Scattering theory as a framework for inversion of ground-penetrating radar
Recently Parth Routh has been teaching me about ground-penetrating radar, which is a terrific and interesting problem (extra bonus: with many similarities to the seismic/Q problem). He and a collaborator posed a geo-radar inverse scattering problem a couple of years ago, and we have been taking a fresh look at it. The idea is to try to determine a distribution of conductivities and dielectric permittivities in the near-surface. Here's one:
Specifically, we'd like to determine them from reflected radar signals. Inverse scattering will permit this. To do synthetic testing of the theory, we used James Irving's [code] to produce shot records of data (you can see two primaries and an internal multiple in the records below), deconvolved the source wavelet (which we assumed we knew beforehand), and produced our input data:
Finally, using a direct linear theory, we reconstructed the permittivity profiles using a variety of angles in the synthetic data. The profiles look pretty good -- the numbers are right and the contrasts are nicely resolved. The "ringiness" is due to the crude deconvolution we did. In particular, if you look at the large angle results and the location of the deeper interface, you can see the remaining problems left for the non-linear components of the inverse scattering problem. That's an ongoing bit of research.
