主 题: Inverse Problems in Geophysics, Regularization and Sparse Solutions
报告人: Professor Yanfei Wang (Institute of Geology and Geophysics, Chinese Academy of Sciences)
时 间: 2015-06-12 15:00 - 16:00
地 点: 理科一号楼 1114(数学所活动）
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, I talk about inverse problems in geophysics and the related solution methods. Inverse problems in geophysics mainly refer to using the observations with various detectors to infer the unknowns, e.g., albedos, temperature distribution, LAI,layer reflectivity, impedance, velocity, density, magnetization, data completion and imaging of an object section. Generally, inverse problems are ill-posedin the sense that one of the three items “existence, uniqueness or stability” of the solution may be violated. Inverse problems use modeling design and optimization methods to provide a better, more accurate and more efficient simulation for practical problems. In geophysics, nearly all inverse problems are ill-posed because of the limitations of observations and instability during inversion computation. For instance, a direct effect of the limitations of acquisition is the sub-sampled data willgenerate 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 our recent work, we develop some sparse optimization methods for the data regularization problem. We consider sparse Gaussian beams decomposition methods and sampling techniques and solve the problem byconstructing different kinds of regularization models. Imaging as an inversion is also considered. Numerical experiments based on theoretical data and field data are performed and interpreted.
