A non-uniform interpolation method for seismic data based on a diffusion probabilistic model

Authors

CHEN Yao, School of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaFollow
YU Siwei, School of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaFollow
LIN Rongzhi, School of Mathematics, Harbin Institute of Technology, Harbin 150001, China

Abstract

Objective The non-uniform interpolation of seismic data is identified as a prolonged challenge in energy exploration. Since geophones cannot be precisely placed at positions corresponding to theoretical grid points, current uniform interpolation techniques frequently suffer deviations and detail distortion. Methods This study proposed a novel non-uniform interpolation method based on a diffusion probabilistic model, which is an emerging generative model in deep learning that involves the diffusion and generation processes. In the diffusion process, noise is added to the complete seismic data iteratively to train the denoising capability of the neural network. In the generation process, the neural network is employed for iterative denoising of data containing noise to obtain the reconstructed data. In this study, interpolation operators were employed to calculate the deviations between iterative and sampled data. These deviations were then used as the additional inputs of the neural network to improve the non-uniform interpolation capability of the diffusion probabilistic model. In the numerical experiments, the non-uniform sampling was tested using 2D synthetic and actual datasets, and the uniform interpolation model was compared with the model in this proposed study. Results and Conclusions The results indicate that the proposed method significantly enhanced the processing capability of the diffusion probabilistic model for non-uniform sampling. The tests of synthetic and actual data revealed an increase of approximately 7 dB in the signal-to-noise ratio. Therefore, the proposed method can effectively improve the precision of deep learning for non-uniform interpolation, providing a new approach for non-uniform interpolation algorithms of seismic data.

Keywords

interpolation of seismic data, non-uniform sampling, deep learning, generative model, diffusion probabilistic model

DOI

10.12363/issn.1001-1986.24.03.0160

Recommended Citation

CHEN Yao, YU Siwei, LIN Rongzhi, et al. (2024) "A non-uniform interpolation method for seismic data based on a diffusion probabilistic model," Coal Geology & Exploration: Vol. 52: Iss. 8, Article 17.
DOI: 10.12363/issn.1001-1986.24.03.0160
Available at: https://cge.researchcommons.org/journal/vol52/iss8/17

Reference

[1] SPITZ S. Seismic trace interpolation in the F–X domain[J]. Geophysics，1991，56(6)：785−794.

[2] PORSANI M J. Seismic trace interpolation using half‐step prediction filters[J]. Geophysics，2012，64(5)：1461−1467.

[3] 刘保童. 一种基于傅里叶变换的去假频内插方法及应用[J]. 煤田地质与勘探，2009，37(2)：63−67.

LIU Baotong. Dealiasing interpolation based on Fourier transform and its application[J]. Coal Geology & Exploration，2009，37(2)：63−67.

[4] RONEN J. Wave–equation trace interpolation[J]. Geophysics，1987，52(7)：973−984.

[5] ABMA R，KABIR N. 3D interpolation of irregular data with a POCS algorithm[J]. Geophysics，2006，71(6)：91−97.

[6] SHAO Jie，WANG Yibo. Seismic data antialiasing interpolation using sparse Radon transform and dynamic mask function[J]. Geophysics，2022，87(5)：437−449.

[7] MANENTI R，SACCHI M D. Tensor tree decomposition as a rank–reduction method for pre–stack interpolation[J]. Geophysical Prospecting，2023，71(8)：1404−1419.

[8] NIU Xiao，FU Lihua，ZHANG Wanjuan，et al. Seismic data interpolation based on simultaneously sparse and low–rank matrix recovery[J]. IEEE Transactions on Geoscience and Remote Sensing，2021，60：9100613.

[9] YU Siwei，MA Jianwei，ZHANG Xiaoqun，et al. Interpolation and denoising of high–dimensional seismic data by learning a tight frame[J]. Geophysics，2015，80(5)：119−132.

[10] ALMADANI M，WAHEED U，MASOOD M，et al. Dictionary learning with convolutional structure for seismic data denoising and interpolation[J]. Geophysics，2021，86(5)：361−374.

[11] WANG Benfeng，ZHANG Ning，LU Wenkai，et al. Deep–learning–based seismic data interpolation：A preliminary result[J]. Geophysics，2019，84(1)：11−20.

[12] 李宇腾，程建远，鲁晶津，等. 基于人工神经网络的矿井直流电阻率法超前预测方法[J]. 煤田地质与勘探，2023，51(6)：185−193.

LI Yuteng，CHENG Jianyuan，LU Jingjin，et al. Direct current resistivity method for the advance prediction of water Hazards in coal mines based on an artificial neural network[J]. Coal Geology & Exploration，2023，51(6)：185−193.

[13] 古瑶，解海军，周子鹏，等. 基于Attention机制的CNN–BiLSTM瞬变电磁实时反演方法[J]. 煤田地质与勘探，2023，51(10)：134−143.

GU Yao，XIE Haijun，ZHOU Zipeng，et al. An Attention mechanism–based CNN–BiLSTM real–time transient electromagnetic method[J]. Coal Geology & Exploration，2023，51(10)：134−143.

[14] FANG Wenqian，FU Lihua，ZHANG Meng，et al. Seismic data interpolation based on U–net with texture loss[J]. Geophysics，2021，86(1)：41−54.

[15] WU Geng，LIU Yang，LIU Cai，et al. Seismic data interpolation using deeply supervised U–Net++ with natural seismic training sets[J]. Geophysical Prospecting，2023，71(2)：227−244.

[16] GUO Yuanqi，FU Lihua，LI Hongwei. Seismic data interpolation based on multi–scale transformer[J]. IEEE Geoscience and Remote Sensing Letters，2023，20：7504205.

[17] PENG Junheng，LI Yong，LIAO Zhangquan. Irregularly spatial seismic missing data reconstruction using transformer with periodic skip connection[J]. IEEE Transactions on Geoscience and Remote Sensing，2023，61：5918613.

[18] 郭元奇，李志明. 基于卷积和Transformer联合网络的地震数据插值[J]. 工程地球物理学报，2023，20(3)：393−401.

GUO Yuanqi，LI Zhiming. Seismic data interpolation based on joint convolutional and transformer networks[J]. Chinese Journal of Engineering Geophysics，2023，20(3)：393−401.

[19] HO J，JAIN A，ABBEEL P. Denoising diffusion probabilistic models[EB/OL]. 2020：2006.11239. http://arxiv.org/abs/2006.11239v2.

[20] XIAO Yi，YUAN Qiangqiang，JIANG Kui，et al. EDiffSR：An efficient diffusion probabilistic model for remote sensing image super–resolution[J]. IEEE Transactions on Geoscience and Remote Sensing，2024，62：1−14.

[21] LUGMAYR A，DANELLJAN M，ROMERO A，et al. RePaint：Inpainting using denoising diffusion probabilistic models[C]. 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR). New Orleans，LA，USA. IEEE，2022：11451–11461.

[22] LI Haoying，YANG Yifan，CHANG Meng，et al. SRDiff：Single image super–resolution with diffusion probabilistic models[J]. Neurocomputing，2022，479：47−59.

[23] LIU Qi，MA Jianwei. Generative interpolation via a diffusion probabilistic model[J]. Geophysics，2024，89(1)：65−85.

[24] YU Siwei，MA Jianwei. Simultaneous off-the-grid regularization and reconstruction for 3D seismic data by a new combined sampling operator[J]. Geophysics，2023，88(4)：291−302.

[25] YU Siwei，MA Jianwei，ZHAO Bangliu. Off-the-grid vertical seismic profile data regularization by a compressive sensing method[J]. Geophysics，2020，85(2)：157−168.

[26] CAROZZI F，SACCHI M. Interpolated multichannel singular spectrum analysis：A reconstruction method that honors true trace coordinates[J]. Geophysics，2021，86(1)：55−70.

[27] ZWARTJES P M，SACCHI M D. Fourier reconstruction of nonuniformly sampled，aliased seismic data[J]. Geophysics，2007，72(1)：21−32.

[28] MA J，PLONKA G. The curvelet transform[J]. IEEE Signal Processing Magazine，2010，27(2)：118−133.

[29] DIAKOGIANNIS F I，WALDNER F，CACCETTA P，et al. ResUNet–a：A deep learning framework for semantic segmentation of remotely sensed data[J]. ISPRS Journal of Photogrammetry and Remote Sensing，2020，162：94−114.

[30] KINGMA D P，BA J. Adam：A method for stochastic optimization[C]//Proceedings of the International Conference on Learning Representations. 2014.

[31] RONNEBERGER O，FISCHER P，BROX T. U–net：Convolutional networks for biomedical image segmentation[M]//NAVAB N，HORNEGGER J，WELLS W M，et al. Lecture notes in computer science. Cham：Springer International Publishing，2015：234–241.