Inversion from Time Domain Backscattering Data for the Wave Equation

时域后向散射数据反演波动方程

• 批准号: 0907909
• 负责人: Rakesh Rakesh
• 金额: $ 7.83万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2013-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0907909&HistoricalAwards=false
• 关键词: Inversion; Time; Domain; Backscattering; Data

The investigator proposes studying a formally determined inverse problem for the plasma wave equation (wave operator plus a zeroth order term) in three space dimensions. The goal is the recovery of a potential, supported in a ball, from time dependent data generated by coincident source-receiver pairs placed on the boundary of the ball. This problem is an imitation, in the time domain, of the frequency domain problem of recovering a potential from back-scattering data. The investigator will study, the analyticity of the map sending potentials to the data, necessary conditions for a function to be in the range of this map, uniqueness when the potentials are restricted to functions which are analytic in the angular variables, and the recovery of the singularities of the potential from the data.The solution of the problems proposed by the investigator and the techniques introduced to solve them would be useful in geophysics, oil exploration, medical imaging, defense and other fields where hidden objects are probed by acoustic or electromagnetic waves.

研究人员提出了一个正式确定的反问题的等离子体波方程（波算子加上零阶项）在三维空间。我们的目标是恢复的潜力，支持在一个球，从时间相关的数据所产生的重合源-接收器对放置在球的边界上。 这个问题是一个模仿，在时域中，恢复从后向散射数据的潜力的频域问题。研究人员将研究，地图的解析性发送潜力的数据，必要条件的功能是在这个地图的范围内，唯一性时，潜力被限制到功能，这是分析的角度变量，研究者提出的问题的解决方案和为解决这些问题而引入的技术将是有用的在物理学、石油勘探、医学成像、国防和通过声波或电磁波探测隐藏物体的其他领域中。