基于梯度增强扩散模型的三维阻抗反演

doi:10.3969/j.issn.2096-1693.2026.01.012

摘要/Abstract

摘要：

传统的模型驱动反演方法依赖于先验信息和正则化，往往会出现过度简化地质特征的现象。随着深度学习的快速发展，扩散模型由于其能学习数据的复杂分布特征，为求解反问题提供了更好的先验信息。受此启发，本文引入扩散模型提高反演结果的可靠性和稳定性。该方法通过对合成阻抗模型的加噪和去噪过程学习其数据分布，之后利用以地震数据为条件的后验采样，引入低频模型约束、三维横向约束和动量估计，提高横向连续性和梯度更新的稳定性，实现地震数据和阻抗模型的稳健映射。合成数据和实际数据的应用结果表明，新方法能够生成服从观测地震数据且细节丰富的阻抗模型，与传统模型驱动方法相比，本文方法对单井反演准确率提升了5%。新的反演框架减弱了对先验信息的依赖并且大大提高了泛化性和可靠性，同时也为求解其他复杂的地球物理反问题提供了新思路。

关键词: 扩散模型, 3D反演, 声波阻抗, 梯度增强, 横向约束

Abstract:

Traditional model-driven inversion methods rely on prior information and regularization, which often lead to oversimplification of geological features. With the rapid development of deep learning, diffusion models have emerged as a powerful alternative for solving inverse problems, as they can learn the complex data distribution characteristics and provide better prior information. Inspired by this, this paper introduces diffusion models to enhance the reliability and stability of inversion results. The method learns the data distribution through the processes of noise addition and denoising applied to a synthetic impedance model. Subsequently, by utilizing posterior sampling conditioned on seismic data, it incorporates low-frequency model constraints, 3D lateral constraints, and momentum estimation to improve lateral continuity and the stability of gradient updates, thereby achieving a robust mapping between seismic data and the impedance model. Application results on both synthetic and real data demonstrate that the new method can recover impedance models that are both detailed and geologically plausible. Compared to traditional model-driven methods, the proposed method improves the accuracy of single-trace inversion by 5%. The new inversion framework reduces reliance on prior information and significantly enhances generalizability and reliability, while also providing new approaches for solving other complex geophysical inverse problems.

Key words: diffusion model, 3D inversion, acoustic impedance, gradient enhancement, lateral constraint

中图分类号:

刘泽洋, 李景叶, 刘达伟, 张伟, 刘国昌, 陈小宏. 基于梯度增强扩散模型的三维阻抗反演[J]. 石油科学通报, 2026, 11(2): 415-428.

LIU Zeyang, LI Jingye, LIU Dawei, ZHANG Wei, LIU Guochang, CHEN Xiaohong. 3D impedance inversion based on a gradient-enhanced diffusion model[J]. Petroleum Science Bulletin, 2026, 11(2): 415-428.

https://sykxtb.cup.edu.cn/CN/Y2026/V11/I2/415

图/表 11

参考文献 37

[1]	张永刚. 地震波阻抗反演技术的现状和发展[J]. 石油物探, 2002, 64(4): 595-621.
	[Zhang Y G. A review of seismic impedance inversion methods based on physics-informed neural network[J]. Geophysical Prospecting for Petroleum, 2002, 64(4): 595-621.]
[2]	LINES L R, TREITEL S. A review of least‐squares inversion and its application to geophysical problems[J]. Geophysical Prospecting, 1984, 32(2): 159-186. doi: 10.1111/gpr.1984.32.issue-2 URL
[3]	孙正心, 金衍, 孟翰, 等. 基于深度学习数据融合的测井数据精细表征[J]. 石油科学通报, 2025, 10(1): 75-86.
	[SUN Z X, JIN Y, MENG H, et al. Fine characterization of logging data based on the deep learning data fusion[J]. Petroleum Science Bulletin, 2025, 10(1): 75-86.]
[4]	COOKE D A, SCHNEIDER W A. Generalized linear inversion of reflection seismic data[J]. Geophysics, 1983, 48(10): 665-676. doi: 10.1190/1.1441497 URL
[5]	OLDENBURG D W, Scheuer T, Levy S. Recovery of the acoustic impedance from reflection seismograms[J]. Geophysics, 1983, 48: 1318-1337. doi: 10.1190/1.1441413 URL
[6]	Walker C, Ulrych T J. Autoregressive recovery of the acoustic impedance[J]. Geophysics, 1983, 48(10): 1338-1350. doi: 10.1190/1.1441414 URL
[7]	Hamid H, Pidlisecky A. Multitrace impedance inversion with lateral constraints[J]. Geophysics, 2015, 80(6): M101-M111.
[8]	陈君青, 杨晓斌, 张潇, 等. 页岩力学性质研究中机器学习的应用: 现状、挑战与展望[J]. 石油科学通报, 2025, 10(5): 849-877, 29.
	[CHEN J Q, YANG X B, ZHANG X, et al. Application of machine learning in the study of shale mechanical properties: Current situation, challenges and prospects[J]. Petroleum Science Bulletin, 2025, 10(5): 849-877, 29.]
[9]	GHOLAMI A. Nonlinear multichannel impedance inversion by total-variation regularization[J]. Geophysics, 2015, 80(5): R217-R224.
[10]	GHOLAMI A. A fast automatic multichannel blind seismic inversion for high-resolution impedance recovery[J]. Geophysics, 2016, 81(5): V357-V364.
[11]	LI C B, Medina M R, Warren M, et al. Seismic super-resolution method: Enhancing reservoir delineation and characterization through high-resolution seismic data[J]. The Leading Edge, 2024, 43(12): 843-851. doi: 10.1190/tle43120843.1 URL
[12]	FU L Y. Joint inversion of seismic data for acoustic impedance[J]. Geophysics, 2004, 69(4): 994-1004. doi: 10.1190/1.1778242 URL
[13]	LIU Z Y, SONG W, CHEN X H, et al. High‐resolution reservoir prediction method based on data‐driven and model‐based approaches[J]. Geophysical Prospecting, 2024, 72(5): 1971-1984. doi: 10.1111/gpr.v72.5 URL
[14]	宋磊, 印兴耀, 宗兆云, 等. 基于先验约束的深度学习地震波阻抗反演方法[J]. 石油地球物理勘探, 2021, 56(4): 716-727. doi: 10.13810/j.cnki.issn.1000-7210.2021.04.005
	[Song L, YIN X Y, ZONG Z Y, et al. Deep learning seismic impedance inversion based on prior constraints[J]. Oil Geophysical Prospecting, 2021, 56(4): 716-727.] doi: 10.13810/j.cnki.issn.1000-7210.2021.04.005
[15]	王泽峰, 许辉群, 杨梦琼, 等. 应用时域卷积神经网络的地震波阻抗反演方法[J]. 石油地球物理勘探, 2022, 57(2): 279-286, 296. doi: 10.13810/j.cnki.issn.1000-7210.2022.02.004
	[Wang Z F, Xu H Q, Yang M Q, et al. Seismic impedance inversion method based on temporal convolutional neural network[J]. Oil Geophysical Prospecting, 2022, 57(2): 279-286, 296.] doi: 10.13810/j.cnki.issn.1000-7210.2022.02.004
[16]	罗功伟, 安小平, 姚卫华, 等. 非常规油气储层测井智能解释应用现状与发展趋势[J]. 石油科学通报, 2025, 10(5): 908-925.
	[LUO G W, AN X P, YAO W H, et al. Application status and development trends of artificial intelligence in logging interpretation for unconventional oil and gas reservoirs[J]. Petroleum Science Bulletin, 2025, 10(5): 908-925.]
[17]	SOHL-DICKSTEIN J, WEISS E, MAHESWARANATHAN N, et al. Deep unsupervised learning using nonequilibrium thermodynamics[C]. International conference on machine learning, Vancouver, Canada, 2025.
[18]	HO J, JAIN A, ABBEEL P. Denoising diffusion probabilistic models[J]. Advances in neural information processing systems, 2020, 33: 6840-6851.
[19]	HO J, SAHARIA C, CHAN W, et al. Cascaded diffusion models for high fidelity image generation[J]. Journal of Machine Learning Research, 2022, 23(47): 1-33.
[20]	DHARIWAL P, NICHOL A. Diffusion models beat gans on image synthesis[J]. Advances in neural information processing systems, 2021, 34: 8780-8794.
[21]	LUO C. Understanding diffusion models: A unified perspective[J/OL]. arXiv preprint arXiv. 2022, 2208.11970. https://arxiv.org/pdf/2208.11970 URL
[22]	CHAN S H. Tutorial on diffusion models for imaging and vision[J/OL]. arXiv preprint arXiv. 2024, 2403.18103. https://arxiv.org/pdf/2403.18103. URL
[23]	DARAS G, CHUNG H, LAI C H, et al. A survey on diffusion models for inverse problems[J/OL] arXiv preprint arXiv. 2024,2410.00083. https://arxiv.org/pdf/2410.00083. URL
[24]	CHOI J, KIM S, JEONG Y, et al. ILVR: Conditioning method for denoising diffusion probabilistic models[C]. 2021 IEEE/CVF International Conference on Computer Vision (ICCV), Montreal, QC, Canada, 2021.
[25]	CHUNG H, KIM J, MCCANN M T, et al. Diffusion posterior sampling for general noisy inverse problems[J/OL]. arXiv preprint arXiv. 2022, 2209.14687. https://arxiv.org/pdf/2209.14687. URL
[26]	WANG Y H, YU J W, ZHANG J. Zero-shot image restoration using denoising diffusion null-space model[J/OL]. arXiv preprint arXiv. 2022, 2212.00490. https://arxiv.org/pdf/2212.00490. URL
[27]	KINGMA D P, BA J. Adam: A method for stochastic optimization[J/OL]. arXiv preprint arXiv:1412.6980. https://arxiv.org/pdf/1412.6980. URL
[28]	TARANTOLA A. Inverse problem theory and methods for model parameter estimation[M]. Philadelphia, PA: Society for industrial and applied mathematics, 2005.
[29]	撒利明, 杨午阳, 姚逢昌, 等. 地震反演技术回顾与展望[J]. 石油地球物理勘探, 2015, 50(1): 184-202,20. doi: 10.13810/j.cnki.issn.1000-7210.2015.01.028
	[SA L M, YANG W Y, YAO F C, et al. Past, present, and future of geophysical inversion[J]. Oil Geophysical Prospecting, 2015, 50(1): 184-202,20.] doi: 10.13810/j.cnki.issn.1000-7210.2015.01.028
[30]	卢占武, 韩立国. 波阻抗反演技术研究进展[J]. 世界地质, 2002, 21(4): 372-377.
	[LU Z W, HAN L G. The Development of the Research of the Wave Impedance Inversion Technique[J]. Global Geology, 2002, 21(4): 372-377.]
[31]	YILMAZ Ö. Seismic data analysis: processing, inversion and interpretation of seismic data[M]. Tulsa: Society of Exploration Geophysicists, 2001.
[32]	SONG J M, MENG C L, ERMON S. Denoising diffusion implicit models[J/OL]. arXiv preprint arXiv. 2020, 2010.02502. https://arxiv.org/pdf/2010.02502. URL
[33]	SONG Y, ERMON S. Generative modeling by estimating gradients of the data distribution[C]. Advances in Neural Information Processing Systems, Vancouver, BC, Canada, 2019.
[34]	FRIEDMAN A. Stochastic differential equations and applications[M]. Berlin, Heidelberg: Springer Berlin Heidelberg, 1975.
[35]	VINCENT P. A connection between score matching and denoising autoencoders[J]. Neural Computation, 2011, 23(7): 1661-1674. doi: 10.1162/NECO_a_00142 pmid: 21492012
[36]	CHUNG H, RYU D, SIM B, et al. Improving diffusion models for inverse problems using manifold constraints[C]. Advances in Neural Information Processing Systems, New Orleans, Louisiana, USA, 2022.
[37]	MERRIFIELD T P, GRIFFITH D P, ZAMANIAN S A, et al. Synthetic seismic data for training deep learning networks[J]. Interpretation, 2022, 10(3): SE31-SE39.

Algorithm 1 DPS	Algorithm 2 GDPS
Require：$T, \boldsymbol{y}, \Sigma_{t}, l_{r}$	Require：$T, \boldsymbol{y}, \Sigma_{t}, l_{r}, \lambda_{1}, \lambda_{2}, \hat{\boldsymbol{x}}_{\text {Low }}$
1: $\boldsymbol{x}_{T} \sim \mathcal{N}(0, \mathbf{I})$	1: $\boldsymbol{x}_{T} \sim \mathcal{N}(0, \mathbf{I}), m_{T+1}=0, v_{T+1}=0$
2: for $t=T$ tol do	2: for $t=T$ tol do
3: $\hat{\boldsymbol{s}} \leftarrow \boldsymbol{s}_{\theta^{*}}\left(\boldsymbol{x}_{t}, t\right)$	3: $\hat{\boldsymbol{s}} \leftarrow \boldsymbol{s}_{\theta^{*}}\left(\boldsymbol{x}_{t}, t\right)$
4:$\hat{\boldsymbol{x}}_{0} \leftarrow\left(\boldsymbol{x}_{t}+\left(1-\bar{\alpha}_{t}\right) \hat{\boldsymbol{s}}\right) / \sqrt{\bar{\alpha}_{t}}$	4:$\hat{\boldsymbol{x}}_{0} \leftarrow\left(\boldsymbol{x}_{t}+\left(1-\bar{\alpha}_{t}\right) \hat{\boldsymbol{s}}\right) / \sqrt{\bar{\alpha}_{t}}$
5:$z \sim \mathcal{N}(0, \mathbf{I})$	5:$\boldsymbol{z} \sim \mathcal{N}(0, \mathbf{I})$
6:$\boldsymbol{x}_{t-1}^{\prime} \leftarrow\left(\boldsymbol{x}_{t}+\left(1-\alpha_{t}\right) \hat{\boldsymbol{s}}\right) / \sqrt{\alpha_{t}}+\Sigma_{t} z$	6:$\boldsymbol{x}_{t-1}^{\prime} \leftarrow\left(\boldsymbol{x}_{t}+\left(1-\alpha_{t}\right) \hat{\boldsymbol{s}}\right) / \sqrt{\alpha_{t}}+\Sigma_{t} z$
7:$\boldsymbol{x}_{t-1} \leftarrow \boldsymbol{x}_{t-1}^{\prime}-l_{r} \nabla_{\boldsymbol{x}_{t}}\left\\|\boldsymbol{y}-\boldsymbol{G}\left(\hat{\boldsymbol{x}}_{0}\right)\right\\|_{2}^{2}$	7:$\mathrm{g}_{t} \leftarrow \nabla_{x_{t}}\left(\boldsymbol{y}-\boldsymbol{G}\left(\hat{\boldsymbol{x}}_{0}\right)_{2}^{2}+\lambda_{1}\left\\|\hat{\boldsymbol{x}}_{0}-\hat{\boldsymbol{x}}_{\text {Low }}\right\\|_{2}^{2}+\lambda_{2}\left\\|\mathrm{D} \hat{\boldsymbol{x}}_{0}\right\\|_{2}^{2}\right)$
8: return $\hat{\boldsymbol{x}}_{0}$	8:$\begin{array}{l}\hat{m}_{t}=\left(\beta_{1} m_{t+1}+\left(1-\beta_{1}\right) \mathrm{g}_{t}\right) /\left(1-\beta_{1}^{T-t+1}\right), \\\hat{v}_{t}=\sqrt{\left(\beta_{2} v_{t+1}+\left(1-\beta_{2}\right) \mathrm{g}_{t}^{2}\right) /\left(1-\beta_{2}^{T-t+1}\right)}\end{array}$
	9:$\boldsymbol{x}_{t-1} \leftarrow \boldsymbol{x}_{t-1}^{\prime}-l_{r} \hat{m}_{t} /\left(\sqrt{\hat{v}_{t}}+\epsilon\right)$
	10:return $\hat{\boldsymbol{x}}_{0}$

Algorithm 1 DPS	Algorithm 2 GDPS
Require：$T, \boldsymbol{y}, \Sigma_{t}, l_{r}$	Require：$T, \boldsymbol{y}, \Sigma_{t}, l_{r}, \lambda_{1}, \lambda_{2}, \hat{\boldsymbol{x}}_{\text {Low }}$
1: $\boldsymbol{x}_{T} \sim \mathcal{N}(0, \mathbf{I})$	1: $\boldsymbol{x}_{T} \sim \mathcal{N}(0, \mathbf{I}), m_{T+1}=0, v_{T+1}=0$
2: for $t=T$ tol do	2: for $t=T$ tol do
3: $\hat{\boldsymbol{s}} \leftarrow \boldsymbol{s}_{\theta^{*}}\left(\boldsymbol{x}_{t}, t\right)$	3: $\hat{\boldsymbol{s}} \leftarrow \boldsymbol{s}_{\theta^{*}}\left(\boldsymbol{x}_{t}, t\right)$
4:$\hat{\boldsymbol{x}}_{0} \leftarrow\left(\boldsymbol{x}_{t}+\left(1-\bar{\alpha}_{t}\right) \hat{\boldsymbol{s}}\right) / \sqrt{\bar{\alpha}_{t}}$	4:$\hat{\boldsymbol{x}}_{0} \leftarrow\left(\boldsymbol{x}_{t}+\left(1-\bar{\alpha}_{t}\right) \hat{\boldsymbol{s}}\right) / \sqrt{\bar{\alpha}_{t}}$
5:$z \sim \mathcal{N}(0, \mathbf{I})$	5:$\boldsymbol{z} \sim \mathcal{N}(0, \mathbf{I})$
6:$\boldsymbol{x}_{t-1}^{\prime} \leftarrow\left(\boldsymbol{x}_{t}+\left(1-\alpha_{t}\right) \hat{\boldsymbol{s}}\right) / \sqrt{\alpha_{t}}+\Sigma_{t} z$	6:$\boldsymbol{x}_{t-1}^{\prime} \leftarrow\left(\boldsymbol{x}_{t}+\left(1-\alpha_{t}\right) \hat{\boldsymbol{s}}\right) / \sqrt{\alpha_{t}}+\Sigma_{t} z$
7:$\boldsymbol{x}_{t-1} \leftarrow \boldsymbol{x}_{t-1}^{\prime}-l_{r} \nabla_{\boldsymbol{x}_{t}}\left\\|\boldsymbol{y}-\boldsymbol{G}\left(\hat{\boldsymbol{x}}_{0}\right)\right\\|_{2}^{2}$	7:$\mathrm{g}_{t} \leftarrow \nabla_{x_{t}}\left(\boldsymbol{y}-\boldsymbol{G}\left(\hat{\boldsymbol{x}}_{0}\right)_{2}^{2}+\lambda_{1}\left\\|\hat{\boldsymbol{x}}_{0}-\hat{\boldsymbol{x}}_{\text {Low }}\right\\|_{2}^{2}+\lambda_{2}\left\\|\mathrm{D} \hat{\boldsymbol{x}}_{0}\right\\|_{2}^{2}\right)$
8: return $\hat{\boldsymbol{x}}_{0}$	8:$\begin{array}{l}\hat{m}_{t}=\left(\beta_{1} m_{t+1}+\left(1-\beta_{1}\right) \mathrm{g}_{t}\right) /\left(1-\beta_{1}^{T-t+1}\right), \\\hat{v}_{t}=\sqrt{\left(\beta_{2} v_{t+1}+\left(1-\beta_{2}\right) \mathrm{g}_{t}^{2}\right) /\left(1-\beta_{2}^{T-t+1}\right)}\end{array}$
	9:$\boldsymbol{x}_{t-1} \leftarrow \boldsymbol{x}_{t-1}^{\prime}-l_{r} \hat{m}_{t} /\left(\sqrt{\hat{v}_{t}}+\epsilon\right)$
	10:return $\hat{\boldsymbol{x}}_{0}$

参数	含义
$T$	迭代次数
$\alpha_{t}, \Sigma_{t}$	次噪声水平和方差
$x_{0}$	原始阻抗
$x_{T}$	纯噪声
$x_{t}$	$x_{0}$添加噪声直至变为$x_{T}$的过程
$\boldsymbol{S}_{\theta^{*}}$	神经网络

参数	含义
$T$	迭代次数
$\alpha_{t}, \Sigma_{t}$	次噪声水平和方差
$x_{0}$	原始阻抗
$x_{T}$	纯噪声
$x_{t}$	$x_{0}$添加噪声直至变为$x_{T}$的过程
$\boldsymbol{S}_{\theta^{*}}$	神经网络

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