基于Lowrank分解的谱方法和有限差分地震正演模拟

项目名称： 基于Lowrank分解的谱方法和有限差分地震正演模拟

项目编号： No.41504109

项目类型： 青年科学基金项目

立项/批准年度： 2016

项目学科： 天文学、地球科学

项目作者： 方刚

作者单位： 青岛海洋地质研究所

项目金额： 20万元

中文摘要： 研究高效高精度的地震正演方法对促进地震勘探技术的发展有重要意义。本项目基于Lowrank分解，研究提高地震正演方法的效率和精度，首先根据递归积分时间延拓（RITE）算子理论，发挥交错网格优势，构建交错网格和旋转交错网格上的RITE算子，分析其稳定性和误差分布；其次在稳定性约束下对构建的RITE算子进行Lowrank分解，推导波场延拓公式，提出高效Lowrank谱方法，给出吸收衰减边界条件；然后利用引入频率加权和稳定约束的最小二乘法在宽频域内用有限差分拟合Lowrank谱算子，优化有限差分系数，提出高精度Lowrank有限差分方法，推导其频散关系和稳定性条件，实现PML边界条件；最后将提出的Lowrank谱方法和Lowrank有限差分方法推广至三维情况，研究其存储优化和并行计算策略，实现复杂模型地震波场正演模拟。研究结果将给出高效高精度的地震正演方法，为发展高精度地震勘探技术提供方法基础。

中文关键词： Lowrank分解；地震正演；波动方程；有限差分；谱方法

英文摘要： Seismic modeling method with high computational efficient and accuracy is significant for the development of seismic exploration technique. Based on Lowrank decomposition, this project improves the efficient and accuracy of seismic modeling methods. First, based on the pseudo-differential operator theory, we construct the recursive integral time-extrapolation (RITE) operator on staggered grid and rotated staggered grid to take the advantage of staggered grid and analyze the stability of RITE operator. Next, we propose high-efficient Lowrank spectral method by applying Lowrank decomposition constrained by stablility condition to the constructed RITE operator, deriving the wave propagation formula and taking absorbing boundary condition. Additionally, we optimize the finite difference coefficients by fitting Lowrank spectral operator with finite difference operator on a wide wavenumber band with constrained weighted least square method. We propose high-accuracy Lowrank finite difference method and derive its dispersion relation and stability condition. We also propose PML boundary condition for Lowrank finite difference. Finally, we expand the proposed Lowrank spectral method and Lowrank finite difference method to three dimension. We optimize the storage and parallel the computation for the three-dimension methods.The proposed methods are tested with seismic mdoeling on complex models. The research results can be used for high-accuracy and high-efficient seismic modeling methods, which also provide a foundation for the development of seismic imaging and seismic inversion techniques.

英文关键词： Lowrank decomposition;seismic modeiling;wave equation;finite difference;spectral method