基于变分PDE的地震资料空间自适应保边缘去噪方法  

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

作　　者：王德华 高静怀[2] 张丽丽[1] WANG De-hua;GAO Jing-huai;ZHANG Li-li(School of Science, Xi'an Technological University, Xi'an 710021;School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049)

机构地区：[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

出　　处：《工程数学学报》2019年第1期33-42,共10页Chinese Journal of Engineering Mathematics

基　　金：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)~~

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.Seismic data denoising is a basic issue of seismic data processing, and its signal-tonoise ratio a ects 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 di usion. 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 e ectiveness and practicability of the new method are verified by comparing with the traditional denoising method.

关 键 词：地震资料去噪 边缘保持 变分正则化 偏微分方程 

分 类 号：O29[理学—应用数学] P631[理学—数学]