Abstract
We linearize the relation between the parameters (density and velocity profiles) of a layered fluid subject to a specified surface point traction and the precitically reflected part of its surface motion. We decompose the resulting linear map into a high-frequency leading term and a lower-order (smoother) remainder and show that the spectral analysis of the leading term may be described in terms of ray geometry. The leading term is generally well conditioned but may become poorly conditioned in low-velocity zones. These results imply stability estimates for the linearized acoustic reflection inversion problem as well as for the nonlinear problem and yield insight into the behavior of numerical algorithms for the determination of the density and velocity of a layered fluid from its surface response.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 318-381 |
| Number of pages | 64 |
| Journal | Journal of Computational Physics |
| Volume | 74 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1988 |
Bibliographical note
Funding Information:* This work was supported in part by the National Science Foundation and by the Office of Naval Research under Contract NOOl-83-KOO51.
Funding Information:
We wish to record our debt to the Cornell ONR/SRO project on inverse problems in wave propagation, led by Professors Y.-H. Pao and L. Payne, uner the auspices of which the research reported here was conducted (Office of Naval Research Contract N-OOl-14-83-KO051). The second author also received partial support from the National Science Foundation under Grant DMS-8403148. We wish expecially to thank Paul Sacks for destroying our complacency about the definition of the Radon transform. We are also grateful to Kenneth Bube, Kenneth Driessel, and Patrick Lailly for useful conversations, and to Cheryl Purcell for checking the calculations in Appendix B.