Inversion from Time Domain Backscattering Data for the Wave Equation

研究人员建议研究三个空间维度中等离子体波方程（波算子加上零阶项）的形式确定的反问题。目标是从放置在球边界上的重合源-接收器对生成的时间相关数据中恢复球所支持的电势。 该问题在时域中模拟了从反向散射数据中恢复电势的频域问题。研究人员将研究将势发送到数据的地图的解析性、函数在该地图范围内的必要条件、当势仅限于在角度变量中解析的函数时的唯一性以及从数据中恢复势的奇点。研究人员提出的问题的解决方案以及解决这些问题所引入的技术将在地球物理学、石油勘探、医学成像、国防和通过声学或电磁探测隐藏物体的其他领域中有用。波浪。

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.