Air gun source array inversion optimization method combining deep learning calculation model and particle swarm optimization
By combining deep learning computational models with particle swarm optimization algorithms, the parameters of air gun arrays are rapidly optimized, solving the problems of low computational efficiency and multiple solutions in air gun array design. This achieves efficient and accurate air gun array optimization and obtains the optimal solution for engineering applications.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN ENG UNIV
- Filing Date
- 2026-01-20
- Publication Date
- 2026-05-12
AI Technical Summary
Existing technologies suffer from low computational efficiency, difficulty in inversion, and high variability in the optimization design of air gun arrays. Furthermore, they suffer from severe dimensionality curse problems, making it difficult to obtain the optimal engineering solution quickly and accurately.
By combining deep learning computational models and particle swarm optimization (PSO) algorithms, a high-fidelity physical sample library is constructed. A forward computational model is established through deep neural networks. Combined with a multi-objective constrained PSO inversion framework, the PSO algorithm is used for global optimization to select the optimal air gun array arrangement parameters that meet the target spectrum requirements.
It enables rapid and accurate optimization of air gun array parameters, reduces computation time, automatically selects the optimal solution with the lowest cost and least construction difficulty, solves the problem of multiple solutions, and improves computational efficiency and accuracy.
Smart Images
Figure CN122017986A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of marine geophysical exploration technology, specifically relating to an inversion optimization method for air gun source arrays that combines deep learning computational models and particle swarm optimization algorithms. Background Technology
[0002] As marine exploration enters the ultra-deepwater era, increasingly high-quality seismic wave data has become a crucial resource for accurate detection of seabed geological structures, assessment of oil and gas resources, and guidance of drilling operations. Air gun arrays, as the primary artificial seismic wave source, directly impact the quality and accuracy of exploration data. The arrangement of the air gun array significantly affects its performance, including the spacing between air guns, the placement depth, and the excitation time. The spectral characteristics of the seismic waves excited by the air gun array (such as angular frequency and bandwidth) directly determine the exploration resolution and penetration depth. To meet the exploration requirements of deep-sea strata (e.g., requiring an angular frequency of 3Hz to detect deeper seabed structures), it is necessary to optimize the design of parameters such as the volume, excitation pressure, placement depth, and air gun spacing of the air gun array. However, obtaining an ideal air gun array from existing air gun libraries remains a challenge.
[0003] In terms of calculation and optimization of air gun arrays, the existing technologies mainly have the following problems: (1) Low computational efficiency: Traditional design relies on solving complex nonlinear bubble dynamics equations (such as Gilmore equations). When performing tens of thousands of parameter iteration searches, the computation time is huge and it is difficult to meet the real-time requirements. (2) Difficulty in inversion and multiple solutions: The design of air gun arrays is essentially a nonlinear inverse problem. For a given target pressure wave or spectrum (such as a turning frequency of 3Hz), there are multiple air gun combination schemes that can meet the requirements. Traditional gradient descent inversion algorithms are prone to getting trapped in local optima and cannot effectively screen out the engineering optimal solution (such as the lowest energy consumption and smallest volume). (3) Curse of dimensionality: When the number of air guns increases, the parameters to be optimized increase exponentially, the search space expands sharply, and the traditional empirical trial and error method fails. Therefore, there is an urgent need for an array optimization design method that can quickly and accurately simulate bubble pressure waves and sound pressure level spectrums, effectively solve multiple solutions, and output the engineering optimal solution. Summary of the Invention
[0004] This invention provides an inversion optimization method for air gun source arrays that combines deep learning computational models and particle swarm optimization algorithms, in order to solve the problems of slow computation and strong multiple solutions in existing air gun array optimization design.
[0005] This invention is achieved through the following technical solution: An optimization method for air gun source array inversion combining deep learning computational models and particle swarm optimization algorithm, the optimization method comprising the following steps: Step 1: Construct a high-fidelity physical sample library; Step 2: Construct a forward computation model for the deep neural network and train it; Step 3: Based on the forward calculation model in Step 2, construct a multi-objective constrained particle swarm inversion framework; Step 4: The particle swarm inversion framework with multi-objective constraints in Step 3 is optimized globally using the particle swarm algorithm until the optimal air gun array arrangement combination parameters that meet the target spectrum requirements are obtained.
[0006] Furthermore, step 1 specifically involves generating an input parameter set containing different numbers, volumes, pressures, immersion depths, and spatial positions of air guns using a Latin hypercube sampling strategy, and calculating the corresponding far-field pressure waves and spectra based on the air gun bubble dynamics model using the Zhang equation as output labels.
[0007] Furthermore, step 2 specifically involves the deep neural network being one or a combination of graph neural networks, long short-term memory networks employing attention mechanisms, fully connected neural networks, or Deep Sets networks, trained with air gun array parameters as input and spectral curves as output; the model can establish a fast positive mapping relationship from "array parameters" to "spectral characteristics".
[0008] Furthermore, step 3 specifically involves establishing an inversion optimization design model that integrates engineering constraints with the goal of reducing the corner frequency.
[0009] Furthermore, step 3 specifically includes the following steps: Step 3.1: Define the optimization goal; Step 3.2: Define the fitness function.
[0010] Furthermore, step 3.1 specifically involves assuming the design goal is to obtain an array with a rotation frequency of 3Hz, and requiring the parameters to be adjusted within a fixed parameter range; Step 3.2 specifically involves constructing the following fitness function F(X):
[0011] In the formula, the first term is the spectral error term. Used to force compliance with the 3Hz requirement, where The corner frequency is calculated using the spectrum output by the calculation model. The first term is the correlation coefficient; the second term is the regularization term. The first term is used to select the optimal solution from multiple solutions; the third term is the geometric constraint term. If the air gun spacing d ij Less than the safe distance Dmin A severe penalty will be imposed to prevent the air gun bubbles from merging:
[0012]
[0013] .
[0014] Furthermore, step 4 specifically involves first randomly generating an initial particle swarm, where each particle represents a set of parameters to be optimized; secondly, using a forward deep neural network model to calculate the fitness of each particle; and thirdly, continuously iterating and updating the particle's velocity and position to guide the particle swarm to search for the optimal solution region until the optimal air gun array arrangement combination parameters that meet the target spectrum requirements are obtained.
[0015] Furthermore, step 4 specifically includes the following steps: Step 4.1: Particle encoding and initialization; Step 4.2: Call the forward computation model to perform fitness evaluation; Step 4.3: Individual and Global Optimal Updates; Step 4.4: Iteration of particle position and velocity; Step 4.5: Termination conditions and verification.
[0016] Furthermore, step 4.1 specifically involves particle definition: each particle represents a set of potential air gun array schemes; its position vector X = [ V 1, P 1, x 1, y 1, z 1,…, V N , P N , x N , y N , z N This contains all the parameters to be optimized for N air guns; Population initialization: Within a preset physical boundary, N initial particles are randomly generated; Velocity initialization: Assign an initial search velocity V to each particle. k This determines its exploration step size in the parameter space; Specifically, step 4.2 involves fast forward modeling: in each iteration, all N array parameters in the particle swarm are input in batches into the trained forward proxy model. Instantaneous feedback: The proxy model outputs the far-field spectrum curves corresponding to these N arrays within milliseconds; Calculate the fitness value F(X): Based on the predicted spectrum, calculate the score of each particle using the formula; Specifically, step 4.3 involves the individual extreme value pbest, which records the best fitness position reached by each particle since the search began. Global extreme value gbest: Records the "particle" found in the entire population that is closest to the target spectrum and best meets the engineering constraints; Step 4.4 specifically involves updating the particle state according to the following classical formula to achieve convergence towards the optimal solution:
[0017]
[0018] Physical significance: Particles not only retain inertia, but also tend to converge towards their own historical best and the group's best. Specifically, in step 4.5, when the fitness value corresponding to gbest tends to stabilize and there is no significant improvement in multiple consecutive iterations of the algorithm, it is determined that the result has converged and the search ends; at this time, the obtained gbest is the final determined inversion design scheme.
[0019] An inversion optimization system for air gun source arrays combining deep learning computational models and particle swarm optimization algorithms is disclosed. The optimization system employs the aforementioned method for inverting and optimizing air gun source arrays using deep learning computational models and particle swarm optimization algorithms. The optimization system includes the following steps: Sample library construction module: Constructs a high-fidelity physical sample library; Computational model building module: Constructs and trains a forward computational model of a deep neural network; Particle swarm inversion framework construction module: Based on the forward computational model constructed by the computational model construction module, a multi-objective constrained particle swarm inversion framework is constructed. The computation module uses a framework built on the "particle swarm inversion framework construction module" to perform particle swarm optimization to achieve global optimization until the optimal air gun array arrangement combination parameters that meet the target spectrum requirements are obtained.
[0020] The beneficial effects of this invention are: This invention utilizes the efficient computing power of neural networks and the global search capability of particle swarm optimization to quickly derive the optimal array parameters that satisfy specific spectral characteristics.
[0021] This invention utilizes a trained neural network to replace the solution of complex differential equations, reducing the time for a single forward modeling computation from seconds to milliseconds, thus enabling large-scale iterative optimization. In the particle swarm optimization (PSO) evaluation process, this invention adds a "regularization penalty term" to the fitness function, such as limiting the total structural volume. This transforms the problem of having multiple solutions satisfying the optimization objective (reducing the corner frequency to below 3Hz) into a constrained optimization problem. This method can automatically select the optimal solution with the lowest cost and least construction difficulty from numerous feasible solutions.
[0022] This invention combines LSTM models and their variants, graph neural networks (GNNs), etc., to train on small-scale array data and achieve parameter optimization for larger-scale air gun arrays. Attached Figure Description
[0023] Figure 1 This is a flowchart of the method of the present invention.
[0024] Figure 2 This is a schematic diagram of the neural network model architecture for the forward computation (i.e., predicting the spectrum from parameters) of the present invention.
[0025] Figure 3 This is a schematic diagram illustrating the interaction between the particle swarm optimization algorithm and the computational model of the present invention.
[0026] Figure 4 These are comparative diagrams of the spectrum curves of the air gun array before and after optimization according to the present invention. (a) is a comparison diagram of the spectrum before and after optimization of the 4-gun array, and (b) is a comparison diagram of the spectrum before and after optimization of the 3-gun array. Detailed Implementation
[0027] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.
[0028] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.
[0029] It should also be understood that the terminology used in this application specification is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this application specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.
[0030] The following is in conjunction with the appendix to this application specification. Figure 1-4 The technical solutions in the embodiments of this application are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0031] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.
[0032] Implementation Method 1 This embodiment provides an inversion and optimization method for air gun source arrays that combines a deep learning computational model with a particle swarm optimization algorithm. The optimization method includes the following steps: Step 1: Construct a high-fidelity physical sample library; Step 2: Construct a forward computation model for the deep neural network and train it; Step 3: Based on the forward calculation model in Step 2, construct a multi-objective constrained particle swarm inversion framework; Step 4: The particle swarm inversion framework with multi-objective constraints in Step 3 is optimized globally using the particle swarm algorithm until the optimal air gun array arrangement combination parameters that meet the target spectrum requirements are obtained.
[0033] Furthermore, step 1 specifically involves generating an input parameter set containing different numbers, volumes, pressures, immersion depths, and spatial positions of air guns using a Latin hypercube sampling strategy, and calculating the corresponding far-field pressure waves and spectra based on the air gun bubble dynamics model using the Zhang equation as output labels.
[0034] Step 1.1: Sample Space Definition and Data Generation Data were obtained using an air gun bubble dynamics model based on the Zhang equation.
[0035] Input Feature (X): Define the air gun array parameter vector X = [ V 1, P 1, x 1, y 1, z 1,…, V N , P N , x N , y N ,z N Where N is the number of air guns. V For volume, P For pressure, ( x , y , z () represents the coordinates for the air gun's placement.
[0036] Output characteristic (Y): Pressure wavelet curve based on far-field measurement points P ( r (Sampling interval 0.5ms), the sound pressure level spectrum curve is obtained after Fourier transform. S ( f ).
[0037] Sampling strategy: Use Latin hypercube sampling (LHS) to generate K sets of samples (e.g., K=3000) to ensure that the samples are uniformly distributed in the multidimensional parameter space.
[0038] Furthermore, step 2 specifically involves the deep neural network being one or a combination of graph neural networks, long short-term memory networks employing attention mechanisms, fully connected neural networks, or Deep Sets networks, trained with air gun array parameters as input and spectral curves as output; the model can establish a fast positive mapping relationship from "array parameters" to "spectral characteristics".
[0039] To address the issue of potential variations in the number of air guns N, this embodiment preferably employs a Bi-LSTM model architecture.
[0040] Sequence construction: The characteristics of each air gun [ V 1, P 1, x 1, y 1, z 1] Arranged in a preset order, forming a shape whose length varies with the number of air guns. N A dynamically adjusted one-dimensional sequence; for the interaction between air guns, the coordinates of the air guns ( x , y , z This implies the characteristics of an air gun, and the sequence simultaneously represents the attributes of a single air gun and the correlation between air guns.
[0041] Network training: The sample dataset generated based on the air gun bubble dynamics model is divided into a training set and a validation set, and the mean squared error (MSE) is used as the loss function; the model parameters are iteratively optimized through backpropagation until the validation set loss converges.
[0042] Once trained, the network becomes a "forward computation model," which takes an air gun array parameter sequence of arbitrary length (corresponding to different numbers of air guns N) as input and outputs the predicted spectrum in milliseconds.
[0043] Furthermore, step 3 specifically involves establishing an inversion optimization design model that integrates engineering constraints with the goal of reducing the corner frequency.
[0044] Furthermore, step 3 specifically includes the following steps: Step 3.1: Define the optimization goal; Assume the design goal is to obtain an array with a rotation frequency of 3Hz, and the parameters need to be adjusted within a fixed parameter range.
[0045] Step 3.2: Define the fitness function.
[0046] This is the core of solving the "multiple solutions" problem; construct the following fitness function F(X) (the goal is to minimize F):
[0047] In the formula, the first term is the spectral error term. This is used to force compliance with the 3Hz requirement. The corner frequency is calculated using the spectrum output by the calculation model. The first term is the correlation coefficient. The second term is the regularization term. This term is used to select the optimal solution from multiple solutions. If two arrays can both achieve 3Hz, this term forces the algorithm to choose the one with the smaller total volume, thus not only meeting the target but also saving gas and costs. The third term is a geometric constraint term. This is to ensure physical feasibility. (Regarding the air gun spacing...) d ij Less than the safe distance D min (e.g., 2m) will inflict a huge penalty to prevent the air gun bubbles from merging.
[0048]
[0049]
[0050] .
[0051] Furthermore, step 4 specifically involves first randomly generating an initial particle swarm, where each particle represents a set of parameters to be optimized; secondly, using a forward deep neural network model to calculate the fitness of each particle; and thirdly, continuously iterating and updating the particle's velocity and position to guide the particle swarm to search for the optimal solution region until the optimal air gun array arrangement combination parameters that meet the target spectrum requirements are obtained.
[0052] In the parameter search space, each specific air gun array configuration can be regarded as a "particle". By simulating the foraging behavior of bird flocks, the particle swarm is guided to move towards the target that meets the 3Hz angular frequency requirement and has the lowest engineering cost.
[0053] Furthermore, step 4 specifically includes the following steps: Step 4.1: Particle Encoding and Initialization; Particle Definition: Each particle represents a set of potential air gun array schemes. Its position vector X=[ V 1, P 1, x 1, y 1, z 1,…, V N , P N , x N , y N , z N This contains all the parameters to be optimized for N air guns.
[0054] Population initialization: at a preset physical boundary (e.g., volume V ranging from 500 to 5000 inches). 3 Within the pressure range of 600~1500Psi, N initial particles are randomly generated (usually N=30~100).
[0055] Velocity initialization: Assign an initial search velocity V to each particle. k This determines its exploration step size in the parameter space.
[0056] Step 4.2: Call the forward computation model to evaluate fitness; the particle swarm algorithm itself does not have physical computation capabilities, it needs to continuously utilize the forward computation model.
[0057] Fast forward modeling: In each iteration, all N array parameters in the particle swarm are input in batches into the pre-trained forward surrogate model (GNN / DNN / LSTM).
[0058] Instantaneous feedback: The proxy model outputs the far-field spectrum curves corresponding to these N arrays within milliseconds.
[0059] Calculate the fitness value F(X): Based on the predicted spectrum, calculate the score of each particle using a formula (including a 3Hz error term, a total volume penalty term, a minimum spacing constraint term, etc.).
[0060] Step 4.3: Individual and Global Optimal Updates; Individual Extreme Value (pbest): Records the best fitness position reached by each particle since the search began.
[0061] Global extreme value (gbest): Records the "particle" found in the entire population that is closest to the target spectrum and best meets the engineering constraints.
[0062] Step 4.4: Particle position and velocity iteration; update the particle state according to the following classical formula to achieve convergence towards the optimal solution:
[0063]
[0064] Physical significance: Particles not only retain inertia ( w Furthermore, it will tend to converge towards its own historical best solution (self-awareness c1) and the group's best solution (social experience c2). By dynamically adjusting the learning factors of individuals and groups, the algorithm's ability to escape local optima and explore regions of better solutions can be effectively improved.
[0065] Step 4.5: Termination Condition and Verification; When the fitness value corresponding to gbest tends to stabilize and there is no significant improvement in multiple consecutive iterations, it is determined that the result has converged and the search ends; At this time, the obtained gbest is the final determined inversion design scheme.
[0066] like Figure 4 The image shows a comparison of the spectrum curves of the air gun array before and after optimization. The table shows a comparison of the parameters of the air gun array before and after optimization. The forward calculation model for the demonstration case uses a Bi-LSTM model, and the optimization objective is to reduce the corner frequency to below 3Hz. The adjustment parameters for the four-gun array are the air gun volume (limited to 1000~5000 in). 3 (Between), the adjustment parameters for the three-gun array are the air gun volume and the excitation pressure (volume limited to 1000~5000 in). 3 (The pressure is limited to between 600 and 1500 psi).
[0067] Table 1: Figure 4 Comparison of parameters of the air gun array before and after optimization under the shown working conditions
[0068] Implementation Method 2 This embodiment provides an airgun source array inversion optimization system combining a deep learning computational model and a particle swarm optimization algorithm. The optimization system uses the airgun source array inversion optimization method combining a deep learning computational model and a particle swarm optimization algorithm as described in Embodiment 1. The optimization system includes the following steps: Sample library construction module: Constructs a high-fidelity physical sample library; Computational model building module: Constructs and trains a forward computational model of a deep neural network; Particle swarm inversion framework construction module: Based on the forward computational model constructed by the computational model construction module, a multi-objective constrained particle swarm inversion framework is constructed. The computation module uses a framework built on the "particle swarm inversion framework construction module" to perform particle swarm optimization to achieve global optimization until the optimal combination of air gun array arrangement parameters that meet the target spectrum requirements are obtained.
[0069] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.
Claims
1. A method for inverting and optimizing air gun source arrays by combining deep learning computational models and particle swarm optimization, characterized in that, The optimization method includes the following steps: Step 1: Construct a high-fidelity physical sample library; Step 2: Construct a forward computation model for the deep neural network and train it; Step 3: Based on the forward calculation model in Step 2, construct a multi-objective constrained particle swarm inversion framework; Step 4: The particle swarm inversion framework with multi-objective constraints in Step 3 is optimized globally using the particle swarm algorithm until the optimal air gun array arrangement combination parameters that meet the target spectrum requirements are obtained.
2. The air gun source array inversion optimization method according to claim 1, characterized in that, Step 1 specifically involves using a Latin hypercube sampling strategy to generate a set of input parameters containing different numbers, volumes, pressures, immersion depths, and spatial positions of air guns, and calculating the corresponding far-field pressure waves and spectra based on the air gun bubble dynamics model using the Zhang equation as output labels.
3. The air gun source array inversion and optimization method according to claim 1, characterized in that, Step 2 specifically involves the deep neural network being one or a combination of graph neural networks, long short-term memory networks employing attention mechanisms, fully connected neural networks, or Deep Sets networks, trained with air gun array parameters as input and spectral curves as output; the model can establish a fast positive mapping relationship from "array parameters" to "spectral characteristics".
4. The air gun source array inversion and optimization method according to claim 1, characterized in that, Step 3 specifically involves establishing an inversion optimization design model that integrates engineering constraints and aims to reduce the corner frequency.
5. The air gun source array inversion and optimization method according to claim 4, characterized in that, Step 3 specifically includes the following steps: Step 3.1: Define the optimization goal; Step 3.2: Define the fitness function.
6. The air gun source array inversion and optimization method according to claim 5, characterized in that, Specifically, step 3.1 assumes that the design goal is to obtain an array with a rotation frequency of 3Hz, and that the parameters are to be adjusted within a fixed parameter range. Step 3.2 specifically involves constructing the following fitness function F(X): In the formula, the first term is the spectral error term. Used to force compliance with the 3Hz requirement, where The corner frequency is calculated using the spectrum output by the calculation model. The first term is the correlation coefficient; the second term is the regularization term. The first term is used to select the optimal solution from multiple solutions; the third term is the geometric constraint term. If the air gun spacing d ij Less than the safe distance D min A severe penalty will be imposed to prevent the air gun bubbles from merging: 。 7. The air gun source array inversion optimization method according to claim 1, characterized in that, Step 4 specifically involves: firstly, randomly generating an initial particle swarm, where each particle represents a set of parameters to be optimized; secondly, using a forward deep neural network model to calculate the fitness of each particle; and thirdly, continuously iterating and updating the particle's velocity and position to guide the particle swarm to search for the optimal solution region until the optimal air gun array arrangement combination parameters that meet the target spectrum requirements are obtained.
8. The air gun source array inversion and optimization method according to claim 7, characterized in that, Step 4 specifically includes the following steps: Step 4.1: Particle encoding and initialization; Step 4.2: Call the forward computation model to perform fitness evaluation; Step 4.3: Individual and Global Optimal Updates; Step 4.4: Iteration of particle position and velocity; Step 4.5: Termination conditions and verification.
9. The air gun source array inversion and optimization method according to claim 8, characterized in that, Specifically, step 4.1 defines a particle as follows: each particle represents a set of potential air gun array schemes. Its position vector X=[ V 1, P 1, x 1, y 1, z 1,…, V N , P N , x N , y N , z N This contains all the parameters to be optimized for N air guns; Population initialization: Within a preset physical boundary, N initial particles are randomly generated; Velocity initialization: Assign an initial search velocity V to each particle. k This determines its exploration step size in the parameter space; Specifically, step 4.2 involves fast forward modeling: in each iteration, all N array parameters in the particle swarm are input in batches into the trained forward proxy model. Instantaneous feedback: The proxy model outputs the far-field spectrum curves corresponding to these N arrays within milliseconds; Calculate the fitness value F(X): Based on the predicted spectrum, calculate the score of each particle using the formula; Specifically, step 4.3 involves the individual extreme value pbest, which records the best fitness position reached by each particle since the search began. Global extreme value gbest: Records the "particle" found in the entire swarm that is closest to the target spectrum and best meets the engineering constraints; Step 4.4 specifically involves updating the particle state according to the following classical formula to achieve convergence towards the optimal solution: Physical significance: Particles not only retain inertia, but also tend to converge towards their own historical best and the group's best. Specifically, in step 4.5, when the fitness value corresponding to gbest tends to stabilize and there is no significant improvement in multiple consecutive iterations of the algorithm, it is determined that the result has converged and the search ends; at this time, the obtained gbest is the final determined inversion design scheme.
10. A system for inverting and optimizing an air gun source array by combining a deep learning computational model and a particle swarm optimization algorithm, characterized in that, The optimization system uses the air gun source array inversion optimization method combining deep learning computational models and particle swarm optimization as described in any one of claims 1-9, and the optimization system includes the following steps: Sample library construction module: Constructs a high-fidelity physical sample library; Computational model building module: Constructs and trains a forward computational model of a deep neural network; Particle swarm inversion framework construction module: Based on the forward computational model constructed by the computational model construction module, a multi-objective constrained particle swarm inversion framework is constructed. The computation module uses a framework built on the "particle swarm inversion framework construction module" to perform particle swarm optimization to achieve global optimization until the optimal combination of air gun array arrangement parameters that meet the target spectrum requirements are obtained.