and vertical component responses received at the surface. In practice, the receiver function is usually obtained by deconvolving the radial component with the vertical component seismic record. The basis of receiver function forward modeling is the calculation of theoretical seismograms of the layered medium. There are various methods for calculating theoretical seismograms, including the generalized ray method (Helmberger, 1968), the reflectivity method (Fuchs and Muller, 1971), the propagation matrix method (Gilbert and Backus, 1966), the discrete wavenumber method (Bouchon, 1979), and the generalized back-transmission R / T coefficient method (Chen, 1999; Kennett, 2009). This embodiment uses the generalized back-transmission R / T coefficient method; for algorithm details, please refer to Chen (1999) and Kennett (2009).

[0055] The UNet architecture used for receiving function inversion is as follows: Figure 2As shown, the network has 4 layers on each side, containing a total of 17 convolutional layers, 3 pooling layers, and 3 transposed convolutional layers. Since the receiver function data contains a large number of negative numbers, the ELU activation function is selected to apply to the output of the convolutional layers. This activation function can avoid information loss in the negative parts and gradient vanishing. After the convolution operation, Batch normalization is used to standardize the data to further prevent gradient vanishing or gradient explosion, while also increasing the regularization effect. This embodiment evaluates the performance of UNet by the mean squared error between the output variable and the observed data, the specific expression of which is: Among them, y i mod It is the output variable, y i obs These are the observed data; RMSE is the L2 norm error (loss function) vector, which gives higher weight to larger errors and is suitable for suppressing larger errors.

[0056] Physics- and data-driven receiver function inversion techniques essentially use deep learning predictions as prior information to feed into the optimization iteration process of BFGS. Assuming the model parameters to be optimized are velocity structures m, the objective function of the inversion problem includes data fitting terms, model smoothing terms, and coupling operators between the deep learning inversion and BFGS inversion models.

[0057] Preferably, the objective function of the inversion problem is expressed as:

[0058]

[0059] Where m represents the model parameters to be optimized, and μ1 and μ2 are the weight coefficients for adjusting different objective functions. For data fitting terms:

[0060]

[0061] Where, d obs For the observed data, G is the forward modeling operator of the receiver function, and W... d This is the data weight matrix or data covariance matrix. This matrix allows observations with large variances to have a smaller weight in the calculation of the objective function, ensuring that the inversion can proceed stably when the quality of the observation data is poor. In the testing of synthetic data, since the data is error-free, the identity matrix is ​​used.

[0062] Model regularization term This is used to adjust the weights between the data fitting term and the model smoothing term, thereby improving the stability of the inversion, and is expressed as:

[0063]

[0064] Where L is the roughness matrix, which is usually a first-order or second-order difference operator;

[0065] The coupling term of the objective function, which combines data-driven and physical-driven approaches, is expressed as follows:

[0066]

[0067] Where, m l =H θ d obs H θ W is a pseudo-inverse operator obtained by training the UNet network, which maps the data space to the model space. m The weight matrix is ​​used to control the constraint parameters.

[0068] Preferably, S1 further includes:

[0069] Using the data in the training set t and model m t For H θ To optimize, the loss function is determined as follows:

[0070]

[0071] By minimizing the loss function The optimized network parameters θ are obtained; the trained network parameters are used to predict new model parameters.

[0072] m l =H θ d obs (6)

[0073] S2, during inversion, the inversion model is determined by performing iterative optimization on the objective function and the coupling terms of the joint data-driven and physics-driven functions.

[0074] Preferably, in step S2, during the inversion, the optimal result of the objective function is determined by performing iterative optimization on the objective function and the coupling terms of the joint data-driven and physical-driven functions, including:

[0075] The objective function of the inversion problem is obtained through the following iterative method:

[0076]

[0077]

[0078] Formula (7) is optimized using BFGS, and formula (8) is optimized using neural network retraining.

[0079] Quasi-Newton methods are the most representative of gradient-based inversion methods and one of the best methods for large-scale nonlinear problems. The essence of quasi-Newton methods is an approximation of Newton's method. They approximate the Hessian matrix, which is the most computationally expensive part of Newton's method, by iteratively solving for it, thus ensuring second-order (curvature) descent of the model. Like most gradient-based methods, only the gradient needs to be calculated during each model update. By calculating the change in the gradient, quasi-Newton methods can construct a sufficiently good optimization model to achieve superlinear convergence. The improvement of quasi-Newton methods over gradient methods in complex large-scale nonlinear optimization problems is undoubtedly significant. The most famous quasi-Newton algorithm is BFGS, named after its four discoverers: Broyden, Fletcher, Goldfarb, and Shanno. Building on this, Byrd et al. (1994, 1995) made further improvements, allowing the Hessian matrix to be better approximated during iterative updates with only a small increase in memory; this is known as the finite-memory quasi-Newton method (L-BFGS). This embodiment uses L-BFGS to optimize the PhyDLI framework. For algorithm details, please refer to Byrd et al., 1994, 1995 (Byrd RH, Nocedal J, Schnabel R B. 1994. Representations of quasi-Newton matrices and their use in limited memory methods. Mathematical Programming, 63(1), 129-156.) and (Byrd Richard H, et al. 1995. A limited memory algorithm for bound constrained optimization. SIAM Journal on scientific computing 16.5: 1190-1208.).

[0080] To verify the effectiveness of the proposed algorithm, three models were designed for validation. In the inversion, the weight coefficients μ1 = μ2 = 0.1, the number of inversion layers for each model was set to 80, and the inversion depth to 60 km. The physics-driven and data-driven models were completely identical (the model layer thickness here is consistent with the model in 3.2.1). The forward modeling window of the receiver function was -5 to 46.2 s, with a sampling interval of 0.1 s and a total of 512 sampling points to facilitate fast Fourier transform. In the inversion, only a portion of the time window was needed, i.e., -5 to 25 s, with 300 sampling points. The ray parameter of the receiver function was set to 0.055, and the Gaussian filter coefficient was set to 2.5. The termination of the objective function is controlled by the maximum component of the gradient and the rate of change of the objective function. According to Byrd et al. (1995), the objective function terminates when one of the following conditions is met:

[0081] max{g[i],i=0,i,…l)≤pgtol (9)

[0082]

[0083] Here f k Let g[i] be the objective function for the k-th iteration, g[i] be the i-th component of the gradient, and pgtol be a manually set parameter, which is set to 10 in this embodiment. -5 epsmch stands for machine precision (typically 2 for 64-bit machines). -53 The factory is set to 10. 10 As can be seen, the physical meaning of the first condition is that the gradient is small enough, and the second condition is that the objective function cannot decrease or bounce.

[0084] Figure 3 and Figure 4 The PhyDLI inversion results for the two models are presented. It can be seen that with iteration, the inverted model gradually approaches the real model, and the UNet prediction model also gradually approaches the real model. During this process, the data fit remains essentially unchanged after the first iteration, indicating that the retraining process promotes the convergence of the inverted model to the real model. Figure 3 and Figure 4 The results show that BFGS inversion is significantly affected by the initial model, resulting in a slower inversion speed for deeper parts of the model compared to the real model. UNet's predictions are closer to the real model than BFGS, but its data fit is comparable to that of BFGS inversion, indicating strong non-uniqueness in the receiver function inversion. PhyDLI's inversion results are significantly better than those of BFGS and UNet alone, and its data fit is higher, suggesting that the prior information provided during retraining helps BFGS optimize to a level closer to the global minimum.

[0085] Furthermore, a second aspect of this embodiment provides a physics- and data-driven receiver function inversion apparatus, the apparatus comprising:

[0086] The module for determining and constructing the model parameters to be optimized is defined, and the objective function for the inversion problem is constructed. The objective function for the inversion problem includes a data fitting term, a model regularization term, and a coupling term that combines data-driven and physics-driven approaches. The coupling term that combines data-driven and physics-driven approaches is a coupling operator of the deep learning inversion and BFGS inversion models.

[0087] The inversion module determines the inversion model by performing iterative optimization on the objective function and the coupling terms of the joint data-driven and physics-driven functions during the inversion process.

[0088] Furthermore, a third aspect of this embodiment provides an electronic device comprising: one or more processors, and a memory for storing one or more computer programs; the computer programs being configured to be executed by the one or more processors, the programs including steps for performing the physics- and data-driven receiver function inversion method as described above.

[0089] Furthermore, a fourth aspect of this embodiment provides a storage medium storing a computer program; the program is loaded and executed by a processor to implement the steps of the physics- and data-driven receiver function inversion method as described above.

[0090] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0091] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. In addition, the mutual coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices or units, or may be electrical, mechanical or other forms of connection.

[0092] The units described as separate components may or may not be physically separate. As will be appreciated by those skilled in the art, the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this specification can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the composition and steps of each example have been generally described in terms of function in the above description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this invention.

[0093] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0094] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or grid device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0095] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A physical and data driven based receiver function inversion method, characterized in that, The method includes: S1, determine the model parameters that need to be optimized and construct the objective function of the inversion problem; the objective function of the inversion problem includes a data fitting term, a model regularization term, and a coupling term of joint data-driven and physical-driven; wherein, the coupling term of joint data-driven and physical-driven is a coupling operator of deep learning inversion and BFGS inversion models; S2, During the inversion, the inversion model is determined by iterative optimization through the introduction of an objective function and a coupling term that combines data-driven and physics-driven approaches. The objective function of the inversion problem is expressed as: （1） in, For the model parameters that need to be optimized, and To adjust the weight coefficients of different objective functions, For data fitting terms: （2） in, For the observed data, G is the forward modeling operator. This is the data weight matrix or data covariance matrix. This matrix allows observations with large variances to have a smaller weight in the calculation of the objective function, ensuring that the inversion can proceed stably when the quality of the observation data is poor. In the testing of synthetic data, since the data is error-free, the identity matrix is ​​used. Model regularization term This is used to adjust the weights between the data fitting term and the model smoothing term, thereby improving the stability of the inversion, and is expressed as: （3） in, For the roughness matrix, a first- or second-order difference operator is usually used; The coupling term of the objective function, which combines data-driven and physical-driven approaches, is expressed as follows: （4） in, , This is a pseudo-inverse operator obtained by training the UNet network, which maps the data space to the model space. The weight matrix for controlling the constraint parameters; S1 further includes: Data from the training set and model right To optimize, the loss function is determined as follows: （5） By minimizing the loss function Optimized network parameters are obtained. The trained network parameters are used to predict new model parameters. （6）； In step S2, during the inversion, iterative optimization is performed on the objective function and the coupling terms of the joint data-driven and physical-driven mechanisms to determine the optimal result of the objective function, including: The objective function of the inversion problem is obtained through the following iterative method: （7） at this time In For neural network prediction models, prior information is used to constrain the model, and the objective function is transformed into a single-variable optimization problem. Since the objective function of formula (7) is continuously differentiable, it is easy to use gradient-based optimization algorithms to find the minimum. The optimal solution under the given conditions is found using the quasi-Newton method (BFGS). After obtaining the inversion model, the network weights need to be updated to predict new values ​​in the next iteration. The update method is as follows: （8） The specific process of inversion can be described as follows: First, establish a training set for the receiving function. , The network for training was set up, using synthetic receptive function data and a one-dimensional layered crustal model as the training set; the deep learning network used the UNet framework; then the network was trained, and the parameters were updated. The observed receiver function data is input, and the trained network makes a prediction on the target model; the prediction result is used as the prior model. Entering the physics-driven objective function Then use BFGS to evaluate the objective function. Optimization is performed to obtain the inversion model at the end of the first iteration. Simultaneously, the main performance Get the receiving function Next, based on the new data and The UNet model is retrained based on formula (8) to update the weight parameters. Then, the prior model is re-predicted. And so on, usually a convergent inversion result can be obtained within 10 iterations.

2. The physical and data-driven receiver function inversion method according to claim 1, characterized in that, The UNet network applies the ELU activation function to the output of the convolutional layer; after the convolution operation, the data is standardized based on Batch_normilization.

3. A physics- and data-driven receiver function inversion apparatus for performing the method described in any one of claims 1-2, characterized in that, The device includes: The module for determining and constructing the model parameters to be optimized is defined, and the objective function for the inversion problem is constructed. The objective function for the inversion problem includes a data fitting term, a model regularization term, and a coupling term that combines data-driven and physics-driven approaches. The coupling term that combines data-driven and physics-driven approaches is a coupling operator between the deep learning inversion model and the BFGS inversion model. The inversion module determines the inversion model by performing iterative optimization on the objective function and the coupling terms of the joint data-driven and physics-driven functions during the inversion process.

4. An electronic device, the electronic device comprising: One or more processors, a memory for storing one or more computer programs; characterized in that the computer programs are configured to be executed by the one or more processors, the programs including steps for performing the physics- and data-driven receiver function inversion method as described in any one of claims 1-2.

5. A storage medium storing a computer program; characterized in that, The program is loaded and executed by a processor to implement the steps of the physical and data-driven receiver function inversion method as described in any one of claims 1-2.

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