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地球物理中的反问题、正则化与稀疏解

发布时间:2013-11-05 12:12:57 发布人:  审核人:

主讲人:王彦飞研究员

报告时间:11月8日(周五)下午15:00—17:00

报告地点:数理楼221会议室

内容提要:

报告人:王彦飞研究员

摘要:Inverse problems are a huge topic in inversion community. Studies on inverse problems represent an exciting research area in recent decades. Inverse problems are typically interdisciplinary subjects related with mathematics, physics, chemistry, geoscience, biology, financial and business, life science, computing technology and engineering. In this talk, we mainly talk about inverse problems in geophysics and the related solution methods.

Using the observations to infer the unknowns (layer reflectivity, impedance, velocity, density, magnetization, data completion, etc.) is called geophysical inversion. In this report, we focus on data completion problems. In geophysical exploration, the process of acquisition records the continuous wavefield (data) which is generated by the seismic source. In order to restore the seismic data correctly, the acquisition should satisfy the Nyquist/Shannon sampling theorem. In seismic acquisition, because of the influence of obstacles at land surface, rivers, bad receivers, noise, acquisition aperture, restriction of topography and investment, the obtained data usually does not satisfy the sampling theorem. A direct effect of the limitations of acquisition is the sub-sampled data will generate aliasing in the frequency domain; therefore, it may affect the subsequent processing such as filtering, de-noising, AVO (amplitude versus offset) analysis, multiple eliminating and migration imaging. In order to remove the influence of sub-sampled data, the seismic data regularization technique is often used. Let us denote by m the original seismic wavefield, d the sampled data, and L the sampling operator, the data regularization can be written as Lm = d. Our purpose is to restore m from the sampled data d. Since d is usually incomplete and L is an underdetermined operator, this indicates that there are infinite solutions satisfying the seismic imaging equation. Hence, seismic data regularization is an ill-posed inverse problem. In our recent work, we develop some sparse optimization methods for the wavefield reconstruction problem. We consider sparse Gaussian beams decomposition methods and sampling techniques and solve the problem by constructing different kinds of regularization models and study sparse optimization methods for solving the regularization model. The lp-lq model with p = 2 and q = 0 or 1 is fully studied. Solving methods for the optimization problem are addressed. Numerical experiments are performed for solving the ill-posed data regularization problem. The results revealed that the proposed method can greatly improve the quality of wavefield recovery.

专家简介:

王彦飞,男,中国科学院地质与地球物理研究所研究员。主要从事计算和勘探地球物理反演问题的理论、计算及应用研究。近年来共承担财政部仪器专项、科技部973、国家自然科学基金、国家杰出青年基金、中科院知识创新工程、国际合作项目及企业项目等一系列科研项目。现任国际反演学会指导委员会委员;担任国际Inverse Problems in Science and EngineeringInternational Journal on GeomathematicsJournal of Inverse and Ill-posed ProblemsEurasian Journal of Mathematical and Computer ApplicationsSCI刊物的编委;任美国数学会(AMS)“数学评论(Mathematical Reviews)” 评论员。应邀出访过美国(2003-2004, 2007)、俄罗斯(2008-2013)、日本(2007)及欧共体的多个国家研究机构进行合作研究。作为大会主席主持了3 次国际学术会议;做国际特邀大会报告6次。2008年获首届中国科学院卢嘉锡青年人才奖,2008年获中国运筹学学会青年科技奖,2011年获中国地球物理学会傅承义青年科技奖。出版学术论著5部,发表学术论文67篇。

               

                         科技处、数学系

                         2013年11月5日