地震勘探中地震道通常分布在非规则网格点上，这一问题在垂直地震勘探（VSP）数据中尤为突出。已有的数据重建算法大多基于规则网格设计，在处理非规则网格问题时需要进行加密来近似，对计算效率和精度都会产生不利影响。申请人在博士期间主要研究了基于压缩感知的规则网格下的地震数据重建问题。本项目针对VSP数据中的非规则网格问题，研究一种非规则网格上的压缩感知理论，重新设计罚项中的采样算子，即利用非等距傅立叶变换实现数据从规则网格到非规则网格的映射。重点研究内容包括：1、针对非规则网格数据的压缩感知重建理论；2、实现曲波变换和蒙特卡洛数据驱动紧框架联合稀疏变换算法，实现合成VSP数据重建；3、在偏移成像结果上验证重建算法的有效性，并应用于大庆三维VSP数据重建。本项目立足应用数学和地震勘探的学科交叉，深度开展非规则VSP数据重建理论研究，有助于降低环境因素对成像质量的影响、提高VSP勘探效率和精度。

Field data traces in seismic exploration are usually irregularly distributed due to the environmental restrictions, especially in vertical seismic profile (VSP). Existing seismic reconstruction algorithms are mainly designed on regular grid. When handling irregular data, we need to use dense regular grid to approximate the irregular grid, leading to low efficiency and low accuracy. I have done researches on reconstruction of seismic traces under regular grid with compressive sensing and achieved satisfying results. For the irregular grid in VSP, we propose to redesign the sampling operator in compressive sensing, using non-equispaced Fourier transform to map the data from regular grid to irregular grid in the fidelity term. This project focuses on the following subjects: (1) Compressive sensing for data on irregular grid. (2) Synthetic VSP data reconstruction by combining curvelet transform and Monte Carlo data driven tight frame in the sparsity constraint. (3) verifying the algorithm with migration on the reconstructed data and applying on 3D field VSP data of Daqing area. This project is based on interdisciplinary of applied mathematics and geophysics. We focus on VSP data reconstruction theory, aiming to reduce the negative effect of environmental factors and increase efficiency and accuracy of seismic exploration.