A vsp time-lapse velocity inversion method of a physically embedded recurrent neural network

Abstract

The application discloses a VSP hourly velocity inversion method of a physical embedding recurrent neural network, applied to the field of seismic velocity inversion, and aims at the problem of low precision of existing seismic velocity inversion methods; on the basis of realizing the embedding of a recurrent neural network of a finite difference acoustic wave equation, the application modifies the back propagation algorithm of the RNN, calculates the residual error of a current wave field and a shot gather wave field at each independent time, takes the residual error as the loss at the current time, and sums the loss at the current time and the loss at the previous time at each time, so as to update the velocity model in the residual error updating range until the residual error meets the condition, and then the velocity inversion area is expanded, so that the step-by-step correction from the shallow part to the deep part is realized; compared with other inversion correction algorithms, the hourly inversion technology proposed by the application significantly improves the accuracy and reliability of the physical embedding RNN velocity inversion.

Description

Technical Field

[0001] This invention belongs to the field of geophysics, and specifically relates to a seismic velocity inversion technique. Background Technology

[0002] Seismic velocity modeling is of great significance in the field of geophysics. Seismic velocity is a crucial parameter describing the physical properties of subsurface media, and it has a key impact on seismic wave propagation, imaging, and interpretation. Accurate seismic velocity models can provide information about subsurface structure, lithological distribution, and stratigraphic variations, which is of great importance in fields such as oil and gas exploration, seismic hazard assessment, and geological structure analysis. Traditional seismic velocity modeling methods are mainly based on seismic data fitting and inversion techniques, such as tomography and full waveform inversion. These methods typically rely on complex mathematical models and assumptions and require significant computational resources and time. With the rapid development of machine learning and deep learning, neural networks have gradually attracted attention in seismic velocity modeling.

[0003] The application of neural networks in seismic velocity modeling mainly focuses on two aspects: regression problems and inversion problems. In regression problems, neural networks directly predict subsurface velocity models by learning the nonlinear mapping relationship between seismic data and actual subsurface velocities. In 1994, Tarantola and others first proposed using neural networks to transform time-domain seismic data into acoustic velocity models. In 1999, Nath et al. trained neural networks using synthetic data, resulting in a network capable of estimating formation velocities using inter-well data. In 2019, Yang and Ma implemented a fully convolutional neural network for inverting P-wave velocity models from raw seismic data. A common feature of these networks is the need for a large amount of labeled data to train them; once trained, the neural network can be used as an inversion solver. However, in the field of seismic exploration, large amounts of labeled datasets are difficult to obtain.

[0004] In seismic velocity inversion, neural networks are used to infer subsurface velocity models from observed seismic data. The inversion problem is typically a nonlinear, multimodal, and non-convex optimization problem, facing various challenges such as initial model dependence, local minima traps, and high computational complexity. Neural networks can improve the stability and accuracy of inversion by learning the complex relationship between seismic data and velocity models. Common inversion methods include Physically-Informed Neural Networks (PINNs) and Generative Adversarial Networks (GANs). The basic idea of ​​PINNs is to approximate unknown functions or parameters using a neural network and incorporate the residuals of the physical equations as part of the loss function. By minimizing the loss function, the neural network is trained to obtain a solution that satisfies physical constraints. Moseley et al. (2020) used PINN as a solver for forward propagation of acoustic waves, while Smith et al. and Waheed et al. applied PINN to the Eikonal equations for first-arrival prediction and travel-time tomography, respectively. Song et al. used PINN to solve the frequency domain anisotropic acoustic wave equations. Furthermore, PINN has successfully performed forward and inverse analyses on various complex systems even with limited sensor measurements or no labeled data.

[0005] RNNs (Recurrent Neural Networks) generally employ two network update algorithms: (1) Calculate the loss and update the network at each time step: At each time step, calculate the loss for the current time step and use this loss to update the network parameters. This is the traditional time-based loss update method. (2) Calculate the loss and then sum the losses at each time step to update the network: At each time step, calculate the loss for the current time step and sum the losses from previous time steps. Then, use the summed loss to update the network parameters. This method incorporates information from previous time steps into the loss at the current time step to provide more global information.

[0006] In RNNs embedding the acoustic wave equation, calculating the loss and updating the network at each time step changes the velocity model at different time steps. However, the velocity of the acoustic wave equation needs to remain consistent across different time steps, which violates the conditions for satisfying the acoustic wave equation, leading to the inversion failing to converge. Inversion algorithms that calculate the loss at each time step and then sum and update the network ignore the causal information of the wave field at different time steps. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention proposes a VSP time-by-time velocity inversion method with a physically embedded recurrent neural network. Based on the recurrent neural network embedding the finite difference acoustic wave equation, this invention modifies the backpropagation algorithm of the RNN. At each independent time step, the residual between the current wavefield and the shot gather wavefield is calculated as the current time step loss. Furthermore, at each time step, the current time step loss is summed with the previous time step loss to update the velocity model within the range using the summed residual. This process continues until the velocity in the current region makes the residual meet the conditions. Then, the velocity inversion region is expanded to achieve gradual correction from shallow to deep regions.

[0008] The technical solution adopted in this invention is: a VSP time-by-time velocity inversion method with physically embedded recurrent neural networks, comprising:

[0009] For the current time step, the wave fields of the two time steps prior to the current time step are used as the hidden layers of the RNN, and the source function of the current time step is used as the input of the RNN;

[0010] At each time step, the residual between the current wavefield and the shot gather wavefield output by the RNN network is independently calculated as the current time loss. At each time step, the current time loss is summed with the previous time loss to update the velocity model within the range using the summed residual. This process continues until the velocity in the current region makes the residual meet a given threshold condition, and then the velocity inversion region is expanded.

[0011] For a velocity model of size 100*100, the residual threshold is generally on the order of 1E-3.

[0012] The beneficial effects of this invention are as follows: Based on the PINN seismic velocity inversion theory, this invention proposes a physical embedded recurrent network method for hourly seismic velocity inversion. It utilizes a recurrent neural network to simulate the two-dimensional time-domain finite-difference acoustic wave equation as the forward modeling process, and uses velocity as a network parameter to correct the velocity model during the network's backpropagation correction process. This method can introduce acoustic wave equation information into the network, guiding the network's optimization direction, and avoid explicitly solving for the wavefield and gradient, reducing computational costs. Furthermore, it leverages the nonlinear fitting capability of the neural network to improve inversion accuracy and robustness. Moreover, given the temporal causal relationship of the wavefield—that is, the currently calculated wavefield is related to previous wavefields—this invention adopts the idea of ​​hourly inversion. This minimizes the residual of the wavefield at each moment, ensuring the correctness of subsequent wavefield calculations, mitigating the ambiguity of velocity inversion, and improving the accuracy and stability of the inversion. Attached Figure Description

[0013] Figure 1 This is a common RNN structure;

[0014] Figure 2 It is a physically embedded recurrent neural network structure;

[0015] Figure 3For physical embedding recurrent neural network operator structures;

[0016] Figure 4 A recurrent neural network embedded in the finite difference acoustic wave equation;

[0017] Figure 5 This is a schematic diagram of time-by-time inversion in RNN;

[0018] Figure 6 For the real model and the initial model;

[0019] Figure 7 The model and inversion results;

[0020] Wherein, (a) is the true model, (b) is the summation and inversion result of the overall loss, and (c) is the time-by-time inversion result;

[0021] Figure 8 For the comparison of lateral speeds at a depth of 500 meters;

[0022] Figure 9 A comparison of lateral velocities at a depth of 800 meters. Detailed Implementation

[0023] First, the relevant prior art of this invention will be described:

[0024] 1. Physically Embedded Recurrent Neural Networks

[0025] Recurrent Neural Networks (RNNs) are a class of neural network models capable of processing sequential data. Unlike traditional feedforward neural networks, RNNs have recurrent connections. At the current time step t, the RNN operates on the current input vector xt and the hidden state vector ht-1 from the previous time step xt-1, generating the current output vector yt and the current hidden state ht. This allows information to be passed and stored within the network, effectively capturing the temporal dependencies in the sequence. Seismic velocity inversion involves the propagation of seismic waves underground, which contains significant temporal correlations. Traditional methods often ignore the temporal dependencies in the propagation process, while RNNs can naturally incorporate time-series information to better model the dynamic process of seismic waves. Furthermore, seismic records in seismic data may vary in length. Traditional methods require data preprocessing or use fixed-length inputs. RNNs, however, can handle variable-length input sequences, flexibly adapting to seismic records of different lengths without additional data processing steps. Therefore, recurrent neural networks have significant advantages in seismic velocity inversion problems, as they can incorporate time-series information to better model the propagation process of seismic waves. The common update equation for RNNs is:

[0026] y t+1 =N(h)t ,x t+1 )

[0027] h t+1 =F(h) t x t+1 )

[0028] A common RNN structure is as follows Figure 1 As shown.

[0029] The propagation structure of the differential acoustic wave equation has a high degree of similarity to the network structure of an RNN, and existing experiments show that the dynamics of the wave equation are conceptually equivalent to those of an RNN. Therefore, the differential acoustic wave equation can be embedded into an RNN structure to better explain the wave propagation characteristics and map them into the neural network structure. Considering the dependence of the differential acoustic wave equation on the previous two time steps, the wave fields of the previous two time steps can be used as the hidden layers of the RNN, the source function at the current time step can be used as the input, and the signal at the wave field detector at each time step t can be used as the signal at time step t of the shot collection. Using the velocity model in the differential equation as the trainable parameters of the network, the process of back-correcting using the error between the observed and predicted values ​​can be regarded as the inversion process of the velocity model. This method can introduce information from the acoustic wave equation into the network, guide the optimization direction of the network, avoid explicit gradient solving, reduce computational costs, and utilize the nonlinear fitting ability of the neural network to improve inversion accuracy and robustness. A physically embedded recurrent neural network structure is as follows: Figure 2 As shown, the operator structure is as follows Figure 3 As shown.

[0030] Based on the recurrent neural network that embeds the finite difference acoustic wave equation, this invention modifies the backpropagation algorithm of the RNN. At each independent time step, the residual between the current wave field and the shot gather wave field is calculated as the current time step loss. At each time step, the current time step loss is summed with the previous time step loss to update the velocity model within the range of the summed residual. This process continues until the velocity in the current region makes the residual meet the conditions. Then, the velocity inversion region is expanded to achieve gradual correction from shallow to deep regions.

[0031] The implementation process of this invention includes:

[0032] A. Recurrent Neural Network Embedded in Finite Difference Acoustic Wave Equation

[0033] For a two-dimensional isodense acoustic medium, the time-domain wave equation is:

[0034]

[0035] Where u(r,t) represents the pressure or displacement at coordinate r at time t, v(r) represents the speed of sound at coordinate r, s(r,t) represents the source function at coordinate r at time t, and δ(rr) represents the source function. s) is a Dirac function, indicating that energy is released only at the source location.

[0036] The two-dimensional medium is spatially discretized, with coordinates (x, y) discretized into grid points (i, j), where i represents the index in the x-direction and j represents the index in the y-direction. A uniform grid is typically used, dividing the space into a series of small, equal-sized cells according to given spatial step sizes Δx and Δy. Time t is discretized into a time step Δt, allowing time to advance at regular intervals. The values ​​of Δx, Δy, and Δt satisfy stability conditions. For example, in a velocity model with a maximum speed of 4000 m / s, Δx, Δy, and Δt take values ​​of 5, 5, and 0.0005 respectively, satisfying the stability condition: Δt ≤ 1 / (v max * Where v max That is the model's maximum speed.

[0037] Based on the discrete spatial grid and discrete time step, the derivative term is replaced by a difference approximation. The central difference approximation is used to approximate the second-order spatial derivative.

[0038]

[0039] Where i,j are the coordinates at r, and Δx and Δy represent the grid spacing in the x and y directions, respectively.

[0040] The second-order time derivative is approximated using the second-order central difference approximation.

[0041]

[0042] Substituting the difference approximation into the time-domain wave equation, we obtain the two-dimensional time-domain finite-difference acoustic wave equation:

[0043]

[0044] Using the differential acoustic wave equation, the pressure or displacement at a certain moment can be expressed as the square of the wave field, source, and velocity model from the previous two moments, v. 2 The calculation is performed on (i,j), and the relationship can be viewed as a function g:

[0045] u(r,t+Δt)=g(u(r,t),u(r,t-Δt),s(r,t),v 2 (r))

[0046] The shot gather record can be viewed as a time-varying sequence of the wavefield at the detector location. Using this time series as a label, the residual is calculated by comparing the network output at each time step with the shot gather sequence at the current time step. Backpropagation is then used to minimize the residual, thus achieving the velocity model inversion process. The wavefield at each time step can be considered a part of the time series data. The recurrent neural network embedded in the finite difference acoustic wave equation is as follows... Figure 4 As shown:

[0047] B. Time-series inversion of RNN

[0048] At each time step, the mean squared loss is calculated using the output and label: δd t =(d t -d′ t ) 2 , where d t Let d′ be the output of the network at time t. t Let be the label sequence at time t. The residual used to calculate the gradient backpropagation at time t is: Here, rs represents different gun sets. The gradient is calculated by examining the residuals at each time step to determine the update amount of the velocity model at time t. The gradient is propagated through the chain rule; therefore, the calculation of the velocity correction is related to the d that causes the residual. t Relevant. From the two-dimensional finite-difference time-domain acoustic wave equation, it can be seen that d t The calculated value is related to the velocity model and the wavefield at the previous two time points, while the spatial domain variation at different time points is caused by the wavefield difference at the previous time point. Therefore, the range of the velocity correction gradually expands with the range of the wavefield. t (r) represents v(r) at time t.

[0049] like Figure 6 The image shows the actual model and the initial model of the velocity model.

[0050] Compared to traditional methods that independently calculate the loss and update the network at each time step or calculate the summation loss across all time steps, this method has significant advantages. First, time-by-time inversion not only minimizes the overall residual but also keeps the residual of the wavefield at each time step as small as possible. Furthermore, by ensuring the wavefield residual is small at the previous time step, wavefield propagation at the next time step is performed, introducing causal information about wavefield propagation and ensuring it satisfies the propagation conditions of the acoustic wave equation, thus avoiding errors at the current time step caused by errors at the previous time step. The correction region of the velocity model is related to the propagation range of the wavefield. Through a time-by-time correction algorithm in the time domain, the velocity model can be progressively corrected in the spatial domain, starting from the epicenter and gradually moving outwards. This progressive correction in the spatial domain results in smaller inversion parameter values, reducing the ambiguity of the inversion problem, and more accurate shallow velocities improve the accuracy and stability of deep velocity correction. A schematic diagram of RNN time-by-time inversion is shown below. Figure 5 As shown.

[0051] The technical effects of the present invention will be explained below with reference to actual data:

[0052] A level-plane model 1 was established, with velocities ranging from [3, 3.5, 4] km / s from shallow to deep. A synthetic dataset was calculated using the VSP observation system via forward propagation. The Adam correction algorithm was used for all inversions, with identical parameter settings. Model 1 and its inversion results are shown below. Figure 7 As shown. By Figure 7 It can be seen that, overall, time-by-time inversion yields smoother results in both shallow and deep regions, especially near the excitation point close to the surface and in the lateral regions. Velocity curves were compared using slices at depths of 500m and 800m, respectively. The comparison results are as follows: Figure 8 , Figure 9 As shown:

[0053] Depend on Figure 8 and Figure 9 It can be seen that, in terms of inversion accuracy, hourly inversion is generally more accurate than loss summation inversion, and the inversion results are closer to the real model. In addition, hourly inversion based on wave propagation ensures higher accuracy of the preceding wave field, making the subsequent wave field propagation calculation more accurate, and the inversion more accurate. This is reflected in the inversion results as greater accuracy in the model's sides and deep regions.

[0054] Model experiments and actual data tests demonstrate that the time-by-time inversion technique proposed in this invention significantly improves the accuracy and reliability of velocity inversion of physically embedded RNNs, and has obvious advantages in utilizing wavefield causal information in a physical sense.

[0055] To facilitate understanding of the technical content of this invention by those skilled in the art, the following description, in conjunction with the accompanying drawings, further illustrates the invention.

[0056] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A VSP time-lapse velocity inversion method of a physically embedded recurrent neural network, characterized in that, Comprise: For the current time, the wave field of two time points before the current time is taken as the hidden layer of the RNN network, and the source function of the current time is taken as the input of the RNN network; From the source, the residual of the wave field output by the RNN network at the current time and the shot gather wave field is independently calculated at each time, which is taken as the loss of the RNN network at the current time, and the loss of the current time and the previous time is summed at each time to update the velocity model in the residual range; The wave field output by the RNN network at a certain time is denoted as Then The calculation is performed by squaring the wave field, the source and the velocity model at two time points, and the calculation formula is as follows: ； wherein, denotes the wavefield at coordinate r at time t, denotes the wavefield at coordinate r at time t, denotes the velocity model, denotes the source function at coordinate r at time t; The residual of the wave field output by the RNN network at the current time and the shot gather wave field is independently calculated at each time, and the calculation formula is: ； wherein, is the wavefield output by the RNN network at time t, is the corresponding shot gather wavefield at time t, denotes the residual.

2. The VSP time-lapse velocity inversion method of claim 1, wherein, The residual for calculating the gradient back propagation at time t is: ； wherein, denotes different shot gathers wavefields.

3. The VSP time-lapse velocity inversion method of claim 2, wherein, The gradient is calculated by calculating the residual for calculating the gradient back propagation at each time, so as to calculate the update amount of the velocity model at time t: 。 4. The VSP time-lapse velocity inversion method of claim 3, wherein, The gradient is transmitted through the chain rule.

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