Tangential Cone Condition for the Full Waveform Forward Operator in the Viscoelastic Regime: The Nonlocal Case

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-03-12 DOI:10.1137/23m1551845

Matthias Eller, Roland Griesmaier, Andreas Rieder

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 412-432, April 2024.
Abstract. We discuss mapping properties of the parameter-to-state map of full waveform inversion and generalize the results of [M. Eller and A. Rieder, Inverse Problems, 37 (2021), 085011] from the acoustic to the viscoelastic wave equation. In particular, we establish injectivity of the Fréchet derivative of the parameter-to-state map for a semidiscrete seismic inverse problem in the viscoelastic regime. Here the finite-dimensional parameter space is restricted to functions having global support in the propagation medium (the nonlocal case) and that are locally linearly independent. As a consequence, we deduce local conditional well-posedness of this nonlinear inverse problem. Furthermore, we show that the tangential cone condition holds, which is an essential prerequisite in the convergence analysis of a variety of inversion algorithms for nonlinear ill-posed problems.

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粘弹性状态下全波形前向算子的切向锥状条件：非局部情况

SIAM 应用数学杂志》第 84 卷第 2 期第 412-432 页，2024 年 4 月。摘要我们讨论了全波形反演的参数到状态图的映射特性，并将 [M. Eller and A. Rieder, Inverse Problems, 37 (2021), 085011] 的结果从声波方程推广到粘弹性波方程。特别是，我们为粘弹性机制中的半离散地震逆问题建立了参数到状态图的弗雷谢特导数的注入性。这里的有限维参数空间仅限于在传播介质中具有全局支持（非局部情况）且局部线性独立的函数。因此，我们推导出了这一非线性逆问题的局部条件好求性。此外，我们还证明了切向锥条件的成立，这是对非线性问题的各种反演算法进行收敛分析的基本前提。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.