First-arrival Tomography Using the Double-square-root Equation Solver Stepping in Subsurface Offset

A.S. Serdyukov, A.A. Duchkov

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Double-square-root (DSR) equation can be viewed as a Hamilton-Jacobi equation describing kinematics of downward data continuation in depth. It describes simultaneous propagation of source and receiver rays assuming that they are nowhere horizontal. Thus it is not suitable for describing diving waves. This equation can be rewritten in a new form when stepping is made in subsurface offset instead of depth. In this form it can be used for describing traveltimes of diving waves in prestack seismic data. This equation can be solved using WENO-RK numerical scheme. Prestack traveltimes (for multiple sources) can be computed in one run thus speeding up solution of the forward problem. We derive linearized version of this new DSR equation that can be used for tomographic inversion of first-arrival traveltimes. Here we used a ray-based tomographic inversion consisting of the following steps: get numerical solution of the offset DSR equation in the background velocity model, back trace DSR rays connecting receivers to sources, update velocity model using truncated SVD pseudoinverse. This approach was tested on a synthetic model generating diving waves.
Original languageEnglish (US)
Title of host publicationLondon 2013, 75th eage conference en exhibition incorporating SPE Europec
PublisherEAGE Publications
ISBN (Print)9789073834484
StatePublished - 2013
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Research was partly supported by Saudi Aramco and KAUST. Authors are grateful to Jean Virieux andTariq Alkhalifah for useful discussions.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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