A travel time tomography method and system

Abstract

The application discloses a travel time tomography method and system, belongs to the technical field of exploration geophysics research, and utilizes a travel function equation to establish a mapping relationship between travel time and a velocity model; a Bayesian-fusion physical mechanism neural network structure based on the travel function equation is designed, Bayesian-fusion physical mechanism neural network parameters are trained based on a Bayesian inference algorithm, posterior distribution samples are obtained, an inversion velocity field of all samples is averaged, and finally, a travel time tomography inversion result is formed. The application has high inversion precision for the velocity model and excellent uncertainty quantification capability.

Description

Technical Field

[0001] This invention belongs to the field of exploration geophysics research technology, specifically relating to a travel-time tomography imaging method and system. Background Technology

[0002] Seismic tomography is a data inference technique that uses travel-time information contained in seismic records to infer subsurface structures. In recent years, due to improvements in data scale and algorithms, neural networks have received considerable attention for their advantages such as the ability to process large-scale data, nonlinear mapping, and noise immunity, and have been extensively and deeply studied in the field of geological inversion. However, in seismic exploration problems, the high cost of measurement data and the difficulty in obtaining large amounts of measurement data limit the accuracy of neural network inversion results.

[0003] In 1972, Aki et al. pioneered the use of seismic tomography to study geological structures. The process function equation, as a high-frequency approximation of the wave equation, is widely used in travel-time tomography. Due to the nonlinearity of the process function equation, numerical methods are usually required for solving it. The two most commonly used numerical methods are the fast travel method and the fast scan method. However, the computational accuracy of travel-time tomography using traditional numerical methods largely depends on the discretization scheme of time and space and the fineness of the mesh generation, and is limited by the selection of the initial model and data noise, thus restricting its practical application.

[0004] In recent years, deep learning has received considerable attention for solving inversion problems based on partial differential equations (PDEs). However, the performance of purely data-driven neural networks largely depends on the amount of training data, and in the field of seismic exploration, acquiring measurement data is often extremely costly. To address this challenge, Raissi proposed the Fusion Physical Mechanism Neural Network (PINN) as a new framework for solving both forward and inverse PDE problems. PINN reduces the network's dependence on training data by integrating prior physical information into the network and adding the residual terms of the governing equations to the network's loss function. In exploration geophysics, Waheed et al. used PINN to solve isotropic equations, establishing a framework for solving inversion problems of isotropic equations. PINN, combined with equations, can solve inverse problems under sparse data conditions, and the PINN method is more flexible and accurate than traditional methods because it does not rely on initial velocity models or mesh generation.

[0005] Due to the scarcity of training data and the presence of noise, neural networks often exhibit multiple solutions when dealing with complex geological structures. However, research on quantifying the uncertainty of training results in traditional networks is limited. Yang et al. proposed an algorithm using Bayesian-Fused Physical Mechanism Neural Network (BPINN) to solve partial differential equation problems with noisy data. BPINN not only quantifies the uncertainty caused by noisy data within the Bayesian framework but also avoids overfitting, achieving more accurate predictions than PINN under high noise conditions. BPINN uses Bayesian inference to estimate the posterior distribution. Inference algorithms mainly include variational inference (VI) and Markov chain Monte Carlo (MCMC). Variational inference approximates the true distribution by minimizing the relative entropy (KL) between the selected distribution family and the true posterior distribution. However, the accuracy of variational inference depends on the selected variational distribution family and may fail to accurately capture the posterior distribution. The Markov chain Monte Carlo method approximates the target distribution by constructing a Markov chain with its equilibrium distribution as the objective. However, its sampling efficiency is too low due to the limitation of random walks, especially in high-dimensional spaces. The Markov chain Monte Carlo (HMC) method based on Hamiltonian dynamics was proposed to solve the random walk phenomenon. HMC calculates the future state of the Markov chain by simulating the trajectory of particles in a physical system, which can explore high-dimensional space more efficiently. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a travel-time tomography method and system that addresses the shortcomings of the prior art. Based on the Hamiltonian Monte Carlo algorithm, the method calculates the posterior distribution of network parameters, realizes the inversion of the velocity model and measures the uncertainty of the inversion results, and analyzes the accuracy and effectiveness of the method. This invention is used to solve the technical problem that traditional neural networks cannot evaluate the uncertainty of prediction results caused by data noise and data scarcity.

[0007] The present invention adopts the following technical solution:

[0008] A travel-time tomography method includes the following steps:

[0009] Determining Bayesian-fusion physical mechanism neural networks based on procedural functional equations;

[0010] The parameters of the Bayesian-fusion physical mechanism neural network are trained based on the Bayesian inference algorithm to obtain the posterior distribution samples. The inversion velocity field of all samples is averaged to form the final travel-time tomography inversion result.

[0011] Preferably, the functional equation is as follows:

[0012]

[0013] in, Indicates the location from the epicenter to the domain any point in When they left, For the time factor, Indicates in The speed defined in [the text].

[0014] Preferably, the Bayesian-fusion physical mechanism neural network comprises two independent fully connected neural networks. and , which are used to approximate the travel time field and the velocity field, respectively.

[0015] Preferably, the Bayesian formula is as follows:

[0016]

[0017] in, Represents observational data, Representative function equation ， Represents network parameters; The prior probability distribution of the parameters of the Bayesian-fusion physical mechanism neural network model; The likelihood distribution represents the distribution of network parameters. Given the observed data sum function equation The predicted probability; Representative on The marginal distribution.

[0018] Preferably, the Bayesian formula is calculated based on a Bayesian inference algorithm. The Bayesian inference algorithm uses the Hamiltonian Monte Carlo algorithm, which uses the trajectory of particles in the Hamiltonian mechanics system to simulate the sampling process. The specific steps are as follows:

[0019] Establish the relationship between Hamiltonian energy and target distribution;

[0020] Determine the method for solving Hamilton's equations;

[0021] Determine the error correction method.

[0022] Preferably, the relationship between Hamiltonian energy and target distribution is as follows:

[0023]

[0024] in, For neural network parameters, As an auxiliary momentum variable, for and The joint probability distribution, Hamiltonian energy.

[0025] Preferably, the Hamiltonian equation is solved using a discrete method. The Hamiltonian equation is as follows:

[0026]

[0027] in, For neural network parameters, As an auxiliary momentum variable, For the quality matrix, This is the Hamiltonian potential.

[0028] Preferably, the error correction adopts the Metropolis-Hasting criterion, which has the following form:

[0029]

[0030] in, To accept probability, To update the Hamiltonian energy by L times, This is the initial Hamiltonian energy before the k-th sampling.

[0031] Preferably, based on samples obtained from a Bayesian-fusion physical mechanism neural network, the final travel-time tomography inversion velocity field is obtained by calculating the mean of all samples, and the uncertainty of the inversion velocity model results is measured by calculating the variance of all samples. The posterior sample mean and variance are specifically as follows:

[0032]

[0033] in, For network input, For network output, For neural network parameters, For observation data, To obtain neural network parameters The number of samples sampled from the posterior distribution. express The i A Bayesian neural network with parameters corresponding to each sample.

[0034] In a second aspect, embodiments of the present invention provide a travel-time tomography system, comprising:

[0035] The network module defines a Bayesian-fusion physical mechanism neural network based on procedural functional equations.

[0036] The output module trains the parameters of the Bayesian-fusion physical mechanism neural network based on the Bayesian inference algorithm to obtain the posterior distribution samples, averages the inversion velocity field of all samples, and constitutes the final travel-time tomography inversion result.

[0037] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described walk-time tomography method.

[0038] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described travel-time tomography method.

[0039] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described travel-time tomography method.

[0040] In a sixth aspect, embodiments of the present invention provide an electronic device including a computer program, which, when executed by the electronic device, implements the steps of the above-described travel-time tomography method.

[0041] Compared with the prior art, the present invention has at least the following beneficial effects:

[0042] A travel-time tomography method is proposed, which establishes a mapping relationship between travel time and velocity model using a functional equation; designs a Bayesian-fusion physical mechanism neural network structure based on the functional equation, and then confirms the Bayesian formula under this network framework; trains the network parameters of the Bayesian-fusion physical mechanism neural network using a Bayesian inference algorithm to obtain the posterior distribution of the network parameters; processes the obtained samples to obtain the final travel-time tomography inversion result and the corresponding uncertainty quantification result; this invention does not rely on the initial velocity model during the inversion process, and has reasonable uncertainty quantification capability, realizing the inversion of the velocity model and the measurement of uncertainty of the inversion result.

[0043] Furthermore, the network structure incorporates a fused physical information neural network, aiming to reduce reliance on data information by introducing prior physical information as a constraint, without depending on a good initial velocity model. The network structure also incorporates a Bayesian neural network, aiming to introduce a probabilistic model to handle problems that traditional neural networks struggle with, such as uncertainty, generalization issues, and the integration of prior knowledge.

[0044] Furthermore, Bayes' formula is extended to allow the application of Bayes' theorem to neural networks, enabling them to perform Bayesian inference using datasets and procedural equations. Probability distributions include prior distributions and likelihood distributions, with the aim of representing the target distribution using these distributions according to Bayes' theorem.

[0045] Furthermore, the sampling process can be simulated by using the particle trajectories in the Hamiltonian mechanics system, thereby improving sampling efficiency;

[0046] Furthermore, by approximately solving the Hamiltonian equation to update the state of the particles and completing the sampling process, the problem that the Hamiltonian equation cannot obtain a theoretical solution is solved.

[0047] Furthermore, the Hamiltonian energy conservation violation caused by discrete numerical integration methods during application can be corrected by refusing parameter updates that cause energy non-conservation, thus ensuring the convergence of the results.

[0048] It is understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0049] In summary, this invention provides high accuracy in velocity model inversion and excellent uncertainty quantification capabilities.

[0050] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0051] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 A schematic diagram of the BPINN structure for travel-time tomography.

[0053] Figure 2 shows the output results of BPINN for the inclusion model, where (a) is the velocity field of the inclusion model, (b) is the inverted velocity field, and (c) is the uncertainty quantification of the inverted velocity field.

[0054] Figure 3 shows the output results of BPINN on the checkerboard model, where (a) is the velocity field of the checkerboard model, (b) is the inverted velocity field, and (c) is the uncertainty quantification of the inverted velocity field.

[0055] Figure 4 shows the output results of BPINN on the arch model, where (a) is the velocity field of the arch model, (b) is the inverted velocity field, and (c) is the uncertainty quantification of the inverted velocity field.

[0056] Figure 5 A schematic diagram of a computer device provided in an embodiment of the present invention;

[0057] Figure 6 This is a block diagram of an electronic device according to an embodiment of the present invention;

[0058] Figure 7 This is a schematic diagram of a travel-time tomography method. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0061] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this 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.

[0062] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0063] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0064] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0065] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0066] This invention provides a travel-time tomography method based on a Bayesian-fusion physical mechanism neural network. By introducing a functional equation as a physical constraint term, the Bayesian-fusion physical mechanism neural network uses travel-time information obtained from a limited number of receivers to invert the velocity structure of the subsurface medium. Furthermore, the Bayesian-fusion physical mechanism neural network is used to measure the uncertainty of the inverted velocity model results, providing a basis for the acceptance of the inversion results or further processing.

[0067] Example 1

[0068] Please see Figure 7 This invention relates to a travel-time tomography method, comprising the following steps:

[0069] S1. Determine the equation of the process function;

[0070] Traveltime tomography establishes a mapping relationship from traveltime to subsurface velocity structure based on ray theory. The equation of process function, as a high-frequency approximation of the wave equation, establishes the relationship between traveltime and velocity models.

[0071]

[0072] in, Indicates the location from the epicenter to the domain any point in When they left, Indicates in The speed defined in [the text].

[0073] When calculating the travel time at the earthquake source, the solution of the equation at the source is singular. To improve the accuracy of the solution of the equation, the following steps are taken: Factorize into the following two factors:

[0074]

[0075] Combining the two equations yields the residuals of the factorization functional equation. :

[0076]

[0077] S2. Determine the structure of the Bayesian-fusion physical mechanism neural network;

[0078] Standard PINN is achieved through... Parameterized Neural Networks Fitting the true solution determined by the partial differential equation However, the initialization and training of neural network parameters are inherently uncertain, resulting in variations in output for each training iteration. Furthermore, due to the scarcity of training data and the presence of noise, neural networks often exhibit multiple solutions when dealing with complex geological structures.

[0079] Therefore, the inversion results of travel-time tomography using PINN contain high uncertainty. BNNs, by introducing a probabilistic model, possess advantages over traditional neural networks in handling uncertainty, generalization problems, and integrating prior knowledge. To leverage the advantages of BNN in uncertainty quantification, a Bayesian inference method is introduced based on PINN, combining neural network parameters generated from a specific probability distribution to solve for the target distribution—this is the Bayesian-Fused Physical Mechanism Neural Network (BPINN). BPINN is then used for travel-time tomography inversion. BPINN employs two independent fully connected neural networks. and To approximate the travel time field and velocity field, network parameters For random variables, in addition to using the observed data as constraints, additional physical constraints are introduced and Bayesian inference is used to obtain the posterior distribution of the model.

[0080] S3. Combining the functional equation obtained in step S1, determine the Bayesian formula under the Bayesian-fusion physical mechanism neural network framework obtained in step S2.

[0081] Bayesian Neural Networks (BNNs) use network parameters As a random variable, Bayesian inference is used to obtain the posterior distribution of the model. The Bayesian formula in the context of deep learning describes the method for calculating the posterior distribution:

[0082]

[0083] in, Represents observational data, Represents network parameters; Let be the prior probability distribution of the network model parameters. Without loss of generality, the prior distribution is usually considered to be the standard normal distribution. The likelihood distribution represents the distribution of network parameters. Given the observed data The predicted probability; Representative on The marginal distribution, due to its relationship with the parameter It is irrelevant and is usually treated as a normalization constant.

[0084] Within the BPINN architecture, in addition to expressing the likelihood estimate of the goodness of fit to the data... In addition, a likelihood estimate of the fit to the given physical equations was added. The posterior distribution can be expressed using Bayes' theorem as:

[0085]

[0086] S4. Determine the Bayesian inference algorithm;

[0087] Bayesian inference methods employ the Hamiltonian Monte Carlo algorithm. Directly solving for the posterior distribution in high-dimensional neural networks is extremely difficult. Researchers have introduced relevant statistical theories, using sampling or fitting to obtain the distribution of the target probability (posterior probability). Markov Chain Monte Carlo (MCMC) is a common Bayesian inference algorithm. MCMC approximates the target distribution by sampling from the current posterior probability based on Markov chains. However, general Markov Chain Monte Carlo methods are prone to random walks due to the high dimensionality of the problem, leading to low sampling efficiency. The Hamiltonian Monte Carlo (HMC) algorithm is an optimization of the Markov Chain Monte Carlo algorithm. This algorithm uses the trajectory of particles in a Hamiltonian mechanics system to simulate the sampling process, effectively avoiding random walks and improving sampling efficiency.

[0088] S401. Establish the relationship between Hamiltonian energy and target distribution;

[0089] The HMC algorithm uses network model parameters Viewed as the mechanical motion of a particle, the particle moves from its current state along a certain trajectory to a new state, and this trajectory follows Hamilton's dynamical equations: the particle's potential energy... With kinetic energy The sum Remain unchanged. Assume a given number of observations. Potential energy is defined as:

[0090]

[0091] HMC introduces an auxiliary momentum variable To construct kinetic energy:

[0092]

[0093] in, It is a mass matrix, usually set as the identity matrix. ,variable Sampling is performed from a standard normal distribution. Then, the HMC is based on the joint probability density distribution. Post-hoc sampling is performed:

[0094]

[0095] Among them, potential energy It is directly related to the target posterior distribution, while the auxiliary variable The samples were discarded, which ensured the network parameters were correct. The marginal distribution of the sample is the target posterior distribution. .

[0096] S402. Determine the method for solving the Hamiltonian equation;

[0097] The samples were generated based on Hamilton's equation.

[0098]

[0099] Specifically, Hamiltonian systems theoretically need to maintain a constant Hamiltonian energy during motion updates. However, in practical applications, the Hamiltonian equation cannot be solved analytically; it can only be approximated using discretization methods. The most commonly used discretization method is the leap-frog method, where samples are generated by leap-frog at time steps of [missing information]. Iterative updates

[0100]

[0101] S403. Determine the error correction method;

[0102] Discrete numerical integration methods inevitably violate Hamiltonian energy conservation during application. Therefore, a correction method is needed after the update to reduce bias, namely the Metropolis-Hasting criterion. This criterion guarantees convergence by rejecting parameter updates that violate energy conservation. Its specific form is as follows:

[0103]

[0104] in, To accept probability, To update the Hamiltonian energy by L times, This represents the initial Hamiltonian energy before the k-th sampling. If a new state is accepted... Then the new state Replace the initial state Otherwise, the state will remain in the initial state. constant.

[0105] S5. Calculate the Bayesian formula obtained in step S3 using the Bayesian inference algorithm obtained in step S4 to obtain the posterior distribution sample.

[0106] Once the network has a specific dataset After training, the predicted results and associated uncertainties can be approximated using the posterior sample mean and variance:

[0107]

[0108] in, The values ​​represent respectively The parameters of the Bayesian neural network corresponding to the i-th sample. From neural network parameters The number of samples drawn from the posterior distribution. and These are the input and output of a neural network.

[0109] Those skilled in the art will understand that various aspects of the present invention can be implemented as systems, methods, or program products. Therefore, various aspects of the present invention can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "platform."

[0110] Example 2

[0111] The present invention provides a time-travel tomography system, which can be used to implement the above-mentioned time-travel tomography method. Specifically, the time-travel tomography system includes a network module and an output module.

[0112] Among them, the network module is determined to be a Bayesian-fusion physical mechanism neural network based on the procedural function equation;

[0113] The output module trains the parameters of the Bayesian-fusion physical mechanism neural network based on the Bayesian inference algorithm to obtain the posterior distribution samples, averages the inversion velocity field of all samples, and constitutes the final travel-time tomography inversion result.

[0114] Example 3

[0115] This invention provides a terminal device comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used for the operation of a walk-time tomography method, including:

[0116] The Bayesian-fusion physical mechanism neural network is determined based on the equation of process; the parameters of the Bayesian-fusion physical mechanism neural network are trained based on the Bayesian inference algorithm to obtain the posterior distribution samples, and the inversion velocity field of all samples is averaged to form the final travel-time tomography inversion result.

[0117] Please see Figure 5The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the processor 61 executes the computer program 63, it implements the travel-time tomography method described in this embodiment. To avoid repetition, these details are not elaborated here. Alternatively, when the processor 61 executes the computer program 63, it implements the functions of each model / unit in the travel-time tomography system of this embodiment. To avoid repetition, these details are not elaborated here.

[0118] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 5 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0119] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processing units (GPUs), tensor processing units (TPUs), digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0120] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0121] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0122] Please see Figure 6 The terminal device is an electronic device 600, which is manifested in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including storage unit 620 and processing unit 610), a display unit 640, etc.

[0123] The storage unit stores program code, which can be executed by the processing unit 610 to perform the steps described in the method section of this specification according to various exemplary embodiments of the present invention. For example, the processing unit 610 can perform actions such as... Figure 7 The steps are shown in the figure.

[0124] Storage unit 620 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 6201 and / or cache memory 6202, and may further include a read-only memory (ROM) 6203.

[0125] Storage unit 620 may also include a program / utility 6204 having a set (at least one) program module 6205, such program module 6205 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0126] Bus 630 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0127] Electronic device 600 can also communicate with one or more external devices 700 (e.g., keyboard, pointing device, Bluetooth device, etc.), and with one or more devices that enable a user to interact with electronic device 600, and / or with any device that enables electronic device 600 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 650. Furthermore, electronic device 600 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 660. Network adapter 660 can communicate with other modules of electronic device 600 via bus 630. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms.

[0128] Example 4

[0129] This invention also provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both built-in storage media in the terminal device and extended storage media supported by the terminal device; it can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor, which can be one or more computer programs (including program code). It should be noted that more specific examples (a non-exhaustive list) of the computer-readable storage medium include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0130] Computer-readable storage media also include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium that can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0131] Program code for performing the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0132] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the travel-time tomography method in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps:

[0133] The Bayesian-fusion physical mechanism neural network is determined based on the procedural function equation; the network parameters of the Bayesian-fusion physical mechanism neural network are trained based on the Bayesian inference algorithm to obtain the posterior distribution samples, and the inversion velocity field of all samples is averaged to form the final travel-time tomography inversion result.

[0134] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0135] Example

[0136] This example studies the use of BPINN for walk-time tomography inversion and uncertainty quantification of inclusion, checkerboard, and arch models.

[0137] Please see Figure 1 , Figure 1 This is a schematic diagram of the BPINN structure for travel-time tomography. This example uses two independent fully connected neural networks to approximate the travel-time field. and velocity field For the time-travel network, the neural network has 3 hidden layers, each with 20 neurons, and uses the tanh activation function. For the velocity network, the neural network has 2 hidden layers, each with 50 neurons, using the tanh activation function and normalizing the network output using the sigmoid activation function.

[0138] Please refer to Figure 2. Figure 2(a) is a schematic diagram of the velocity field distribution of the inclusion model. In the inclusion model, 5 sources (marked in black) and 51 receivers (marked in red) are set at the left boundary (X=0 km) and the right boundary (X=2 km), respectively. Figure 2(b) shows the inversion results of the inclusion model by BPINN. It can be seen that BPINN has restored the shape and values ​​of the inclusion model. Figure 2(c) shows the uncertainty quantification of the inverted velocity model output by BPINN. The uncertainty is mainly concentrated in the high-speed body region without travel time information constraints, showing a reasonable uncertainty distribution.

[0139] Please refer to Figure 3. Furthermore, we studied a more complex checkerboard model. Figure 3(a) is a schematic diagram of the velocity field distribution of the checkerboard model. In the checkerboard model, 5 seismic sources (marked in black) and 101 receivers (marked in red) were set at the left boundary (X=0 km) and the right boundary (X=2 km), respectively. Figure 3(b) shows the inversion results of the checkerboard model by BPINN. It can be seen that BPINN can capture the location and magnitude of each velocity region. Figure 3(c) shows the uncertainty quantification of the inverted velocity model output by BPINN. Regions with high uncertainty correspond to regions with poor velocity field inversion, which proves the rationality of the method of this invention in quantifying uncertainty.

[0140] Please refer to Figure 4. Figure 4(a) is a schematic diagram of the velocity field distribution of the Arch model. Eleven seismic sources (marked in black) are evenly distributed on the surface of the model (Z=0 km), and 121 receivers (marked in red) are also evenly distributed on the surface of the model (Z=0 km). Figure 4(b) shows the inversion results of the Arch model by BPINN, which shows that BPINN can reconstruct the velocity field. Figure 4(c) shows the uncertainty quantification of the inverted velocity model output by BPINN, which is consistent with the ray path, proving the excellent inversion and uncertainty quantification capabilities of the method of this invention.

[0141] In summary, the present invention provides a travel-time tomography method and system for travel-time tomography inversion. This not only solves the dependence of traditional neural networks on data information but also addresses the difficulties traditional neural networks face in uncertainty quantification, generalization, and prior knowledge integration by introducing a probabilistic model. Furthermore, the use of the Hamiltonian Monte Carlo algorithm as a Bayesian inference method offers advantages such as high computational efficiency, accurate results, and ease of implementation.

[0142] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments 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. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0143] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0144] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. 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.

[0145] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or 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. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0146] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0147] 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.

[0148] If the integrated module / 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, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random-access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0149] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0150] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0151] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0152] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A travel-time tomography method, characterized in that, Includes the following steps: Determining Bayesian-fusion physical mechanism neural networks based on procedural functional equations; The parameters of the Bayesian-fusion physical mechanism neural network are trained based on the Bayesian inference algorithm to obtain posterior distribution samples. The inversion velocity field of all samples is averaged to form the final travel-time tomography inversion result. The Bayesian formula is calculated based on the Bayesian inference algorithm, which uses the Hamiltonian Monte Carlo algorithm to simulate the sampling process using the trajectory of particles in the Hamiltonian mechanics system. The specific steps are as follows: The relationship between Hamiltonian energy and target distribution is established as follows: in, For neural network parameters, As an auxiliary momentum variable, for and The joint probability distribution, Hamiltonian energy; Determine the method for solving the Hamiltonian equation; determine the error correction method; and use a discrete method to solve the Hamiltonian equation, which is as follows: in, For neural network parameters, As an auxiliary momentum variable, For the quality matrix, This is the Hamiltonian potential.

2. The travel-time tomography method according to claim 1, characterized in that, The specific equation is as follows: in, Indicates the location from the epicenter to the domain any point in When they left, For the time factor, Indicates in The speed defined in [the text].

3. The travel-time tomography method according to claim 1, characterized in that, Bayesian-fusion physical mechanism neural network contains two independent fully connected neural networks and , which are used to approximate the travel time field and the velocity field, respectively.

4. The travel-time tomography method according to claim 1, characterized in that, The Bayes formula is as follows: in, Represents observational data, Representative function equation ， Represents neural network parameters; The prior probability distribution of the network model parameters of the Bayesian-fusion physical mechanism neural network; The likelihood distribution represents the distribution of parameters in the neural network. Given the observed data sum function equation The predicted probability; Representative on The marginal distribution.

5. The travel-time tomography method according to claim 1, characterized in that, Error correction uses the Metropolis-Hasting criterion, which has the following form: in, To accept probability, To update the Hamiltonian energy by L times, This is the initial Hamiltonian energy before the k-th sampling.

6. The travel-time tomography method according to claim 1, characterized in that, Based on samples obtained from a Bayesian-fusion physical mechanism neural network, the final travel-time tomography inversion velocity field is obtained by calculating the mean of all samples. The uncertainty of the inversion velocity model results is measured by calculating the variance of all samples. The posterior sample mean and variance are as follows: in, For network input, For network output, For neural network parameters, For observation data, To obtain neural network parameters The number of samples sampled from the posterior distribution. express The i A Bayesian neural network with parameters corresponding to each sample.

7. A travel-time tomography system, characterized in that, include: The network module defines a Bayesian-fusion physical mechanism neural network based on procedural functional equations. The output module trains the parameters of the Bayesian-fusion physical mechanism neural network based on the Bayesian inference algorithm to obtain posterior distribution samples. It averages the inversion velocity fields of all samples to form the final travel-time tomography inversion result. The module calculates the Bayesian formula based on the Bayesian inference algorithm, which employs the Hamiltonian Monte Carlo algorithm. This algorithm uses the particle trajectories in the Hamiltonian mechanics system to simulate the sampling process. The specific steps are as follows: The relationship between Hamiltonian energy and target distribution is established as follows: in, For neural network parameters, As an auxiliary momentum variable, for and The joint probability distribution, Hamiltonian energy; Determine the method for solving the Hamiltonian equation; determine the error correction method; and use a discrete method to solve the Hamiltonian equation, which is as follows: in, For neural network parameters, As an auxiliary momentum variable, For the quality matrix, This is the Hamiltonian potential.

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