# Linearization Ill-Posedness for 2.5-D Wave Equation Inversion Model

Linearization Ill-Posedness for 2.5-D Wave Equation Inversion Model For the weakly inhomogeneous acoustic medium in Ω={(x, y, z:z>0}, we consider the inverse problem of determining the density function p(x, y). The inversion input for our inverse problem is the wave field given on a line. We get an integral equation for the 2-D density perturbation from the linearization. By virtue of the integral transform, we prove the uniqueness and the instability of the solution to the integral equation. The degree of ill-posedness for this problem is also given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Linearization Ill-Posedness for 2.5-D Wave Equation Inversion Model

, Volume 18 (2) – Jan 1, 2002
12 pages      /lp/springer-journals/linearization-ill-posedness-for-2-5-d-wave-equation-inversion-model-QYhgNLWbjY
Publisher
Springer Journals
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s102550200021
Publisher site
See Article on Publisher Site

### Abstract

For the weakly inhomogeneous acoustic medium in Ω={(x, y, z:z>0}, we consider the inverse problem of determining the density function p(x, y). The inversion input for our inverse problem is the wave field given on a line. We get an integral equation for the 2-D density perturbation from the linearization. By virtue of the integral transform, we prove the uniqueness and the instability of the solution to the integral equation. The degree of ill-posedness for this problem is also given.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2002

Access the full text.

Sign up today, get DeepDyve free for 14 days.