Multiple reflections on Huygens' principle
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913979022966784 |
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| author | Wapenaar, Kees |
| author_facet | Wapenaar, Kees |
| contents | According to Huygens' principle, all points on a wave front act as secondary sources emitting spherical waves, and the envelope of these spherical waves forms a new wave front. In the mathematical formulation of Huygens' principle, the waves emitted by the secondary sources are represented by Green's functions. In many present-day applications of Huygens' principle, these Green's functions are replaced by their time-reversed versions, thus forming a basis for backpropagation, imaging, inversion, seismic interferometry, etc. However, when the input wave field is available only on a single open boundary, this approach has its limitations. In particular, it does not properly account for multiply reflected waves. This is remedied by a modified form of Huygens' principle, in which the Green's functions are replaced by focusing functions. The modified Huygens' principle forms a basis for imaging, inverse scattering, monitoring of induced sources, etc., thereby properly taking multiply reflected waves into account. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13833 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Multiple reflections on Huygens' principle Wapenaar, Kees Geophysics According to Huygens' principle, all points on a wave front act as secondary sources emitting spherical waves, and the envelope of these spherical waves forms a new wave front. In the mathematical formulation of Huygens' principle, the waves emitted by the secondary sources are represented by Green's functions. In many present-day applications of Huygens' principle, these Green's functions are replaced by their time-reversed versions, thus forming a basis for backpropagation, imaging, inversion, seismic interferometry, etc. However, when the input wave field is available only on a single open boundary, this approach has its limitations. In particular, it does not properly account for multiply reflected waves. This is remedied by a modified form of Huygens' principle, in which the Green's functions are replaced by focusing functions. The modified Huygens' principle forms a basis for imaging, inverse scattering, monitoring of induced sources, etc., thereby properly taking multiply reflected waves into account. |
| title | Multiple reflections on Huygens' principle |
| topic | Geophysics |
| url | https://arxiv.org/abs/2412.13833 |