Abstract
Seismic reflection tomography attempts to match traveltimes obtained from surface seismic data with the corresponding traveltimes of rays traced through a model of the subsurface. Traveltimes along rays from surface shot locations down to reflecting interfaces and then back up to surface receiver locations are used; the goal is to determine both the position of the reflectors and the slowness field above the reflectors. Seismic reflection tomography is closely related to the inversion of a limited-angle Radon transform. The author formulates a continuum version of reflection tomography analogous to the discrete version appropriate for much of surface seismic data; the continuum version models a finite cable length with positive minimum offset, where the shot and receiver spacing are small compared with the cable length. It is proven that in a continuum formulation of reflection tomography with infinite horizontal extent, linearized about a constant background, the reflector depth perturbations are uniquely determined by the traveltime perturbations. Moreover, the slowness perturbations in the null space of this linearized problem can be completely characterized: they are polynomials in the horizontal variable with coefficients which are functions of the depth variable satisfying integral orthogonality constraints.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: 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.