Inverse Resonance Problem for Love Seismic Surface Waves

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-07-01 DOI:10.1137/23m155877x

Samuele Sottile

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1288-1311, August 2024.
Abstract. In this paper, we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb’s problem. Using a semiclassical approach, we are able to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schrödinger equation with Robin boundary conditions on the half-line. We obtain asymptotic values on the number and the location of the resonances with respect to the wave number. Moreover, we prove that the mapping from real compactly supported potentials to the Jost functions in a suitable class of entire functions is one-to-one and onto and we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances.

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爱地震表面波的反共振问题

SIAM 应用数学杂志》，第 84 卷第 4 期，第 1288-1311 页，2024 年 8 月。摘要本文求解了表面应力消失的半固体的反共振问题：兰姆问题。利用半经典方法，我们能够将这个半固体弹性波方程的三维问题简化为半线上具有罗宾边界条件的薛定谔方程。我们得到了共振的数量和位置与波数的渐近值。此外，我们还证明了在合适的全函数类别中，从实的紧凑支撑势到约斯特函数的映射是一一对应的，并产生了一种算法，以便从特征值和共振中检索剪切模量。

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.