地球物理学进展 ›› 2018, Vol. 33 ›› Issue (6): 2441-2449.doi: 10.6038/pg2018BB0499

• 应用地球物理学Ⅰ(油气及金属矿产地球物理勘探) • 上一篇    下一篇

基于Shearlet稀疏变换基的压缩感知重建技术

王常波   

  1. 中国石油化工股份有限公司胜利油田分公司物探研究院,山东东营 257022
  • 收稿日期:2018-04-06 修回日期:2018-09-17 出版日期:2018-12-20 发布日期:2019-03-03
  • 作者简介:王常波,男,1967年生,山东菏泽人,硕士,高级工程师,主要从事地震资料处理等研究工作.(E-mail:wangchangbo775.slyt@sinopec.com)
  • 基金资助:
    十三五国家科技重大专项“渤海湾盆地精细勘探关键技术”(2016ZX05006);胜利油田重点科技攻关项目“地震数据压缩感知重建技术研究”(YKW1704)

Compressed sensing seismic data reconstruction with Shearlet transformation

WANG Chang-bo   

  1. Shengli Geophysical Research Institute of Sinopec, Shandong Dongying 257022, China
  • Received:2018-04-06 Revised:2018-09-17 Online:2018-12-20 Published:2019-03-03

摘要:

压缩感知是一种新的地震数据表征框架,能够利用信号的稀疏性代替频带宽度更好地进行信号描述,为地震数据重建提供了有力的理论基础.本文在压缩感知理论框架下,构建了基于Shearlet稀疏变换基的地震数据重建算法,利用快速凸集投影(FPOCS)算法和指数阈值模型求取最优解,并采用地震数据指标参数(信噪比、峰值信噪比以及结构相似性)对重建结果进行定量评价.数值测试结果验证了本文方法的正确性和实用性,与Fourier变换基和Curvelet变换基相比,Shearlet变换基具有更敏感的方向性以及更优秀的稀疏表示能力,数据重建精度最高,引入的噪声较少.

关键词: Shearlet变换基, 压缩感知, 地震数据重建, FPOCS算法, 阈值函数

Abstract:

Compressed sensing is a new framework for seismic data expression, uses the sparse property instead of frequency band to do signal description, which provides a powerful theoretical basis for seismic data reconstruction. In this paper, seismic data reconstruction algorithm with Shearlet sparse transformation base have been built under the framework of Compressed Sensing, which use the Fast Convex Projection (FPOCS) algorithm and exponential threshold model to obtain optimal solution, and apply seismic data index parameters (signal-to-noise ratio, peak signal-to-noise ratio and structural similarity) to quantitatively evaluate the reconstruction results. Numerical testing results verify the correctness and effectiveness of the proposed method, compared with the results of Fourier transform and Curvelet transform, the Shearlet transform have more sensitive directionality and anisotropy, higher sparse expression ability, therefore, the seismic data reconstruction using Shearlet sparse transform has higher reconstruction precision and less noise.

Key words: Shearlet transformation base, compressed sensing, seismic data reconstruction, FPOCS method, threshold function

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