Abstract
Formulae involving double integrals over spheres arise naturally in inverse scattering problems since the scattered data are measured in the space R*S2*S2. The authors derive a relation between differential forms on the space Sn-1*Sn-1, and those on the space I*Sn-2*Sn-1, where I is a real interval. Specifically, d xi d eta =sinn-2 theta d theta d psi d nu ( xi , eta ) in Sn-1*Sn-1 and ( theta , psi , nu ) in I*Sn-2*Sn-1. This allows them to derive the results of John relating the iterated spherical mean of a function to its spherical mean in a simple way; to obtain new inversion formulae for the Fourier and Radon transforms; to extend formulae for linearised inverse quantum scattering and diffraction tomography to the multifrequency case; and also to establish a relation between multifrequency diffraction tomography and seismic migration algorithms.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
