| Автор | M L Oristaglio |
| Дата выпуска | 1989-12-01 |
| dc.description | An inverse scattering formula is derived for an ensemble of experiments in which a three-dimensional scattering object is illuminated by an impulsive point source which successively occupies all positions on a surface surrounding the object. For each source position, the scattered field is recorded by receivers at all positions on the surface. The data from such a complete set of experiments contains redundant information about the scattering potential. The formula provides a way of integrating over the redundancy to give a perfect reconstruction of the scattering potential within the Born approximation. The formula involves three steps: first, the data as a function of receiver position are backpropagated (or focused) to an arbitrary image point inside the surface using the Kirchhoff integral; second, the source array is focused on the same point by a second Kirchhoff integral over source positions; finally, the image field created by the double focusing is filtered as a function of frequency and integrated over all frequencies. The formula relies upon an unusual representation of the spatial delta function which follows from an integral relation between the causal Green function, the anti-causal Green function, and their difference. The method can be extended to the case of an arbitrary background medium if ray-asymptotic approximations are used for the Green functions. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | An inverse scattering formula that uses all the data |
| Тип | paper |
| DOI | 10.1088/0266-5611/5/6/015 |
| Electronic ISSN | 1361-6420 |
| Print ISSN | 0266-5611 |
| Журнал | Inverse Problems |
| Том | 5 |
| Первая страница | 1097 |
| Последняя страница | 1105 |
| Аффилиация | M L Oristaglio; Schlumberger Austin Syst. Center, TX, USA |
| Выпуск | 6 |
