A least squares reverse-time migration method guided by a conditional diffusion model

Abstract

The present application belongs to the field of deep-sea oil and gas field exploration and development, and provides a least square reverse time migration method guided by a condition diffusion model. The present application aims to solve the problems of limited resolution, low amplitude fidelity and poor geological adaptability of the conventional LSRTM method under band-limited illumination conditions. The synthetic and actual data experiments show that the proposed method is significantly better than the conventional LSRTM in terms of deep interface continuity, amplitude fidelity and artifact suppression, and can achieve a comparable residual threshold with fewer iterations, thereby achieving a synergistic improvement in imaging quality and computational efficiency.

Description

Technical Field

[0001] This invention belongs to the field of deep-sea oil and gas field exploration and development, and specifically relates to a least-squares reverse time migration method guided by a conditional diffusion model. Background Technology

[0002] Existing techniques for retrieving subsurface reflectivity by iteratively minimizing data residuals face resolution limitations under band-limited illumination. To avoid explicitly constructing a huge Hessian matrix, historical gradients or low-rank approximation strategies are typically used to implicitly construct the inverse Hessian operator. This proposed scheme achieves gradient curvature correction and amplitude compensation at a controllable cost, effectively suppressing aliasing and improving the signal-to-noise ratio and resolution of imaging in complex tectonic regions while accelerating convergence.

[0003] However, existing approximate second-order strategies suffer from insufficient phase correction in complex regions such as underwater salt fields due to low-rank simplification, making it difficult to characterize long-range couplings in strongly inhomogeneous media. Furthermore, their reliance on time-consuming precise line searches leads to high iteration costs and reduces overall efficiency. Simultaneously, gradient-difference-based information update mechanisms are extremely sensitive to data noise and early gradient errors, easily causing oscillations. This makes it difficult to balance accuracy, efficiency, and robustness, becoming a key bottleneck restricting large-scale high-resolution imaging. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a least-squares reverse-time migration method guided by a conditional diffusion model, thereby resolving the issues in the prior art. The technical solution adopted by this invention is as follows:

[0005] A least-squares reverse-time migration method guided by a conditional diffusion model includes:

[0006] Step 1: Construct the least-squares inverse time migration inversion framework;

[0007] Step 2: Construct a U-Net network with a temporal embedding module and an attention mechanism;

[0008] Step 3: Pre-train the conditional denoising diffusion probability model;

[0009] Step 4: Perform the inversion using an alternating iterative strategy of data consistency and deterministic denoising projection;

[0010] Step 5: Introduce a skip sampling strategy for the denoising diffusion implicit model to accelerate the inversion process.

[0011] Furthermore, step 1 includes: establishing the correspondence between forward modeling of seismic data and migration imaging based on the propagation law of seismic wavefield; constructing an inversion objective function with regularization constraints by minimizing the residuals between simulated and measured seismic data; and forming a least squares inverse time migration inversion framework.

[0012] Furthermore, step 2 includes: building a multi-resolution layer U-Net network, integrating time-step embedding, self-attention mechanism and cross-layer residual connection, setting self-attention modules in the bottleneck layer and specified resolution layer of the U-Net network, and incorporating RTM images as conditional features into the U-Net network.

[0013] Furthermore, step 3 includes: using RTM images as conditional information, constructing paired training samples of reflectance and corresponding RTM images, and through iterative training, enabling the conditional denoising diffusion probability model to learn the mapping relationship from noise to reflectance, thereby obtaining generative geological priors that can be used for inversion.

[0014] Furthermore, step 4 includes: first completing data consistency correction through least squares inverse time offset gradient update, and then completing deterministic denoising projection guided by a fixed RTM image.

[0015] Furthermore, step 5 includes: based on the trained conditional denoising diffusion probability model, replacing it with a denoising diffusion implicit model sampler to construct a skip sampling strategy.

[0016] The present invention has the following beneficial effects:

[0017] (1) By injecting powerful, data-driven geological structural priors through the conditional diffusion model, DLSRTM outperforms traditional LSRTM in terms of deep interface continuity, amplitude fidelity and artifact suppression, and can effectively recover high wavenumber reflection information, significantly improving imaging quality.

[0018] (2) The DDIM deterministic skip sampling strategy is adopted, which greatly reduces the number of times the diffusion model is called. While ensuring imaging quality, the overall computational cost is significantly reduced, and the synergistic optimization of imaging quality and efficiency is achieved.

[0019] (3) The inversion results are generated based on RTM images, which ensures that the macroscopic structure of the inversion results is highly consistent with the physical imaging results, thus improving the geological interpretability of the imaging.

[0020] (4) By organically combining the physical-driven LSRTM with the data-driven diffusion model, a new hybrid-driven inversion paradigm is formed, providing a new approach to solving ill-conditioning problems in other geophysical inversions.

[0021] (5) With its explicit modeling capability for data distribution, this invention exhibits stronger generalization and detail recovery capabilities in complex geological scenarios. It not only performs better in the continuous reconstruction of deep weak reflection interfaces, but also more effectively suppresses imaging artifacts and maintains the relative fidelity of amplitude. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the process of the present invention.

[0023] Figure 2 This is an improved U-Net network structure.

[0024] Figure 3 This is the convergence curve of the network's loss function during training.

[0025] Figure 4 The outputs are reflectivity, RTM, and conditional diffusion model; where: Figure 4 (a) True reflectance; Figure 4 (b) Counter-clockwise offset; Figure 4 (c) Results generated by the diffusion model;

[0026] Figure 5 The model consists of a velocity model and a smoothed velocity model. The model size is 64×64, the grid spacing is 10 meters, and the velocity range is 1500-4500 m / s. Figure 5 (a) Actual speed; Figure 5 (b) Offset velocity;

[0027] Figure 6 The images show the reflectance of traditional LSRTM and DLSRTM; where: Figure 6 (a) True reflectance; Figure 6 (b) Least squares reverse time offset; Figure 6 (c) Least squares reverse time migration guided by conditional diffusion model;

[0028] Figure 7 Vertical offset profiles at positions of 0.16 km, 0.32 km, and 0.48 km are shown for different imaging results; where: Figure 7 (a) Vertical profile at 0.16 km; Figure 7 (b) Vertical profile at 0.32 km; Figure 7 (c) Vertical profile at 0.48 km;

[0029] Figure 8 A comparison of the iterative convergence curves of the traditional LSRTM and DLSRTM;

[0030] Figure 9 Imaging results of DDPM with 30, 50, and 100 samples and imaging results of DDIM with 3, 5, and 10 samples; where: Figure 9 (a) DDPM sampling was performed 30 times; Figure 9 (b) DDPM sampling 50 times; Figure 9 (c) DDPM sampling was performed 100 times; Figure 9 (d) DDIM was sampled 3 times; Figure 9 (e) DDIM was sampled 5 times; Figure 9(f) DDIM sampling was performed 10 times;

[0031] Figure 10 This section compares the structural similarity, peak signal-to-noise ratio, and computation time of the generated results when using DDPM and DDIM sampling in DLSRTM, respectively. Detailed Implementation

[0032] The following will be described in conjunction with embodiments of the present invention. Figures 1-10 The technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0033] This invention aims to address the limitations of traditional LSRTM methods in terms of resolution and amplitude fidelity under band-limited illumination, as well as the poor geological adaptability of traditional regularization methods. Experiments using synthetic and real-world data demonstrate that the proposed method significantly outperforms traditional LSRTM in terms of deep interface continuity, amplitude fidelity, and artifact suppression, achieving a comparable residual threshold with fewer iterations, thus synergistically improving imaging quality and computational efficiency.

[0034] like Figure 1 This invention proposes a least-squares reverse-time migration method guided by a conditional diffusion model, comprising the following steps:

[0035] Step 1: Construct the least-squares inverse time migration inversion framework;

[0036] Step 2: Construct a U-Net network with a temporal embedding module and an attention mechanism;

[0037] Step 3: Pre-train the conditional denoising diffusion probability model;

[0038] Step 4: Perform the inversion using an alternating iterative strategy of data consistency and deterministic denoising projection;

[0039] Step 5: Introduce a skip sampling strategy for the denoising diffusion implicit model to accelerate the inversion process.

[0040] This invention uses RTM images as physical conditions to train a C-DDPM model to learn a nonlinear mapping from noise to high-resolution reflectivity, obtaining generative priors that can be used for inversion. During the inversion stage, an alternating strategy of data consistency steps and deterministic denoising projection is employed to construct an implicit regularization term driven by both data and physics. Simultaneously, a deterministic skip-step sampling strategy of the Denoising Diffusion Implicit Model (DDIM) is utilized to significantly reduce computational costs while maintaining imaging quality, achieving high-resolution, high-fidelity, and efficient seismic imaging.

[0041] Specifically, the technical solutions for each step are as follows:

[0042] Step 1: Construct the LSRTM inversion framework, i.e., the least squares inverse time migration inversion framework;

[0043] Based on the propagation laws of seismic wavefields, a correspondence between forward modeling and migration imaging of seismic data is established. By minimizing the residuals between simulated and measured seismic data, an inversion objective function with regularization constraints is constructed, forming a least-squares inverse time migration inversion framework, which specifically includes:

[0044] Under the weak scattering approximation, located at the receiving point For the source of the earthquake The uplink reflected wave field in the frequency domain can be expressed as:

[0045]

[0046] In the formula, It is any underground scattering point. It's frequency. It is the epicenter The frequency domain representation, and These are the ascending and descending Green's functions excited by the smooth background velocity field, respectively. This is a model perturbation. Therefore, the observed data is a weighted linear integral of the model perturbation after a two-way propagation path. We introduce a linear forward modeling operator. Data vector With model perturbation vector Equation (1) can be written as:

[0047]

[0048] To construct the inversion framework, the forward operators need to be defined. The adjoint operator :

[0049]

[0050] In the formula, It is a complex conjugate, and this equation corresponds to the migration result obtained under the frequency domain cross-correlation imaging condition, denoted as... .

[0051] Furthermore, substituting equation (1) into equation (3), we obtain:

[0052]

[0053] In the formula, It is a Hessian matrix. (From...) The band-limited nature and propagation geometry are known. The column vectors characterize the offset response of a single-point scatterer, therefore Only the truth value is fuzzy kernel The approximation after convolution.

[0054] To overcome the Hessian blurring effect and improve image quality, LSRTM solves for the optimal reflectance model by minimizing the residual between simulated and observed data. Considering regularization constraints, its objective function can be written as:

[0055]

[0056] in, This represents the reflectance / offset image to be determined. For regularization terms, This is a weighting factor.

[0057] Step 2: Construct a U-Net network with a temporal embedding module and an attention mechanism;

[0058] This invention employs iterative denoising to train a nonlinear mapping from noise to a high-resolution subsurface reflectivity model, obtaining generative priors that can be used for inversion. The network backbone is designed based on a conditional U-Net generator, integrating time-step embedding, self-attention mechanisms, and cross-level residual connections to achieve accurate reconstruction of multi-scale details and modeling of long-range dependencies. Figure 2 As shown, this architecture comprises five resolution layers (decreasing from 64×64 to 4×4), performing data compression and reconstruction through four downsampling / upsampling processes. The encoder uses stride convolution (stride=2) for downsampling, while the decoder employs nearest-neighbor interpolation combined with convolution for upsampling. Each layer consists of two residual blocks, with an initial channel count of 64; when the channel count changes, 1×1 convolutions are used to adjust the channel size to maintain consistency. Symmetrical layers between the encoder and decoder enhance gradient propagation and detail enhancement through skip connections, thereby improving training stability.

[0059] To better capture the interrelationships between long-distance features and reduce spatial aliasing during the diffusion deconvolution process, self-attention modules are introduced in the bottleneck layer (4×4) and the 8×8 resolution layer. The time steps during the diffusion process are represented by sinusoidal positional encoding and injected into each residual block after affine modulation. Simultaneously, the RTM image undergoes shallow encoding to obtain conditional features. These features are combined with multi-scale features from various layers of the backbone network, working together through affine modulation or feature fusion to ensure that noise prediction is constrained by the RTM structure throughout the entire network. This design not only retains U-Net's advantage in handling local details but also enhances the consistency of the overall structure through conditional guidance and attention mechanisms.

[0060] Step 3: Pre-train the conditional denoising diffusion probability model;

[0061] Diffusion models are a type of generative model based on progressive denoising. The core idea is to construct a learnable inverse diffusion path from pure random noise to the target data distribution: the forward process (diffusion) gradually perturbs the real data into Gaussian noise according to a preset noise schedule; the reverse process (generation) learns to remove an appropriate amount of noise at each time step, thereby restoring the noise to the data sample.

[0062] The pre-training phase, centered on the conditional diffusion model, aims to learn the reconstruction mapping from noise to high-resolution reflectivity under the physical guidance of RTM images, providing data-driven and consistent implicit regularization for LSRTM iteration. Based on the true velocity model, the corresponding reflectivity is calculated, and RTM images are generated on a matching smooth background, forming paired samples with a one-to-one correspondence between reflectivity and RTM images, and scale normalization is uniformly performed.

[0063] The forward process is a non-learned linear Gaussian Markov chain, with a given variance and scheduling. For real samples Gaussian noise is injected sequentially to obtain a sequence of latent variables. The single-step transition probability distribution of this Markov chain is defined as follows:

[0064] (6)

[0065] make , . The signal retention coefficients at step t are... For the noise variance scheduling at step t; The cumulative signal retention coefficients for the previous t steps; Let be the noisy latent variable at step t; The symbol for the normal distribution (Gaussian distribution) is [symbol missing]. It is the identity matrix; This represents the true distribution of the forward diffusion process; due to the linearity of the Markov chain, the distribution from the initial state can be directly derived. At any time Closed edge distribution:

[0066] (7)

[0067] Using the reparameterization technique, the sampling process in the above equation can be rewritten as:

[0068] (8)

[0069] In the formula, This represents random noise sampled from a standard normal distribution. The cumulative signal retention coefficients for the previous t steps; The initial clean sample is the real data. This formula shows that at any given time... Noisy samples All can be derived from initial samples and random noise It can be obtained directly through linear combination.

[0070] The goal of the reverse process is to start from... Gradually reduce noise and restore to Due to the true posterior Difficult to obtain directly, based on parameters The neural network models the transition probability at each step:

[0071] (9)

[0072] In the formula, It is usually fixed as the diagonal variance related to time, and only the mean is learned. . Predict the mean for the model.

[0073] The model is trained with the goal of maximizing the variational lower bound (VLB) of the log-likelihood.

[0074] (10)

[0075] in, and The correlation with network parameters can be ignored or treated as a constant term; the main learnable part comes from the KL terms at each step. . As the variational lower bound, Let be the mathematical expectation of the forward distribution q. Let KL divergence be the KL divergence. This represents the true distribution of the forward diffusion process. For the prior distribution of the reverse generation process, The model distribution for the reverse generation process; This is the initial clean sample, i.e., the real data; Let be the latent variable after adding noise at step t; Let T be the latent variable at step T (the final step); T is the total number of time steps in the diffusion process.

[0076] Based on known real data Under the condition of posterior Still follows a Gaussian distribution:

[0077] (11)

[0078] in,

[0079] , (12)

[0080] To improve numerical stability, the KL terms corresponding to equations (9) and (11) are usually written as simplified quadratic forms:

[0081] (13)

[0082] Where C is a constant. Commonly used . This represents the true posterior mean. This represents the true posterior variance. Let V be the variance of the posterior distribution of the model;

[0083] From (8) and (12), we can... Transformed into noise Format:

[0084] (14)

[0085] Therefore, if we let the neural network predict noise... Then there is

[0086] (15)

[0087] at this time Degenerates into the quadratic difference of two Gaussian means. Minimizing KL is equivalent to minimizing the mean square error between the predicted noise and the actual noise, resulting in a widely adopted simplified training objective:

[0088] (16)

[0089] in Usually according to Uniformly distributed sampling, .

[0090] After training, from Departure, according to Iteration:

[0091] , (17)

[0092] in Consistent with (13) This ensures that the sampling noise matches the variance setting during the training phase. To simplify the training loss; For mathematical expectation; To predict noise; denoted as σ0, where σ0 is the standard deviation of the sampling noise; z is the random sampling noise.

[0093] To achieve controlled generation guided by structure imaging in a migration background, a conditional diffusion model is introduced, allowing the model to learn the conditional distribution. ,in This indicates conditional information, i.e., RTM images.

[0094] In the reverse denoising process, it is necessary to calculate from time step arrive Transition probability:

[0095] (18)

[0096] Because the noise prediction network incorporates conditional information as input, a simplified conditional training objective is adopted:

[0097] (19)

[0098] To simplify the training loss, the corresponding single-step sampling update is:

[0099] (20)

[0100] During training, for any sample pair, random sampling time steps are performed, and noisy samples are generated by forward diffusion. The noise prediction network is then instructed to minimize the mean square error between the predicted noise and the actual noise under the constraints (Equation (19)). Specifically, the training process of the diffusion model includes the following steps.

[0101] 1) Randomly select a batch of training sample pairs.

[0102] 2) Gaussian noise is generated to destroy the clean reflectivity sample, which is called the diffusion process over time.

[0103] 3) Explicitly introduce the RTM image as a condition to impose structural constraints on subsequent denoising.

[0104] 4) Different Noise samples are fed into the U-Net network to output a response to added noise. The estimate.

[0105] 5) The loss is measured by taking the difference between the estimated noise and the reference noise, and then the difference is backpropagated to update the U-Net network.

[0106] Step 4: Perform the inversion using an alternating iterative strategy of data consistency steps and conditional denoising steps;

[0107] In the data consistency step, the current image... LSRTM gradient updates are performed to ensure the model evolves in a direction consistent with physical laws by minimizing the residuals between synthetic and observed data. The update formula is as follows:

[0108] (twenty one)

[0109] in, For learning rate, For the orthogonal operator, For the companion operator, For observational data. The updated model vector;

[0110] In the conditional denoising step, in order to seamlessly connect with the LSRTM iteration, the noise-free expectation part in equation (20) is denoted as the conditional denoising operator. :

[0111] (twenty two)

[0112] make To avoid introducing uncontrollable random noise in the inversion process, the inverse denoising process of equation (20) is updated as follows:

[0113] (twenty three)

[0114] With fixed RTM condition images Guided diffusion denoising, The model is updated using a regularized gradual weakening strategy that prioritizes structure over detail, starting from coarse to fine:

[0115] (twenty four)

[0116] Equation (21) ensures consistency with observed data by correcting kinematic and amplitude residuals, while Equation (24) will... The projected seismic imaging manifold, constrained by RTM, is used to suppress sidelobes and noise, and to fill in structural priors in underiluted regions. These two processes alternate to ensure that the solution simultaneously satisfies data consistency and conditional denoising prior consistency.

[0117] Equation (24) can be interpreted as a proximal update:

[0118] (25)

[0119] in, These are the weighting coefficients for the proximal terms. Here is the regularization strength parameter. This is a regularization term based on the conditional diffusion model.

[0120] Deterministic denoising operator ,Right now It can be regarded as a regularization term. The proximal operator, in substitution (5) As an implicit regularization in LSRTM, it can be seen that the alternating iteration strategy is equivalent to minimizing in an optimization sense. A solution method that combines explicit and implicit regularization, where regularization is given by a conditional diffusion model and adaptively adjusted with sampling time.

[0121] Step 5: Introduce a skip sampling strategy for the denoising diffusion implicit model to accelerate the inversion process.

[0122] The core of the denoising diffusion implicit model lies in not changing the forward edge distribution. By using a non-Markovian construction, a deterministic reverse trajectory with skip-step capability is obtained, thus significantly accelerating sampling. Since the training objective of DDPM depends only on the edges... Therefore, while reusing the already trained model, a more efficient DDIM sampler can be replaced. Since the alternation of Equation (25) requires frequent calls to forward modeling / adjoint modeling and prior projection, the overall computational efficiency is low. Subsequently, an acceleration scheme based on DDIM skip sampling was used, which can significantly reduce the iteration cost and shorten the convergence time.

[0123] DDIM defines a parameterized forward distribution. :

[0124] (26)

[0125] in, Controlling the randomness of the reverse, It is the original, clear image. This is the noisy image at the current moment, and T is the predefined total number of diffusion steps. It is the sequence of noisy images from step 1 to step T.

[0126] The crucial single-step posterior can be written in Gaussian form:

[0127] (27)

[0128] in, It is a predefined variance scheduling. , Control the randomness of the reverse process.

[0129] This leads to the skip-step reverse sampling: given a subsequence ,right We can obtain:

[0130] (28)

[0131] in, This represents the prediction of noise in the noisy image at the current time step.

[0132] Estimate the initial model after denoising:

[0133] (29)

[0134] randomness parameter Defined as:

[0135] (30)

[0136] when hour, The reverse chain becomes a completely deterministic DDIM trajectory.

[0137] Specific embodiments of the present invention are as follows:

[0138] During training, the maximum forward diffusion time step is set to Linear noise scheduling is employed. The optimizer is Adam, and the initial learning rate is... A total of 400 training cycles were conducted. Figure 3 The loss convergence curve shows that the loss decreases rapidly in the early stage of training and then converges smoothly to a low level. No overfitting or gradient anomalies were found, which verifies the effectiveness of the above scheduling and structure configuration.

[0139] To intuitively evaluate the usability of the generated prior, conditional generation tests were performed using samples from outside the training set. DDIM sampling was employed, with the number of subsequence steps S=100, recursively calculated from t=100 to t=0. Under fixed RTM conditions... Figure 4 (b)] Under the constraint, the generated trajectory starts from random noise and is gradually reconstructed through iterative denoising to obtain a reflectivity with continuous boundaries, reliable amplitude, and clear structure. The generation results of the diffusion model [ Figure 4 (c) and true reflectance Figure 4 [(a)] The comparison shows that the two are highly consistent in terms of construction geometry, indicating that the model has effectively learned the nonlinear mapping from RTM to reflectivity, which can be used as a robust prior projection for subsequent DLSRTM iterations.

[0140] After training the diffusion model, the proposed sampling method was used to reconstruct the subsurface reflection coefficient model to verify the effectiveness of the method in least squares inverse time migration. The experiment followed the established settings, and the pre-trained diffusion model has plug-and-play characteristics, which can be directly integrated into the LSRTM inversion process without the need for model updates or hyperparameter optimization.

[0141] A velocity model with a resolution of 64×64 was selected. Figure 5 (a)], with a spatial sampling interval of 10m in both the x and z directions, this model is distributed in the same way as the training set but was not used in the training. A Ricker wavelet with a dominant frequency of 25Hz was used to generate seismic records by solving the acoustic equation with a time sampling interval of 1ms and a recording duration of 1s. Ten seismic sources and 64 receivers were deployed on the observation surface. The seismic sources were located on the surface, spaced 60m apart, with the first shot located 20m from the left boundary; the receivers were also located on the surface, spaced 10m apart, with the first receiver located at the left boundary. The initial velocity model was obtained by Gaussian smoothing the velocity model. Figure 5 (b)].

[0142] DLSRTM can be understood as embedding LSRTM into the sampling process of the diffusion model. To ensure fairness in the comparison, in this example, DLSRTM uses the last 10 denoising steps, and after each denoising step, two LSRTM iterations are performed. We compared the imaging results of the true reflectance model, LSRTM, and the DLSRTM proposed in this paper on the above data. Figure 6 The denoising results generated by the conditional diffusion model at each time step will serve as the initial model for LSRTM iteration. DLSRTM balances the geological rationality of the data with minimizing the residuals in the seismic data, effectively recovering high wavenumber reflection information and improving imaging resolution.

[0143] To quantitatively assess differences in imaging performance, Figure 7 Vertical profiles at several representative horizontal locations are presented, and point-by-point comparisons are made with the true reflectance. The results show that DLSRTM outperforms traditional LSRTM in terms of spatial resolution, amplitude fidelity, and migration artifact suppression at deep structural interfaces. Especially in sections with significant interference due to insufficient illumination, DLSRTM can better mitigate the blurring kernel effect caused by Hessian band limiting, and its reflectance coefficient amplitude and phase characteristics are in better agreement with the true values. Figure 8The evolution of the objective function with each iteration step in the inversion process for two methods is presented. The loss of the traditional LSRTM exhibits a monotonically and gradually decreasing trend; in contrast, DLSRTM shows a quasi-periodic pattern of first decreasing, then increasing, and then decreasing again. This is because under each diffusion sampling step, the conditional prior performs structural sharpening on the offset image, which may temporarily introduce a small amount of non-physical high-frequency components, causing a temporary increase in the data residuals; subsequent model constraint steps then identify and correct these high-frequency components, causing the loss to decrease again. Overall, the loss curve of DLSRTM converges in a sawtooth pattern and eventually stabilizes at a level lower than that of LSRTM, indicating that the alternating mechanism of prior projection and data consistency maintains good convergence stability while suppressing artifacts and improving resolution.

[0144] Figure 1 This is a flowchart illustrating the complete workflow of the least squares reverse time migration (DLSRTM) guided by the conditional diffusion model. It includes the forward pass of the original conditional denoising diffusion probability model and the generation process of conditional information in C-DDPM, i.e., the process of obtaining the reverse time migration profile from the velocity model. In the figure, U-Net represents a U-shaped network, the backbone neural network of the conditional diffusion model in this invention; x represents a general symbol in the diffusion model, representing a latent variable. This represents the initial clean sample, i.e., the real data; Represents the noisy latent variable at step t; This represents the pure Gaussian noise in the final step of the diffusion process. Figure 1 In the middle, the reverse process starts from pure noise. Begin by gradually removing noise to restore the target data. . , The output of the diffusion model is an intermediate result obtained by subtracting the U-Net's prediction of the current noise, which is the result of stepwise denoising.

[0145] Figure 2 This is an improved U-Net network structure. The backbone adopts the U-Net generator architecture, containing 5 resolution levels. Through skip connections between the encoder and decoder and residual block design, it balances the stability of multi-scale detail reconstruction and gradient propagation. Self-attention modules introduced in the bottleneck layer and the 8×8 layer effectively model long-distance construction relationships and suppress spatial aliasing. Furthermore, the network embeds the diffusion time step into the residual block through affine modulation and deeply fuses conditional RTM image features with multi-scale features of the backbone, ensuring that noise prediction is constrained by the RTM structure at all scales. This significantly enhances the consistency of the overall construction while preserving local detail advantages. Figure 2In the diagram, the improved U-Net network takes 2-channel data as input. The left encoder downsamples the data step-by-step, increasing the number of channels from 64 to 512, while retaining gradient information through residual connections ("+"). The bottleneck layer introduces a self-attention module (A) to capture global dependencies and fuses temporal embeddings (t) to model dynamic changes. The right decoder gradually restores spatial resolution through upsampling, reducing the number of channels from 512 to 64, and fuses high-resolution details from the encoder using skip connections. Finally, a 1x1 convolution outputs 1-channel data. In the diagram, the numbers represent the number of channels in the feature maps of each layer, "A" represents self-attention, and "t" represents temporal embedding.

[0146] Figure 6 This paper visually demonstrates the superior performance of the DLSRTM method proposed in overcoming the limitations of traditional imaging and restoring high-resolution geological details. Figure 6 (a) As a true reflectance model, it establishes the geological "standard answer" that includes complex folds and sharp stratigraphic boundaries; Figure 6 (b) shows the imaging results of traditional LSRTM. Although it can infer the general tectonic trend, it is limited by the band-limited characteristics of seismic data and the ill-posedness of the inverse problem. The image shows obvious low-frequency smoothing effect, high-frequency details are blurred and layer boundaries are diffuse. Figure 6 (c) shows the reconstruction result of DLSRTM. This method innovatively embeds LSRTM into the sampling process of the diffusion model (i.e., interspersing physical iterations in the last 10 denoising steps), utilizing the powerful generative priors of the diffusion model to constrain the solution space. This dual-driven mechanism of "physics + data" enables... Figure 6 (c) Not only does it preserve the fidelity of LSRTM for the observed data, it also more effectively "illusions" and recovers the missing high wavenumber information, making it significantly superior in texture clarity, stratigraphic continuity, and boundary sharpness. Figure 6 (b) Achieved visual harmony with Figure 6 (a) Reconstruction results that are highly consistent with the real model.

[0147] Figure 7 By extracting vertically migrated profiles at three representative horizontal locations of 0.16 km, 0.32 km, and 0.48 km, a quantitative analysis of imaging accuracy was provided, further validating the superiority of DLSRTM in imaging deep and complex structures. Figure 7 In (a), when facing a deep, highly reflective interface, the traditional LSRTM is limited by the band-limiting effect of the Hessian matrix, exhibiting obvious amplitude underestimation and waveform broadening, while DLSRTM accurately reproduces the peak amplitude and phase characteristics of the real reflectivity model. Figure 7(b) demonstrates imaging capabilities at locations with drastic structural changes. LSRTM exhibits significant oscillation artifacts and resolution degradation, while DLSRTM, thanks to the effective prior constraints of the diffusion model, successfully suppresses migration noise and maintains waveform purity. Figure 7 (c) further confirms that even in areas with insufficient deep illumination, DLSRTM can still overcome the blurring effect of traditional methods and achieve accurate reconstruction of the amplitude and phase of the reflection coefficient. In summary, this series of comparisons strongly demonstrates that DLSRTM is significantly superior to the traditional LSRTM method in improving spatial resolution, enhancing amplitude fidelity, and suppressing migration artifacts.

[0148] Figure 9 By comparing the imaging results of the DDPM and DDIM sampling algorithms at different number of steps, the impact of sampling strategies on the final reconstruction quality and efficiency is intuitively demonstrated. Figure 9 (a)- Figure 9 (c) shows the performance of DDPM at 30, 50, and 100 sampling steps. The results show that DDPM is highly sensitive to the number of sampling steps. With fewer steps, image details are severely lost and noise is obvious. It is necessary to increase the number of steps to 100 to obtain a relatively clear structure, indicating that its computational cost is high. In contrast, Figure 9 (d)- Figure 9 (f) shows that DDIM can recover clear geological structures and sharp boundaries with only 3, 5, and 10 sampling steps. This comparison strongly demonstrates that the DDIM algorithm has excellent convergence speed and sampling efficiency. It breaks the limitation of traditional diffusion models that must rely on long chains of iterations to obtain high-quality samples. It can achieve imaging results comparable to or even better than DDPM with high number of steps at a very low computational cost, verifying its effectiveness and robustness in accelerating the seismic imaging inversion process.

[0149] Figure 9 This demonstrates the migration imaging results obtained using DDPM and DDIM sampling under the same data and velocity conditions. Figure 10 A quantitative evaluation of both is given. Figure 10 This comparison shows the structural similarity, peak signal-to-noise ratio (PSNR), and computation time of the generated results when using DDPM and DDIM sampling in DLSRTM. Compared to DDPM, DDIM significantly improves both SSIM and PSNR, and requires a marked reduction in the number of LSRTM iterations. The fundamental reason is that DDIM's deterministic sampling achieves the mapping from noise to image with a larger time step (fewer steps), effectively suppressing variance accumulation and inefficient backtracking caused by random sampling while maintaining key imaging quality such as edges. Therefore, DDIM can generate inversion results closer to the true values ​​with lower computational cost within the LSRTM framework.

[0150] In summary, the LSRTM guided by the conditional diffusion model can not only reconstruct a reflectance model that combines prior geological structure with observational fitting, but also, when combined with the DDIM sampling strategy, it exhibits clear advantages in overall computational efficiency and imaging quality, providing a feasible technical path for high-fidelity, low-cost imaging in complex tectonic areas.

[0151] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, alterations, alterations, or substitutions made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A least-squares reverse-time migration method guided by a conditional diffusion model, characterized in that, include: Step 1: Construct the least-squares inverse time migration inversion framework; Step 2: Construct a U-Net network with a temporal embedding module and an attention mechanism; Step 3: Pre-train the conditional denoising diffusion probability model; Step 4: Perform the inversion using an alternating iterative strategy of data consistency and deterministic denoising projection; Step 5: Introduce a skip sampling strategy for the denoising diffusion implicit model to accelerate the inversion process.

2. The least squares reverse time migration method guided by a conditional diffusion model according to claim 1, characterized in that, Step 1 includes: establishing the correspondence between forward modeling and migration imaging of seismic data based on the propagation law of seismic wavefield; constructing an inversion objective function with regularization constraints by minimizing the residuals between simulated and measured seismic data; and forming a least squares inverse time migration inversion framework.

3. The least-squares reverse-time migration method guided by a conditional diffusion model according to claim 1, characterized in that, Step 2 includes: building a multi-resolution layer U-Net network, integrating time-step embedding, self-attention mechanism and cross-layer residual connection, setting self-attention modules in the bottleneck layer and specified resolution layer of the U-Net network, and incorporating RTM images as conditional features into the U-Net network.

4. The least squares reverse time migration method guided by a conditional diffusion model according to claim 1, characterized in that, Step 3 includes: using RTM images as conditional information, constructing paired training samples of reflectance and corresponding RTM images, and through iterative training, enabling the conditional denoising diffusion probability model to learn the mapping relationship from noise to reflectance, thereby obtaining generative geological priors that can be used for inversion.

5. The least-squares reverse-time migration method guided by a conditional diffusion model according to claim 1, characterized in that, Step 4 includes: first, data consistency correction is completed by least squares inverse time offset gradient update, and then deterministic denoising projection is completed by using a fixed RTM image as a guide.

6. The least squares reverse time migration method guided by a conditional diffusion model according to claim 1, characterized in that, Step 5 includes: based on the trained conditional denoising diffusion probability model, replacing it with a denoising diffusion implicit model sampler to construct a skip sampling strategy.

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