基于低秩约束矩阵恢复的高维地震数据重建

项目名称： 基于低秩约束矩阵恢复的高维地震数据重建

项目编号： No.91330108

项目类型： 重大研究计划

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 马坚伟

作者单位： 哈尔滨工业大学

项目金额： 70万元

中文摘要： 地震数据不规则丢失道（相当于矩阵的列丢失）的重建以及规则稀疏采样数据的抗假频道加密重建是地震数据处理中非常重要的一个环节，其重建的效果严重关系到多次波去除、偏移、成像和AVO分析的质量。近几年比较流行的方法是稀疏约束优化的地震数据重建，它将重建问题转化为L1范数最小化问题来求解。近期出现了基于降秩方法的地震数据重建，主要有Trickett的SVD截断和Sacchi的多道奇异谱方法。申请人与S.Osher合作，首次把地震数据重建转化为核范数最小化的低秩矩阵恢复，并推广到三维数据重建。但是目前的低秩矩阵恢复方法仍不能有效抗噪和抗假频；所用的算法只是对原降秩模型求解的一种近似；基于矩阵恢复的高维地震数据（五维）重建仍是挑战。本项目立足应用数学和地震勘探的交叉研究，深入开展基于抗噪和抗假频矩阵列丢失恢复的高维数据重建理论研究，以及快速算法和软件程序的开发，为油田大规模数据的重建提供一条新途径。

中文关键词： 矩阵恢复；低秩约束；地震数据重构；高维重构；地球物理勘探

英文摘要： Due to physical and economic constraints, missing data is one of the common issues in seismic data acquisition. Reconstruction and interpolation of missing traces in seismic records is a critical element of the data processing chain, which is very important for subsequent processing steps including improvement of spatial resolution, multiple suppression, migration, imaging, and amplitude-versus-offset analysis. In last a few years, one of popular methods for seismic interpolation is sparsity-promoting L1-norm (SPL1) regularized optimization much improved the reconstruction of missing traces. It shifts the problem of seismic interpolation to a L1-norm regularized minimization. Recently, rank-reduction methods have been used for seismic data reconstruction, including Trickett’s truncated SVD and Sacchi’s MSSA. The principle investigator (co-work with Prof. S. Osher from UCLA) presented nuclear-norm minimization matrix completion for seismic data reconstruction for the first time, and develop this method for three-dimensional cases. However, there still exists many open problems: the current algorithm is not anti-noise and anti-aliasing; the used algorithm is only an approximately solve to original rank-reduction model; how to construct higher dimensional (e.g. five dimensions) seismic data via low-rank methods i

英文关键词： Matric completion；Low-rank constraint；Seismic data reconstrtuction；High-dimentional reconstruction；Geophysical exploration