| Registro completo |
| Provedor de dados: |
ArchiMer
|
| País: |
France
|
| Título: |
Path-summation waveforms
|
| Autores: |
Lomax, A
|
| Data: |
1999-09
|
| Ano: |
1999
|
| Palavras-chave: |
Inversion
Lateral heterogeneity
Synthetic waveforms
Wave equation
Wave propagation
|
| Resumo: |
In this paper, we examine an efficient, practical method to calculate approximate, finite-frequency waveforms for the early signals from a point source in 3-D acoustic media with smoothly varying velocity and constant density. In analogy to the use of Feynman path integrals in quantum physics, we obtain an approximate waveform solution for the scalar wave equation by a Monte Carlo summation of elementary signals over a representative sample of all possible paths between a source and observation point. The elementary signal is formed from the convolution of the source time function with a time derivative of the Green's function for the homogeneous problem. For each path, this elementary signal is summed into a time series at a travel time obtained from an integral of slowness along the path. The constructive and destructive interference of these signals produces the approximate waveform response for the range of traveltimes covered by the sampled paths. We justify the path-summation technique for a smooth medium using a heuristic construction involving the Helmholtz-Kirchhoff integral theorem. The technique can be applied to smooth, but strongly varying and complicated velocity structures. The approximate waveform includes geometrical spreading, focusing, defocusing and phase changes, but does not fully account for multiple scattering. We compare path-summation waveforms with the exact solution for a 3-D geometry involving a low-velocity spherical inclusion, and with finite-difference waveforms for a 2-D structure with realistic, complicated velocity variations. In contrast to geometrical-ray methods, the path-summation approach reproduces finite-frequency wave phenomena such as diffraction and does not exhibit singular behaviour. Relative to the finite-difference numerical method, the path-summation approach requires insignificant computer memory and, depending on the number of waveforms required, up to one to two orders of magnitude less computing time. The sampled paths and associated traveltimes produced by the path summation give a relation between the medium and the signal on the waveform that is nut available with finite-difference and finite;element methods. Furthermore, the speed and accuracy of the path-summation method may be sufficient to allow 3-D waveform inversion using stochastic, non-linear, global search methods.
|
| Tipo: |
Text
|
| Idioma: |
Inglês
|
| Identificador: |
https://archimer.ifremer.fr/doc/00466/57771/60028.pdf
DOI:10.1046/j.1365-246x.1999.00889.x
https://archimer.ifremer.fr/doc/00466/57771/
|
| Editor: |
Oxford Univ Press
|
| Formato: |
application/pdf
|
| Fonte: |
Geophysical Journal International (0956-540X) (Oxford Univ Press), 1999-09 , Vol. 138 , N. 3 , P. 702-716
|
| Direitos: |
info:eu-repo/semantics/openAccess
restricted use
|
|
