Vibrations of an Elastic Half-Space

We report on the resolution of the vibration problem for a homogeneous and isotropic elastic half-space (the Lamb problem), with application to the seismic tensorial force. We assume a homogeneous and isotropic half-space with a localized force which produces vibrations. The solution is achieved by...

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Main Author: Bogdan Felix Apostol
Format: Article
Language:English
Published: MDPI AG 2025-04-01
Series:Geosciences
Subjects:
Online Access:https://www.mdpi.com/2076-3263/15/4/144
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author Bogdan Felix Apostol
author_facet Bogdan Felix Apostol
author_sort Bogdan Felix Apostol
collection DOAJ
description We report on the resolution of the vibration problem for a homogeneous and isotropic elastic half-space (the Lamb problem), with application to the seismic tensorial force. We assume a homogeneous and isotropic half-space with a localized force which produces vibrations. The solution is achieved by introducing vector plane-wave functions. Explicit results are given for an isotropic tensorial force and a half-space with free surface. The contribution of the Rayleigh surface waves to vibrations is analyzed in the special case of a temporal-impulse force, where the solution exhibits unphysical features, as expected: it extends over the entire free surface and time domain, with a (scissor-like) double-wall propagating both in the future and the past.
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spelling doaj-art-eba213f5cf5b43cfb4ea248645a5083f2025-08-20T03:13:54ZengMDPI AGGeosciences2076-32632025-04-0115414410.3390/geosciences15040144Vibrations of an Elastic Half-SpaceBogdan Felix Apostol0National Institute for Earth Physics, MG-6, P.O. Box MG-35, 077125 Magurele, RomaniaWe report on the resolution of the vibration problem for a homogeneous and isotropic elastic half-space (the Lamb problem), with application to the seismic tensorial force. We assume a homogeneous and isotropic half-space with a localized force which produces vibrations. The solution is achieved by introducing vector plane-wave functions. Explicit results are given for an isotropic tensorial force and a half-space with free surface. The contribution of the Rayleigh surface waves to vibrations is analyzed in the special case of a temporal-impulse force, where the solution exhibits unphysical features, as expected: it extends over the entire free surface and time domain, with a (scissor-like) double-wall propagating both in the future and the past.https://www.mdpi.com/2076-3263/15/4/144elastic half-spacevibrationsvector plane-wave functionsRayleigh surface waves
spellingShingle Bogdan Felix Apostol
Vibrations of an Elastic Half-Space
Geosciences
elastic half-space
vibrations
vector plane-wave functions
Rayleigh surface waves
title Vibrations of an Elastic Half-Space
title_full Vibrations of an Elastic Half-Space
title_fullStr Vibrations of an Elastic Half-Space
title_full_unstemmed Vibrations of an Elastic Half-Space
title_short Vibrations of an Elastic Half-Space
title_sort vibrations of an elastic half space
topic elastic half-space
vibrations
vector plane-wave functions
Rayleigh surface waves
url https://www.mdpi.com/2076-3263/15/4/144
work_keys_str_mv AT bogdanfelixapostol vibrationsofanelastichalfspace