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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2019, Vol. 36 ›› Issue (1): 33-42.doi: 10.3969/j.issn.1005-3085.2019.01.003

• • 上一篇    下一篇

基于变分PDE的地震资料空间自适应保边缘去噪方法

王德华1,   高静怀2,   张丽丽1   

  1. 1- 西安工业大学理学院，西安  710021
    2- 西安交通大学电信学院，西安  710049
  • 收稿日期:2017-11-27 接受日期:2018-04-11 出版日期:2019-02-15 发布日期:2019-04-15
  • 基金资助:
    国家自然科学基金(41390454; 11471202)；陕西省教育厅专项科研计划项目(18JK0385)；西安工业大学校长基金(XAGDXJJ17026).

A Spatially Adaptive Edge-preserving Denoising Method for Seismic Data Based on Variational PDE

WANG De-hua1,   GAO Jing-huai2,   ZHANG Li-li1   

  1. 1- School of Science, Xi'an Technological University, Xi'an 710021 
    2- School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049
  • Received:2017-11-27 Accepted:2018-04-11 Online:2019-02-15 Published:2019-04-15
  • Supported by:
    The National Natural Science Foundation of China (41390454; 11471202); the Scientific Research Program Funded by Shaanxi Provincial Education Department (18JK0385); the President Fund of Xi'an Technological University (XAGDXJJ17026).

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摘要： 地震资料去噪是地震资料处理的一个基本环节，其信噪比的好坏会直接影响地震资料的可靠性及地质解释的精度．本文主要针对已有方法在去噪的同时不能很好地保持边缘信息这一问题，通过构造空间自适应边缘检测函数，建立了基于分数阶偏微分方程的自适应变分去噪模型；然后，推导了求解新模型的分数阶Euler-Lagrange方程，并给出其离散格式；最后，将本文提出的方法用于合成地震数据及实际地震数据去噪，通过与传统去噪方法相比较，验证了新方法的有效性与实用性．

关键词: 地震资料去噪, 边缘保持, 变分正则化, 偏微分方程

Abstract: Seismic data denoising is a basic issue of seismic data processing, and its signal-to-noise ratio affects directly the reliability of seismic data and the accuracy of geological interpretation. In this paper, we firstly construct an edge detection function based on a nonlinear diffusion. On the basis, we establish a fractional adaptive edge-preserving denoising model in the variational framework, and calculate the fractional Euler-Lagrange equation for solving the proposed model. Finally, the proposed method is applied to synthetic seismic data and field seismic data denoising, and the effectiveness and practicability of the new method are verified by comparing with the traditional denoising method.

Key words: seismic data denoising, edge-preserving, variational regularization, partial differential equations

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