Abstract
Original GLM (Gel’fand-Levitan-Marchenko) theory is for potential recovery of Schrödinger equation. Ware and Aki (1969) applied the theory to solve the 1-D elastic equation, but the solution is limited to the case of smooth impedance variation. Coen (1981) formulated the GLM equation for oblique incidence to recover both velocity and density. The reduced GLM equation becomes an equation for refractive index, and the solution is also limited to smooth media. In this paper, we formulate the GLM impedance equation for oblique incidence for simultaneous inversion of velocity and density including boundary jumps. Numerical tests demonstrate clearly the recovery of velocity and density, verified the validity of the theory. The theory of Schrödinger impedance inverse-scattering studied in this paper is closely related to direct envelope inversion (DEI).
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1475-1479 |
| Number of pages | 5 |
| Journal | SEG Technical Program Expanded Abstracts |
| DOIs | |
| State | Published - Aug 10 2019 |
| Externally published | Yes |
| Event | Society of Exploration Geophysicists International Exposition and 89th Annual Meeting, SEG 2019 - San Antonio, United States Duration: Sep 15 2019 → Sep 20 2019 |
Bibliographical note
Funding Information:This work is supported by WTOPI (Wavelet Transform On Propagation and Imaging for seismic exploration) Research Consortium and other funding resources at the Modeling and Imaging Laboratory, University of California, Santa Cruz.
Publisher Copyright:
© 2019 SEG