A multi-model fast tomography method with physical information hard constraints
A multi-model rapid tomography method combining a hard-constrained PIUFNO network model with seismic wave propagation physics criteria solves the problems of low efficiency and insufficient generalization ability of traditional seismic travel-time tomography, achieving rapid and accurate imaging of subsurface medium velocity, and is suitable for oil and gas exploration and investigation under complex geological conditions.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JILIN UNIVERSITY
- Filing Date
- 2026-06-08
- Publication Date
- 2026-07-03
AI Technical Summary
Traditional seismic travel-time tomography methods are computationally inefficient, highly dependent on the initial model, and lack generalization ability, making them difficult to adapt to diverse geological structures and observation configurations.
A multi-model fast tomography method with hard constraints based on physical information is adopted. By constructing a PIUFNO network model under hard constraints, an end-to-end nonlinear mapping relationship is established using observation data from different seismic sources and physical criteria for seismic wave propagation. The physical constraint loss function is embedded for training, thereby achieving rapid imaging of subsurface medium velocity.
It achieves efficient and accurate imaging of multiple models, improving the imaging speed from hours to seconds. It is applicable to different speed models, reduces computational costs and time cycles, and is suitable for oil and gas exploration, engineering surveys, and underground metal ore detection.
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Figure CN122330983A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of seismic exploration technology, specifically relating to a multi-model rapid tomography method with hard constraints of physical information. Background Technology
[0002] Seismic travel-time tomography is a geophysical method that uses the travel time of seismic waves to invert the velocity structure of subsurface media. This method comprises two core components: forward modeling and inversion. Forward modeling, assuming a known subsurface velocity model, calculates the theoretical travel time and ray path of seismic waves from the source to the receiver by solving ray tracing or equation functions. Inversion, based on the forward modeling results, utilizes the difference between observed travel time data and theoretical travel time—the travel time residual—and iteratively optimizes the velocity model using algorithms to gradually reduce the residual. The goal of inversion is to infer the true spatial distribution of subsurface velocities. This method is now widely used in oil and gas exploration, engineering surveys, and underground metal ore detection, and is a key technology for revealing subsurface structures and physical parameters.
[0003] Traditional seismic travel-time tomography primarily relies on ray theory methods, which suffer from three significant limitations. First, it is slow and computationally expensive: each iteration requires extensive ray tracing calculations and solving large linear equations, often taking tens to hundreds of iterations to converge, making it unsuitable for rapid imaging. Second, it is highly dependent on the initial model: as a local optimization method, the inversion results are severely limited by the accuracy of the initial model, easily getting trapped in local extrema and causing imaging distortion. Third, it lacks generalization ability: traditional methods typically invert based on a single geological model and a fixed observation system. When the actual scene differs from the preset conditions, remodeling and inversion are required, making it difficult to adapt to diverse geological structures and observation configurations.
[0004] Therefore, there is an urgent need to develop a fast tomographic imaging method for multiple models with hard constraints on physical information, so as to effectively solve the problems of low training efficiency and weak generalization performance of traditional methods. Summary of the Invention
[0005] The purpose of this invention is to provide a fast tomographic imaging method for multiple models with hard constraints of physical information, so as to solve the problem that traditional algorithms can only perform tomographic imaging on a single model and are difficult to generalize to new models, thus significantly improving computational efficiency and imaging applicability.
[0006] This invention is achieved through the following technical solution:
[0007] A fast multi-model tomography method with hard constraints based on physical information includes the following steps:
[0008] S1. Construct a PIUFNO network model under hard constraints;
[0009] S11, the hard-constrained PIUFNO network takes background travel time and travel time disturbance data corresponding to multiple sets of different seismic source observation data as input features, and finally outputs the underground medium velocity field and travel time factor parameters synchronously.
[0010] S12. The velocity distribution characteristics of the subsurface medium and the seismic wave travel time data are correlated and solved using the equation to realize the inversion of the subsurface velocity structure; the overall travel time parameters are decomposed into two independent components; the background travel time is calculated based on the medium velocity value at the source point.
[0011] S13. Using the theory of connection function, the measured travel time data collected by the surface geophone is introduced into the equation as a hard constraint. The travel time field is decomposed in a second optimization. The decomposed equation is substituted into the original equation to derive an improved equation with factorization form and incorporating measured hard constraint data.
[0012] S2. Using the travel time disturbance and background travel time of data collected from different seismic sources as network inputs, the network directly outputs the corresponding underground velocity structure, establishing an end-to-end nonlinear mapping relationship between input and output.
[0013] S3. Embed the physical criteria for seismic wave propagation as a hard constraint into the loss function, construct the physical constraint loss function, and complete the network training.
[0014] S4. After the network training converges and the parameters are optimized, the new measured travel time disturbance data and the corresponding background travel time data are input into the model to deduce the velocity distribution structure of the underground medium and realize rapid imaging of the underground velocity structure.
[0015] Furthermore, in step S12, the functional equation can be expressed as:
[0016] ;
[0017] Where T represents the travel time of the first arrival wave of the earthquake. Represents the velocity of the underground medium. Represents the gradient operator, Represents the coordinates of the model.
[0018] Furthermore, the travel time T can be decomposed into the following form:
[0019] ;
[0020] in, Expressed as the travel time factor, it is used to characterize the deviation between the actual travel time and the travel time in an ideal homogeneous medium. This represents the background travel time under the assumption of a homogeneous medium.
[0021] Furthermore, assuming the subsurface medium has a uniform velocity at the earthquake source, the calculation formula is as follows:
[0022] ;
[0023] in, For seismic waves from the source coordinates Position propagation to spatial measuring points The straight-line distance This represents the medium velocity at the earthquake source point.
[0024] Furthermore, in step S13, all field observation data are combined with the actual working conditions of seismic exploration. All samples were collected at a constant depth at the Earth's surface. On the plane, the travel time field T is decomposed by a second optimization, as follows:
[0025] ;
[0026] in, It represents the vertical direction in space, i.e., the z-axis coordinate. This represents the parameters output by the network. It is obtained by converting measured ground travel time data, specifically calculated using the following formula:
[0027] ;
[0028] in, This represents the actual travel time collected by surface geophones during seismic exploration.
[0029] Furthermore, the equation is improved as follows:
[0030] .
[0031] Furthermore, the core computational unit of the PIUFNO network is the U-Net FNO module, whose input features... After sequentially performing Fourier forward transform, high-frequency component linear filtering, inverse Fourier transform, U-net feature transformation, and local linear transformation to complete multi-dimensional feature fusion, the final calculation result is output. .
[0032] Further, in step S2, input [ ; ] and output [ ; The mapping relationship between them, that is, based on the time perturbation. Time travel with the background As input, with travel time factor and underground medium velocity This represents the end-to-end nonlinear mapping relationship for the output.
[0033] Further, in step S3, the physical constraint loss function is expressed as follows:
[0034] ;
[0035] in, The number of speed models participating in training. This is the index value for the corresponding velocity model.
[0036] Compared with the prior art, the beneficial effects of the present invention are:
[0037] This invention provides a fast multi-model tomographic imaging method with hard constraints based on physical information. For the first time, it combines the hard constraint mechanism with the physical information U-Net Fourier neural operator, effectively overcoming the limitation of traditional tomographic imaging, which can only train a single model. This invention enables efficient and accurate imaging of multiple models through a single training iteration, applicable to different velocity models. After a single training iteration, by inputting travel time perturbations from different seismic sources and the corresponding background travel times, the underground velocity structure can be quickly obtained, improving the seismic travel time inversion from the hourly level of traditional numerical methods to the second level. This efficiency improvement provides an efficient and feasible technical means for rapid imaging and real-time monitoring in fields such as oil and gas exploration, engineering surveying, and underground metal ore detection. Attached Figure Description
[0038] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0039] Figure 1 This is a flowchart of the steps of the multi-model fast tomography method with hard constraints of physical information according to the present invention;
[0040] Figure 2 A travel-time tomography network framework for PIUFNO under hard constraints;
[0041] Figure 3 For U-Net Fourier neural operator modules;
[0042] Figure 4 The actual velocity models corresponding to the data input to the network are as follows: (a) is the horizontal layered velocity model, (b) is the low-speed velocity model of folds and depressions, and (c) is the high-speed velocity model of folds and depressions.
[0043] Figure 5The true velocity model corresponding to the new underground data input after training is given, where (a) is the high-speed layered velocity model of folded undulations, and (b) is the low-speed layered velocity model of folded undulations.
[0044] Figure 6 The above are the underground velocity models predicted by PIUFNO under hard constraints, where (a) is the high-velocity prediction model for folded undulations and (b) is the low-velocity prediction model for folded undulations. Detailed Implementation
[0045] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.
[0046] This invention integrates hard constraint mechanisms, the U-Net network architecture, and Fourier neural operators to construct a new paradigm for PIUFNO tomography under hard constraints. This method does not rely on an initial model, overcoming the limitation of traditional inversion methods that can only train a single model, and achieves efficient and accurate inversion of multiple models. Inversion calculations for new models can be quickly completed through a single network training iteration, demonstrating good generalization ability to untrained models. This effectively solves the problems of low training efficiency and weak generalization performance in traditional methods, providing a new technical approach for velocity modeling under complex geological conditions.
[0047] like Figure 1 As shown, the physical information hard-constrained multi-model fast tomography method of this invention is a deep learning method that integrates hard-constrained physical information U-Net Fourier neural operator (PIUFNO). It achieves rapid and accurate imaging of underground velocity structure through a modular process, including: constructing a PIUFNO network model under hard constraints; using travel time perturbations and background travel time from different seismic sources as network inputs, and the network directly outputting the corresponding underground velocity structure, establishing an end-to-end nonlinear mapping relationship between input and output; incorporating the physical criteria of seismic wave transmission as a hard constraint condition into the loss function to construct a physical constraint loss function and complete model training; determining whether convergence has occurred; if convergence has occurred, inputting new measured travel time perturbation data and corresponding background travel time data into the model to deduce the underground medium velocity distribution structure, thereby achieving rapid imaging of the underground velocity structure.
[0048] The present invention provides a multi-model fast tomography method with hard constraints based on physical information, comprising the following steps:
[0049] S1. Construct a PIUFNO network model under hard constraints;
[0050] S11, the hard-constrained PIUFNO network takes background travel time and travel time disturbance data corresponding to multiple sets of different seismic source observation data as input features, and finally outputs the underground medium velocity field and travel time factor parameters synchronously.
[0051] S12. The velocity distribution characteristics of the subsurface medium and the seismic wave travel time data are correlated and solved using the equation to realize the inversion of the subsurface velocity structure; the overall travel time parameters are decomposed into two independent components; the background travel time is calculated based on the medium velocity value at the source point.
[0052] S13. Using the theory of connection function, the measured travel time data collected by the surface geophone is introduced into the equation as a hard constraint. The travel time field is decomposed in a second optimization. The decomposed equation is substituted into the original equation to derive an improved equation with factorization form and incorporating measured hard constraint data.
[0053] S2. Using the travel time disturbance and background travel time of data collected from different seismic sources as network inputs, the network directly outputs the corresponding underground velocity structure, establishing an end-to-end nonlinear mapping relationship between input and output.
[0054] S3. Embed the physical criteria for seismic wave propagation as a hard constraint into the loss function, construct the physical constraint loss function, and complete the network training.
[0055] S4. After the network training converges and the parameters are optimized, the new measured travel time disturbance data and the corresponding background travel time data are input into the model to deduce the velocity distribution structure of the underground medium and realize rapid imaging of the underground velocity structure.
[0056] Step S12, the functional equation can be expressed as:
[0057] ;
[0058] Where T represents the travel time of the first arrival wave of the earthquake. Represents the velocity of the underground medium. Represents the gradient operator, Represents the coordinates of the model.
[0059] The travel time T can be decomposed into the following form:
[0060] ;
[0061] in, Expressed as the travel time factor, it is used to characterize the deviation between the actual travel time and the travel time in an ideal homogeneous medium. This represents the background travel time under the assumption of a homogeneous medium.
[0062] Assuming the subsurface medium has a uniform velocity from the earthquake source, the calculation formula is as follows:
[0063] ;
[0064] in, For seismic waves from the source coordinates Position propagation to spatial measuring points The straight-line distance This represents the medium velocity at the earthquake source point.
[0065] Step S13: Based on the actual working conditions of seismic exploration, all field observation data... All samples were collected at a constant depth at the Earth's surface. On the plane, the travel time field T is decomposed by a second optimization, as follows:
[0066] ;
[0067] in, It represents the vertical direction in space, i.e., the z-axis coordinate. This represents the parameters output by the network. It is obtained by converting measured ground travel time data, specifically calculated using the following formula:
[0068] ;
[0069] in, This represents the actual travel time collected by surface geophones during seismic exploration.
[0070] Furthermore, the equation is improved as follows:
[0071] .
[0072] The core computational unit of the PIUFNO network is the U-Net FNO module, whose input features... After sequentially performing Fourier forward transform, high-frequency component linear filtering, inverse Fourier transform, U-net feature transformation, and local linear transformation to complete multi-dimensional feature fusion, the final calculation result is output. .
[0073] Step S2, input [ ; ] and output [ ; The mapping relationship between them, that is, based on the time perturbation. Time travel with the background As input, with travel time factor and underground medium velocity This represents the end-to-end nonlinear mapping relationship for the output.
[0074] Step S3, the physical constraint loss function, its expression is as follows:
[0075] ;
[0076] in, The number of speed models participating in training. This is the index value for the corresponding velocity model.
[0077] Example 1:
[0078] A fast multi-model tomography method with hard constraints based on physical information includes the following steps:
[0079] S1. Construct a hard-constrained Physical Information U-Net Fourier Neural Operator (PIUFNO) network model, and build the overall architecture of the hard-constrained PIUFNO network, as follows: Figure 2 As shown. Unlike traditional deep learning models, this network uses background travel times corresponding to multiple sets of observation data from different seismic sources. Travel disturbance data Using the input features, the final output is the velocity field of the underground medium. With travel factor parameters .
[0080] For seismic imaging of isotropic subsurface media, the velocity distribution characteristics of the subsurface media and seismic wave travel time data can be correlated and solved by solving the equation, thereby achieving accurate inversion of the subsurface velocity structure. The equation can be expressed as:
[0081] ;
[0082] Where T represents the travel time of the first arrival wave of the earthquake. Represents the velocity of the underground medium. Represents the gradient operator, The coordinates represent the model. Seismic wave source locations are highly susceptible to numerical singularities. To avoid source singularities and improve the stability of the equation solution, this invention decomposes the original travel time field, breaking down the overall travel time parameters into two independent components. Specifically, the travel time T is decomposed into the following form:
[0083] ;
[0084] in, Expressed as the travel time factor, it is used to characterize the deviation between the actual travel time and the travel time in an ideal homogeneous medium. This represents the background travel time under the assumption of a homogeneous medium. The background travel time is calculated based on the medium velocity at the seismic source point, assuming that the subsurface medium has a uniform velocity at the source. The calculation formula is as follows:
[0085] ;
[0086] in, For seismic waves from the source coordinates Position propagation to spatial measuring points The straight-line distance This represents the medium velocity at the earthquake source point.
[0087] To incorporate measured travel time data acquired by surface geophones as hard constraints into the equations, this invention employs connection function theory for derivation. Combined with actual seismic exploration conditions, all field observation data... All samples were collected at a constant depth at the Earth's surface. On the plane. Based on this, the travel time field T is decomposed into a secondary optimization as follows:
[0088] ;
[0089] in, It represents the vertical direction in space, i.e., the z-axis coordinate. This represents the parameters output by the network. It is obtained by converting measured ground travel time data, specifically calculated using the following formula:
[0090] ;
[0091] in, This represents the actual travel time collected by surface geophones during seismic exploration. Substituting the factorized expression into the original equation, we finally derive the improved equation, which has a factorized form and incorporates measured hard constraint data, as follows:
[0092] ;
[0093] In this invention, the core computational unit of the PIUFNO network is the U-Net FNO module (U-Net FNO block), and the module structure is as follows: Figure 3 As shown. This module integrates a multi-feature transformation mechanism, where F represents the forward Fast Fourier Transform; R represents the inverse Fourier transform; R represents the linear transform to filter out high-frequency components; U represents the U-net feature transform; W represents the local linear transform. This represents the ReLU activation function; feature superposition is implemented using an addition operator. The module's input features... After sequentially performing Fourier forward transform, high-frequency component linear filtering, inverse Fourier transform, U-net feature transformation, and local linear transformation to complete multi-dimensional feature fusion, the final calculation result is output. .
[0094] S2. Define the mapping relationship between network inputs and outputs. Based on the PIUFNO network built in step S1, perform rapid modeling of different underground data, establishing a model based on travel-time perturbations. Time travel with the background As input, with travel time factor and underground medium velocity The end-to-end nonlinear mapping relationship for the output, i.e., the input [ ; ] and output [ ; The mapping relationship between [the two entities] is established. This mapping model is adaptable to various underground medium velocity modeling scenarios. After the model has been iteratively trained, it can directly achieve rapid prediction and reconstruction of underground velocity structures.
[0095] S3. Construct the physical constraint loss function and complete model training. Compared to traditional deep learning modeling methods that rely on massive amounts of manually labeled data, the physical information-driven deep learning framework proposed in this invention eliminates the need to generate training samples and manual labels, effectively reducing data generation costs. Simultaneously, it significantly improves the physical interpretability of the model by relying on physical equation constraints. This invention, for the first time, embeds the physical criteria for seismic wave propagation as a hard constraint into the loss function, constructing the physical constraint loss function, the expression of which is as follows:
[0096] ;
[0097] in, The number of speed models participating in training. This is the index value for the corresponding velocity model.
[0098] S4. Rapid imaging of underground velocity structure. After the network training converges and the parameters are optimized, the new measured travel-time perturbation data will be... Corresponding background time data By inputting the model, high-precision underground medium velocities can be quickly derived. The distributed structure enables automated and efficient seismic velocity imaging.
[0099] Will as Figure 4 (a) Figure 4 (b) and Figure 4 The travel time disturbances corresponding to the three velocity models shown in (c) Time travel with the background The data is input into the network for training. This model contains 70×280 grid points, a spatial sampling interval of 25m, and undergoes 20,000 training iterations. The Adam optimizer is used for network optimization training. The learning rate is 0.0005, and after 5,000 training iterations, the learning rate is halved. By training PIUFNO under hard constraints, the underground velocity structure that was not included in the training can be quickly predicted. After the network training is completed, it will be as follows: Figure 5 (a) Figure 5 The travel time disturbance corresponding to the velocity model shown in (b) Time-lapse with corresponding background The input to the network, and the underground velocity structure predicted by PIUFNO, are as follows: Figure 6 (a) Figure 6 As shown in (b) of the figure. Experiments show that this method requires only 0.22 seconds for rapid imaging of subsurface velocity structures, while traditional numerical methods require 65 seconds for tomographic imaging of the same model, significantly improving overall imaging efficiency. This revolutionary improvement in efficiency will significantly reduce the computational cost and time cycle of seismic imaging in fields such as oil and gas resource development, providing unprecedented technical support for high-precision subsurface structure analysis, real-time reservoir monitoring, and rapid decision-making response. It has significant practical application value for improving the exploration success rate and development benefits of complex oil and gas reservoirs.
[0100] It will be understood by those skilled in the art that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments, and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.
Claims
1. A fast multi-model tomography method with hard constraints based on physical information, characterized in that, Includes the following steps: S1. Construct a PIUFNO network model under hard constraints; S11, the hard-constrained PIUFNO network takes background travel time and travel time disturbance data corresponding to multiple sets of different seismic source observation data as input features, and finally outputs the underground medium velocity field and travel time factor parameters synchronously. S12. The velocity distribution characteristics of the subsurface medium and the seismic wave travel time data are correlated and solved using the equation to realize the inversion of the subsurface velocity structure; the overall travel time parameters are decomposed into two independent components; the background travel time is calculated based on the medium velocity value at the source point. S13. Using the theory of connection function, the measured travel time data collected by the surface geophone is introduced into the equation as a hard constraint. The travel time field is decomposed in a second optimization. The decomposed equation is substituted into the original equation to derive an improved equation with factorization form and incorporating measured hard constraint data. S2. Using the travel time disturbance and background travel time of data collected from different seismic sources as network inputs, the network directly outputs the corresponding underground velocity structure, establishing an end-to-end nonlinear mapping relationship between input and output. S3. Embed the physical criteria for seismic wave propagation as a hard constraint into the loss function, construct the physical constraint loss function, and complete the network training. S4. After the network training converges and the parameters are optimized, the new measured travel time disturbance data and the corresponding background travel time data are input into the model to deduce the velocity distribution structure of the underground medium and realize rapid imaging of the underground velocity structure.
2. The multi-model fast tomography method with hard constraints based on physical information according to claim 1, characterized in that, Step S12, the functional equation can be expressed as: ； Where T represents the travel time of the first arrival wave of the earthquake. Represents the velocity of the underground medium. Represents the gradient operator. Represents the coordinates of the model.
3. The multi-model fast tomography method with hard constraints based on physical information according to claim 2, characterized in that, The travel time T can be decomposed into the following form: ； in, Expressed as the travel time factor, it is used to characterize the deviation between the actual travel time and the travel time in an ideal homogeneous medium. This represents the background travel time under the assumption of a homogeneous medium.
4. The fast multi-model tomography method with hard constraints based on physical information according to claim 3, characterized in that, Assuming the subsurface medium has a uniform velocity from the earthquake source, the calculation formula is as follows: ； in, For seismic waves from the source coordinates Position propagation to spatial measuring points The straight-line distance This represents the medium velocity at the earthquake source point.
5. The fast multi-model tomography method with hard constraints based on physical information according to claim 4, characterized in that, Step S13: Based on the actual working conditions of seismic exploration, all field observation data... All samples were collected at a constant depth at the Earth's surface. On the plane, the travel time field T is decomposed by a second optimization, as follows: ； in, It represents the vertical direction in space, i.e., the z-axis coordinate. This represents the parameters output by the network. It is obtained by converting measured ground travel time data, specifically calculated using the following formula: ； in, This represents the actual travel time collected by surface geophones during seismic exploration.
6. The fast multi-model tomography method with hard constraints based on physical information according to claim 5, characterized in that, The improved equation is as follows: 。 7. The multi-model fast tomography method with hard constraints based on physical information according to claim 6, characterized in that, The core computational unit of the PIUFNO network is the U-Net FNO module, whose input features... After sequentially performing Fourier forward transform, high-frequency component linear filtering, inverse Fourier transform, U-net feature transformation, and local linear transformation to complete multi-dimensional feature fusion, the final calculation result is output. .
8. The fast multi-model tomography method with hard constraints based on physical information according to claim 1, characterized in that, Step S2, input [ ; ] and output [ ; The mapping relationship between them, that is, based on the time perturbation. Time travel with the background As input, with travel time factor and underground medium velocity This represents the end-to-end nonlinear mapping relationship for the output.
9. The fast multi-model tomography method with hard constraints based on physical information according to claim 1, characterized in that, Step S3, the physical constraint loss function, its expression is as follows: ； in, The number of speed models participating in training. This is the index value corresponding to the speed model.