Skip to Main content Skip to Navigation
Journal articles

First-arrival Travel-Time Tomography using Second Generation Wavelets

Abstract : Wavelet decomposition of the slowness model has been proposed as a multiscale strategy for seismic first-arrival time tomography. We propose the introduction of so-called second generation wavelets which could be used for any mesh structure and does not need a number of samples as the power of two in each direction. Moreover, one can handle easily boundary effects. A linearized procedure for inverting delayed travel-times considering either slowness coefficients or wavelet coefficients. The ray tracing is solved at each iteration through an eikonal solver while the linear system to be solved at each iteration goes through an iterative solver as LSQR algorithm. We develop wavelet decomposition over constant patches (Haar wavelet) or over linear patches (Battle-Lemarie wavelet) of coefficients at different scales. This decomposition is introduced in the linear system to be solved and wavelet coefficients are considered as unknowns to be inverted. Synthetic examples show that the inversion behaves in a better way as wavelet decomposition seems to act as a preconditioner of the linear system. Local discretisation is possible but requires additional implementation as artefacs once built inside the model description never disappear because of the linearized approach. A binary mask operator is designed for each scale grid and could be applied locally leading to quite different spatial resolution depending on the analysis we could perform of the expected resolution at a given position of the medium. We show that indeed it is possible to design this binary operator and we apply it to synthetic examples as a crosswell experiment inside the Marmousi model. An application to a surface-surface experiment has been performed and the waveled decomposition shows that indeed we may recover detailed features nearby the free surface while preventing imprints of ray coverage at greater depths giving us smooth features at that depths. In spite of the increase demand of computer resources, the wavelet decomposition seems to be a rather promising alternative for controlling the resolution variation of seismic first-arrival tomography.
Complete list of metadatas

Cited literature [51 references]  Display  Hide  Download

https://hal-insu.archives-ouvertes.fr/insu-00200074
Contributor : Pascale Talour <>
Submitted on : Thursday, December 20, 2007 - 11:35:19 AM
Last modification on : Wednesday, October 14, 2020 - 4:22:59 AM
Long-term archiving on: : Monday, April 12, 2010 - 8:37:48 AM

File

article_soumis_figures_ok-1.pd...
Files produced by the author(s)

Identifiers

Citation

Matthieu Delost, J. Virieux, Stéphane Operto. First-arrival Travel-Time Tomography using Second Generation Wavelets. Geophysical Prospecting, Wiley, 2008, 56, pp.505-526. ⟨10.1111/j.1365-2478.2008.00710.x⟩. ⟨insu-00200074⟩

Share

Metrics

Record views

898

Files downloads

670