On the linearization of operators related to the full waveform inversion in seismology. (27th December 2013)

• Record Type: Journal Article
• Authors: Kirsch, Andreas; Rieder, Andreas
• Is Part Of: Mathematical methods in the applied sciences. Volume 37:Number 18(2014:Dec. 15)
• Page Start: 2995
• Page End: 3007
• Publication Date: 2013-12-27
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3037
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma3037-abs-0001"> <title>Abstract</title> <p id="mma3037-para-0001">In this work, we analyze the parameter‐to‐solution map of the acoustic wave equation with respect to its parameters wave speed and mass density. This map is a mathematical model for the seismic inverse problem where one wants to recover the parameters from measurements of the acoustic potential. We show its complete continuity and Fréchet differentiability. To this end, we provide necessary existence, stability, and regularity results. Moreover, we discuss various implications of our findings on the inverse problem and comment on the Born series. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>