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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MDPI AG
2025-04-01
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| 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. |
| format | Article |
| id | doaj-art-eba213f5cf5b43cfb4ea248645a5083f |
| institution | DOAJ |
| issn | 2076-3263 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Geosciences |
| 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 |