Travel time tomography method and system

Abstract

The invention discloses a travel time tomography method and system, and belongs to the technical field of exploration geophysical research, and the method comprises the steps: building a mapping relation between travel time and a speed model through an eikonal equation; and designing a Bayesian-fusion physical mechanism neural network structure based on a eikfunction equation, training Bayesian-fusion physical mechanism neural network parameters based on a Bayesian inference algorithm to obtain posteriori distribution samples, averaging inversion velocity fields of all the samples, and forming a final travel time tomography inversion result. According to the method, the inversion precision of the speed model is high, and the method has excellent uncertainty quantification capability.

Description

Background Art

[0002] Seismic tomography is a data inference technology that uses the travel time information contained in seismic records to infer underground structures. In recent years, due to the improvement of data scale and algorithms, neural networks have received great attention due to their ability to process large-scale data, nonlinear mapping and noise resistance, and have been widely and deeply studied in the field of geological inversion; however, in seismic exploration, due to the high cost of measurement data, a large amount of measurement data is difficult to obtain, which limits the accuracy of neural network inversion results.

[0003] In 1972, Aki et al. pioneered the method of using seismic tomography to study geological structures; the Eikonal equation, as a high-frequency approximate expression of the wave equation, is widely used in the field of travel-time tomography. Due to the nonlinearity of the Eikonal equation, numerical methods are usually required to solve it. The two commonly used numerical methods are the fast march method and the fast scanning method; however, the calculation accuracy of travel-time tomography using traditional numerical methods depends largely on the discretization scheme of time and space and the fineness of the grid division, and is limited by the selection of the initial model and data noise, which has limited its practical application.

[0004] In recent years, deep learning has received great attention in solving inversion problems based on partial differential equations. However, the performance of purely data-driven neural networks depends largely on the amount of training data. In the field of seismic exploration, the cost of obtaining measurement data is often very high. Faced with this difficulty, Raissi proposed a physical mechanism-integrated neural network (PINN) as a new framework for solving direct and inverse problems of partial differential equations. PINN reduces the dependence of network training on training data by integrating prior physical information into the network and adding the residual term of the control equation to the loss function of the neural network. In the field of exploration geophysics, Waheed et al. used PINN to solve isotropic eikonal equations and established a framework for solving the inversion problem of isotropic eikonal equations. PINN combined with the eikonal equation can solve the inverse problem under the condition of sparse data, and the PINN method does not rely on the initial velocity model and grid division, which is more flexible and accurate than traditional methods.

[0005] Due to the scarcity of training data and the existence of noise, neural networks are usually multi-solution in the face of complex geological structures; however, there are few studies on the uncertainty quantification of training results by traditional networks. Yang et al. proposed an algorithm to solve partial differential equation problems with noisy data using Bayesian-Physical Mechanism Integrated Neural Network (BPINN). BPINN not only quantifies the uncertainty generated by noisy data under the Bayesian framework, but also avoids overfitting and can obtain more accurate predictions than PINN under large noise conditions. The inference algorithms that BPINN uses Bayesian inference to estimate the posterior distribution 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 not accurately capture the posterior distribution. Markov chain Monte Carlo approximates the target distribution by constructing a Markov chain with its equilibrium distribution as the target. However, due to the limitation of random walk phenomenon, its sampling efficiency is too low, especially in high-dimensional space. The Markov Chain Monte Carlo method (HMC) based on Hamiltonian dynamics was proposed to solve the random walk phenomenon. HMC calculates the future state of the Markov chain by simulating the motion trajectory of particles in the physical system, which can explore high-dimensional space more efficiently. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a travel time tomography method and system in view of the deficiencies in the above-mentioned prior art, calculate the posterior distribution of network parameters based on the Hamiltonian Monte Carlo algorithm, realize the inversion of the velocity model and the uncertainty measurement of the inversion result, and analyze the accuracy and effectiveness of the method, so as 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 solutions: A travel time tomography method comprises the following steps: Determine the Bayesian-fusion physical mechanism neural network based on the eikonal equation; Based on the Bayesian inference algorithm, the parameters of the Bayesian-fusion physical mechanism neural network are trained to obtain the posterior distribution samples, and the inverted velocity fields of all samples are averaged to form the final travel-time tomography inversion results.

[0008] Preferably, the eikonal equation is as follows:

[0009] in, Indicates the location of the earthquake source To the domain Any point in When walking, is the travel time factor, Indicated in The speed defined in .

[0010] 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 velocity field respectively.

[0011] Preferably, the Bayesian formula is as follows:

[0012] in, represents the observed data, Representative Eikonal Equation ， represents network parameters; It is the prior probability distribution of the parameters of the Bayesian-fusion physical mechanism neural network model; is the likelihood distribution, which means that the network parameters Given the known observation data Eikonal equation The predicted probability of Representative About The marginal distribution of .

[0013] Preferably, the Bayesian formula is calculated based on a Bayesian inference algorithm, which uses a Hamiltonian Monte Carlo algorithm to simulate the sampling process using the motion trajectory of particles in a Hamiltonian mechanics system. The specific steps are: Establish the relationship between Hamiltonian energy and target distribution; Determine the method for solving Hamilton's equations; Determine the error correction method.

[0014] Preferably, the relationship between Hamiltonian energy and target distribution is as follows:

[0015] in, are neural network parameters, is the auxiliary momentum variable, for and The joint probability distribution of is the Hamiltonian energy.

[0016] Preferably, a discrete method is used to solve the Hamiltonian equation, which is specifically as follows:

[0017] in, are neural network parameters, is the auxiliary momentum variable, is the mass matrix, is the Hamiltonian potential energy.

[0018] Preferably, the error correction adopts the Metropolis-Hasting criterion, which has the following form:

[0019] in, is the acceptance probability, To update the Hamiltonian energy L times, is the initialization Hamiltonian energy before the kth sampling.

[0020] Preferably, based on the samples obtained from the 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 result is measured by calculating the variance of all samples. The posterior sample mean and variance are specifically:

[0021] in, For network input, For network output, are neural network parameters, is the observed data, From the neural network parameters The number of samples sampled from the posterior distribution of express No. i The Bayesian neural network with parameters corresponding to samples.

[0022] In a second aspect, an embodiment of the present invention provides a travel time tomography system, comprising: The network module determines the Bayesian-fusion physical mechanism neural network based on the eikonal equation; The output module trains the parameters of the Bayesian-fusion physical mechanism neural network based on the Bayesian inference algorithm, obtains the posterior distribution samples, and averages the inverted velocity fields of all samples to form the final travel-time tomography inversion results.

[0023] In a third aspect, a computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned travel time tomography method when executing the computer program.

[0024] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, including a computer program, which implements the steps of the above-mentioned travel time tomography method when executed by a processor.

[0025] In a fifth aspect, a chip comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned travel time tomography method when executing the computer program.

[0026] In a sixth aspect, an embodiment of the present invention provides an electronic device, including a computer program, which implements the steps of the above-mentioned travel time tomography method when executed by the electronic device.

[0027] Compared with the prior art, the present invention has at least the following beneficial effects: A travel time tomography method uses an eikonal equation to establish a mapping relationship between travel time and a velocity model; designs a Bayesian-fusion physical mechanism neural network structure based on the eikonal equation, and then confirms the Bayesian formula under the network framework; uses a Bayesian inference algorithm to train network parameters of the Bayesian-fusion physical mechanism neural network 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; the present invention does not rely on an initial velocity model during the inversion process, and has a reasonable uncertainty quantification capability, thereby realizing the inversion of the velocity model and the uncertainty measurement of the inversion result.

[0028] Furthermore, the network structure is combined with a fusion physical information neural network, the purpose of which is to reduce the dependence on data information by introducing additional prior physical information as a constraint, and not relying on a good initial velocity model. The network structure is combined with a Bayesian neural network, the purpose of which is to introduce a probabilistic model to deal with uncertainty, generalization problems, and prior knowledge integration, which are difficult to solve with traditional neural networks.

[0029] Furthermore, the Bayesian formula is extended to introduce Bayesian theorem into neural networks, so that neural networks can use data sets and eikonal equations for Bayesian inference. Probability distribution includes prior distribution and likelihood distribution, and its purpose is to use prior distribution and likelihood distribution to represent target distribution according to Bayesian theorem.

[0030] Furthermore, the motion trajectory of particles in the Hamiltonian mechanics system is used to simulate the sampling process to improve the sampling efficiency; Furthermore, the Hamiltonian equation is approximately solved to update the state of the particle to complete the sampling process, which solves the problem that the Hamiltonian equation cannot obtain a theoretical solution.

[0031] Furthermore, the Hamiltonian energy conservation violation caused by the application of the corrected discrete numerical integration method can be guaranteed to converge by refusing to accept parameter updates that make energy non-conservative.

[0032] It can be understood that the beneficial effects of the second to sixth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0033] In summary, the present invention has high inversion accuracy for the velocity model and excellent uncertainty quantification capability.

[0034] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following briefly introduces the drawings required for use in the embodiments of the present application. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0036] Figure 1 Schematic diagram of the BPINN structure for travel-time tomography; Figure 2 shows the output results of BPINN for the inclusion model, where (a) is the inclusion model velocity field, (b) is the inverted velocity field, and (c) is the uncertainty quantification of the inverted velocity field; Figure 3 shows the output results of BPINN for the checkerboard model, where (a) is the checkerboard model velocity field, (b) is the inverted velocity field, and (c) is the uncertainty quantification of the inverted velocity field; Figure 4 shows the output results of BPINN for the arch model, where (a) is the arch model velocity field, (b) is the inverted velocity field, and (c) is the uncertainty quantification of the inverted velocity field; Figure 5 A schematic diagram of a computer device provided by an embodiment of the present invention; Figure 6 A block diagram of an electronic device provided according to an embodiment of the present invention; Figure 7 Schematic diagram of a travel-time tomography method. DETAILED DESCRIPTION

[0037] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0038] In the description of the present invention, it should be understood that the terms “include” and “comprises” indicate the presence of described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0039] It should also be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include plural forms.

[0040] It should be further understood that the term "and / or" used in the present specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in the present invention generally indicates that the associated objects are in an "or" relationship.

[0041] It should be understood that, although the terms first, second, third, etc. may be used to describe preset ranges, etc. in the embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are only used to distinguish preset ranges from each other. 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.

[0042] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0043] Various structural schematic diagrams of the embodiments disclosed in the present invention are shown in the accompanying drawings. These figures are not drawn to scale, and some details are magnified and some details may be omitted for the purpose of clear expression. The shapes of various regions and layers shown in the figures and the relative sizes and positional relationships therebetween are only exemplary, and may deviate in practice due to manufacturing tolerances or technical limitations, and those skilled in the art may additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0044] The present invention provides a travel-time tomography method, which is based on a Bayesian-fusion physical mechanism neural network. By introducing the eikonal equation as a physical constraint term in the Bayesian-fusion physical mechanism neural network, the travel-time information obtained by a finite receiver is used to invert the velocity structure of the underground medium, and the Bayesian-fusion physical mechanism neural network is used to measure the uncertainty of the inversion velocity model result, so as to provide a basis for the acceptance or further processing of the inversion result.

[0045] Example 1 See also Figure 7 The present invention is a travel time tomography method, comprising the following steps: S1. Determine the eikonal equation; Travel-time tomography establishes a mapping relationship from travel time to underground velocity structure based on ray theory. The Eikonal equation, as a high-frequency approximation of the wave equation, establishes the relationship between travel time and velocity model:

[0046] in, Indicates the location of the earthquake source To the domain Any point in When walking, Indicated in The speed defined in .

[0047] When calculating the travel time at the earthquake source, the solution of the Eikonal equation at the earthquake source is singular. In order to make the solution of the Eikonal equation more accurate, Factorize into the following two factors:

[0048] Combining the two equations, we get the residual of the factorized eikonal equation :

[0049] S2, determine the Bayesian-fusion physical mechanism neural network structure; The standard PINN is Parameterized Neural Networks Fitting the true solution determined by the partial differential equation However, the initialization and training of neural network parameters are uncertain, and the output results of each training will be different. In addition, due to the scarcity of training data and the existence of noise, neural networks usually have multiple solutions when facing complex geological structures.

[0050] Therefore, the inversion results of travel time tomography using PINN contain a high degree of uncertainty. By introducing a probabilistic model, BNN has advantages that traditional neural networks cannot achieve in dealing with uncertainty, generalization problems, and integration of prior knowledge. In order to take advantage of BNN uncertainty quantification and other advantages, based on PINN, Bayesian inference is introduced to solve the target distribution in combination with the neural network parameters generated in a specific probability distribution, namely, the Bayesian-fused physical mechanism neural network (BPINN), and BPINN is used for travel time tomography inversion. BPINN uses two independent fully connected neural networks and To approximate the travel time field and velocity field, the network parameters For random variables, in addition to taking the observed data as constraints, additional physical constraints are introduced and Bayesian inference is used to obtain the posterior distribution of the model.

[0051] S3, combining the eikonal equation obtained in step S1, determining the Bayesian formula under the Bayesian-fusion physical mechanism neural network framework obtained in step S2; Bayesian neural network (BNN) transforms the 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 of calculating the posterior distribution:

[0052] in, represents the observed data, represents network parameters; is the prior probability distribution of the network model parameters. Without loss of generality, the prior distribution is usually considered to be a standard normal distribution; is the likelihood distribution, which means that the network parameters Given the known observation data The predicted probability of Representative About The marginal distribution of It is irrelevant and is usually treated as a normalizing constant.

[0053] In the framework of BPINN, in addition to expressing the likelihood estimate of the degree of data fit , and the likelihood estimate of the degree of fit of a given physical equation is added , the posterior distribution can be expressed using the Bayesian formula as:

[0054] S4. Determine the Bayesian inference algorithm; The Bayesian inference method uses the Hamiltonian Monte Carlo algorithm. Faced with high-dimensional neural networks, it is very difficult to directly solve the posterior distribution. Researchers introduced relevant statistical theories and obtained the distribution of target probability (posterior probability) based on sampling or fitting. The Markov Chain Monte Carlo (MCMC) method is a common Bayesian inference algorithm. MCMC approximates the target distribution by sampling from the current posterior probability based on the Markov chain. However, the general Markov Chain Monte Carlo method is prone to random walk phenomenon due to the high dimensionality of the problem, resulting in low sampling efficiency. The Hamiltonian Monte Carlo algorithm (HMC) is an optimization of the Markov Chain Monte Carlo algorithm. The algorithm uses the motion trajectory of particles in the Hamiltonian mechanics system to simulate the sampling process, which effectively avoids the random walk phenomenon and improves the sampling efficiency.

[0055] S401, establish the relationship between Hamiltonian energy and target distribution; The HMC algorithm transforms the network model parameters As a mechanical motion of a particle, the particle moves from its current state along a certain trajectory to a new state, and the trajectory of the particle follows the Hamiltonian dynamics equation: the potential energy of the particle With kinetic energy The sum of remain unchanged. Assume that given a certain number of observations , define potential energy as:

[0056] HMC introduces an auxiliary momentum variable To construct kinetic energy:

[0057] in, is a mass matrix, usually set to the identity matrix ,variable Sampling from a standard normal distribution. Then HMC is applied to the joint probability density distribution Perform posterior sampling in:

[0058] Among them, potential energy is directly related to the target posterior distribution, while the auxiliary variables The samples of are discarded, which ensures that the network parameters The marginal distribution of the samples is the target posterior distribution .

[0059] S402, determining a method for solving the Hamiltonian equation; The samples are generated according to the Hamiltonian equation

[0060] Specifically, the Hamiltonian system theoretically needs to keep the Hamiltonian energy constant during the motion update process. In practical applications, the Hamiltonian equation cannot be solved analytically and can only be solved approximately through discrete methods. The most commonly used discrete method is the leap-frog method, in which samples are obtained by leap-frog at a time step of Iterative update

[0061] S403, determining an error correction method; Discrete numerical integration methods will inevitably destroy Hamiltonian energy conservation during application, so a correction method needs to be added after the update to reduce the deviation, namely the Metropolis-Hasting criterion, which guarantees the convergence of the results by refusing to accept parameter updates that do not conserve energy. Its specific form is as follows:

[0062] in, is the acceptance probability, To update the Hamiltonian energy L times, is the initial Hamiltonian energy before the kth sampling. If the new state is accepted , then the new state Replace the initial state , otherwise the state will remain in the initial state constant.

[0063] S5, calculating the Bayesian formula obtained in step S3 using the Bayesian inference algorithm obtained in step S4 to obtain a posterior distribution sample; Once the network is trained on a specific dataset After training, the predicted results and the associated uncertainty can be approximated by the posterior sample mean and variance:

[0064] in, The values ​​of The i-th sample corresponds to the parameter of the Bayesian neural network. is the neural network parameter The number of samples drawn from the posterior distribution of . and are the input and output of the neural network.

[0065] It will be appreciated by those skilled in the art that various aspects of the present invention may be implemented as systems, methods or program products. Therefore, various aspects of the present invention may be specifically implemented in the following forms, namely: complete hardware implementation, complete software implementation (including firmware, microcode, etc.), or a combination of hardware and software implementations, which may be collectively referred to herein as "circuits", "modules" or "platforms".

[0066] Example 2 The present invention provides a travel-time tomography system, which can be used to implement the travel-time tomography method. Specifically, the travel-time tomography system includes a network module and an output module.

[0067] Among them, the network module determines the Bayesian-fusion physical mechanism neural network based on the eikonal equation; The output module trains the parameters of the Bayesian-fusion physical mechanism neural network based on the Bayesian inference algorithm, obtains the posterior distribution samples, and averages the inverted velocity fields of all samples to form the final travel-time tomography inversion results.

[0068] Example 3 The present invention provides a terminal device, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, graphics processors (GPU), tensor processors (TPU), digital signal processors (DSP), application specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, and is specifically suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of the travel time tomography method, including: The Bayesian-fusion physical mechanism neural network is determined based on the Eikonal equation. 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 inverted velocity fields of all samples are averaged to form the final travel time tomography inversion result.

[0069] See also Figure 5 , the terminal device is a computer device, and the computer device 60 of this embodiment 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 computer program 63 is executed by the processor 61, the travel time tomography method of the embodiment is implemented. To avoid repetition, it is not described one by one here. Alternatively, when the computer program 63 is executed by the processor 61, the functions of each model / unit in the travel time tomography system of the embodiment are implemented. To avoid repetition, it is not described one by one here.

[0070] The computer device 60 may be a computing device such as a desktop computer, a notebook, a PDA, or a cloud server. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will appreciate that Figure 5 This is only an example of the computer device 60 and does not constitute a limitation of the computer device 60. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, buses, etc.

[0071] The processor 61 may be a central processing unit (CPU), or other general-purpose processors, graphics processing units (GPU), tensor processing units (TPU), digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc.

[0072] The memory 62 may be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc., equipped on the computer device 60.

[0073] Furthermore, the memory 62 may include both an internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or is to be output.

[0074] See also Figure 6 The terminal device is an electronic device 600, which is 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 the storage unit 620 and the processing unit 610), a display unit 640, etc.

[0075] The storage unit stores program codes, which can be executed by the processing unit 610, so that the processing unit 610 performs the steps according to various exemplary embodiments of the present invention described in the above method section of this specification. For example, the processing unit 610 can perform the following steps: Figure 7 Follow the steps shown in .

[0076] The storage unit 620 may include a readable medium in the form of a volatile storage unit, such as a random access memory unit (RAM) 6201 and / or a cache memory unit 6202 , and may further include a read-only memory unit (ROM) 6203 .

[0077] The storage unit 620 may also include a program / utility 6204 having a set (at least one) of program modules 6205, such program modules 6205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0078] Bus 630 may represent one or more of several types of bus structures, including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0079] The electronic device 600 may also communicate with one or more external devices 700 (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may also communicate with one or more devices that enable a user to interact with the electronic device 600, and / or communicate with any device that enables the electronic device 600 to communicate with one or more other computing devices (e.g., routers, modems, etc.). Such communication may be performed via an input / output (I / O) interface 650. Furthermore, the electronic device 600 may also communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) via a network adapter 660. The network adapter 660 may communicate with other modules of the electronic device 600 via a bus 630. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the 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, etc.

[0080] Example 4 The present invention also provides a storage medium, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It is understandable 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, and can be any tangible medium containing or storing a program, which can be used by an instruction execution system, device or device or used in combination with it. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by a processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that more specific examples (non-exhaustive list) of the computer-readable storage medium here include: an electrical connection with one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0081] Computer readable storage media also include data signals propagated in baseband or as part of a carrier wave, which carry readable program codes. Such propagated data signals can take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The readable storage medium can also be any readable medium other than a readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, device, or device. The program code contained on the readable storage medium can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical cable, RF, etc., or any suitable combination of the above.

[0082] Program code for performing the operations of the present invention may be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java, C++, etc., and conventional procedural programming languages ​​such as "C" or similar programming languages. The program code may be executed entirely on the user computing device, partially on the user device, as a separate software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device may be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computing device (e.g., through the Internet using an Internet service provider).

[0083] One or more instructions stored in a computer-readable storage medium may be loaded and executed by a processor to implement the corresponding steps of the travel-time tomography method in the above embodiment; one or more instructions in the computer-readable storage medium may be loaded and executed by a processor as follows: The Bayesian-fusion physical mechanism neural network is determined based on the Eikonal 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 inverted velocity fields of all samples are averaged to form the final travel time tomography inversion result.

[0084] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings here can usually be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0085] Example This example studies the travel time tomography inversion and uncertainty quantification of the inclusion model, checkerboard model and arch model using BPINN.

[0086] See also Figure 1 , Figure 1 This example uses two independent fully connected neural networks to approximate the travel time field. and velocity field ,For the travel time network, the neural network has 3 hidden layers, 20 neurons in each layer, and the tanh activation function is used. ,In the speed network, the neural network has 2 hidden layers, 50 neurons in each layer, and the tanh activation function is used and the sigmoid activation function is used to ,normalize the network output.

[0087] 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 (black marks) and 51 receivers (red marks) are set at the left boundary (X=0 km) and the right boundary (X=2 km), respectively. Figure 2(b) is the inversion result of the inclusion model by BPINN. It can be seen that BPINN has restored the shape and value of the inclusion model. Figure 2(c) is the uncertainty quantification of the inversion velocity model output by BPINN. The uncertainty is mainly concentrated in the high-speed body area without travel time information constraints, showing a reasonable uncertainty distribution.

[0088] Please refer to Figure 3. We further 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 sources (black marks) and 101 receivers (red marks) are set at the left boundary (X=0 km) and the right boundary (X=2 km), respectively. Figure 3(b) is the inversion result of the checkerboard model by BPINN. It can be seen that BPINN can capture the position and velocity size of each velocity area. Figure 3(c) is the uncertainty quantification of the inversion velocity model output by BPINN. The areas with high uncertainty correspond to the areas with poor velocity field inversion, which proves the rationality of the method of the present invention in quantifying uncertainty.

[0089] Please refer to Figure 4. Figure 4(a) is a schematic diagram of the velocity field distribution of the arch model. 11 seismic sources (black marks) are evenly distributed on the surface of the model (Z=0 km), and 121 receivers (red marks) are also evenly distributed on the surface of the model (Z=0 km). Figure 4(b) is the inversion result of the arch model by BPINN, from which it can be seen that BPINN can reconstruct the velocity field. Figure 4(c) is the uncertainty quantification of the inversion velocity model output by BPINN, which is consistent with the ray path, proving the excellent inversion and uncertainty quantification capabilities of the method of the present invention.

[0090] In summary, the travel-time tomography method and system of the present invention perform travel-time tomography inversion, which not only solves the dependence of traditional neural networks on data information, but also solves the problems of uncertainty quantification, generalization problems and prior knowledge integration of traditional neural networks by introducing probability models. At the same time, the Hamiltonian Monte Carlo algorithm is used as the Bayesian inference method, which has the advantages of high computational efficiency, accurate calculation results, and easy implementation.

[0091] The technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by 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 embodiment can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0092] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0093] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0094] In the embodiments provided by the present 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 only schematic. For example, the division of the modules or units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0095] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0096] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0097] If the integrated module / unit is implemented in the form of 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 present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased 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 electric carrier signals and telecommunication signals.

[0098] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices, and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0099] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0100] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0101] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A travel time tomography method, characterized in that: The following steps are involved: Determine the Bayesian-fusion physical mechanism neural network based on the eikonal equation; Based on the Bayesian inference algorithm, the parameters of the Bayesian-fusion physical mechanism neural network are trained to obtain the posterior distribution samples, and the inverted velocity fields of all samples are averaged to form the final travel-time tomography inversion results.

2. The travel time tomography method according to claim 1, characterized in that: The eikonal equation is as follows: in, Indicates the location of the earthquake source To the domain Any point in When walking, is the travel time factor, Indicated in The speed defined in .

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

4. The travel time tomography method according to claim 1, characterized in that: The Bayesian formula is as follows: in, represents the observed data, Representative Eikonal Equation ， represents network parameters; The prior probability distribution of the network model parameters of the Bayesian-fusion physical mechanism neural network; is the likelihood distribution, which means that the network parameters Given the known observation data Eikonal equation The predicted probability of Representative About The marginal distribution of .

5. The travel time tomography method according to claim 1, characterized in that: The Bayesian formula is calculated based on the Bayesian inference algorithm. The Bayesian inference algorithm adopts the Hamiltonian Monte Carlo algorithm and uses the motion trajectory of particles in the Hamiltonian mechanics system to simulate the sampling process. The specific steps are: Establish the relationship between Hamiltonian energy and target distribution; Determine the method for solving Hamilton's equations; Determine the error correction method.

6. The travel time tomography method according to claim 5, characterized in that: The relationship between Hamiltonian energy and target distribution is as follows: in, are neural network parameters, is the auxiliary momentum variable, for and The joint probability distribution of is the Hamiltonian energy.

7. The travel time tomography method according to claim 5, characterized in that: The Hamiltonian equation is solved using a discrete method. The Hamiltonian equation is as follows: in, are neural network parameters, is the auxiliary momentum variable, is the mass matrix, is the Hamiltonian potential energy.

8. The travel time tomography method according to claim 5, characterized in that: The error correction adopts the Metropolis-Hasting criterion, which has the following form: in, is the acceptance probability, To update the Hamiltonian energy L times, is the initialization Hamiltonian energy before the kth sampling.

9. The travel time tomography method according to claim 1, characterized in that: Based on the samples obtained from the 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 result is measured by calculating the variance of all samples. The posterior sample mean and variance are specifically: in, For network input, For network output, are neural network parameters, is the observed data, From the neural network parameters The number of samples sampled from the posterior distribution of express No. i The Bayesian neural network with parameters corresponding to samples.

10. A travel time tomography system, characterized in that: include: The network module determines the Bayesian-fusion physical mechanism neural network based on the eikonal equation; The output module trains the parameters of the Bayesian-fusion physical mechanism neural network based on the Bayesian inference algorithm, obtains the posterior distribution samples, and averages the inverted velocity fields of all samples to form the final travel-time tomography inversion results.

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