Optimal Experimental Design for Seismic Tomography
Speciality : Mathématiques Appliquées
6/11/2024 - 14:00 Amine Abdellaziz (Université Grenoble Alpes) Amphitéatre Kilian, ISTerre, 1381, rue de la Piscine, 38610 GIERES
In exploration geophysics, the operational complexity of seismic surveys, involv- ing sometimes hundred thousands of receiver and source devices, lead operators to consider the question of optimal experimental design as an economical cost- effectivity problem. However, the question can also be approached from an imaging perspective. Andrzej Kijko’s seminal work on the optimal design of seismic stations for earthquake localization, dating back to the seventies, has encouraged several works related to optimal design of acquisition in exploration geophysics. A common choice for the optimality criterion is the conditioning of the Hessian operator of the misfit function. In this PhD thesis, we choose our optimality criterion to be the regularity of the wavenumber sampling at a specified target: using the theory of diffraction tomogra- phy we can estimate the wavenumber sampling at a target point, and we notice that for a regularly-spaced acquisition, the corresponding sampling is not regular. In our target-oriented approach we want to find the best positions of sources and receivers to improve the regularity of this sampling. We develop our work in the context of Full Waveform Inversion, although our approach is more general. Using a simple formula for the estimation of the wavenumber points, we are able to get a geometric characterization of the accessible wavenumber space that helps us define its envelope. We describe the problem as finding the geometry for which the sampling points are regular in terms of spacing inside this envelope. For this purpose we incorporate in our workflow the notion of centroidal Voronoi tessellation, a tool from computa- tional geometry that links the regularity of the sampling to the uniformity of the domain tessellation. To assess the uniformity of the tessellation, we consider an energy function the minimal values of which provide regular samplings. By com- bining this energy function with a map that estimates the wavenumber content of an acquisition, we define a new objective function that assesses the quality of such acquisition with respect to our regularity criterion. We then mathematically express our problematic as a minimization problem which we solve using local optimization strategies. We first introduce this method in a relatively simple settings in 2D case and we later extend it to a more realistic framework. This extension consists in considering a fully 3D geometry, as well as specific constraints with polygonal shaped deploy- ment zones and non-accessible (exclusion) zones for the sources and receivers. Such type of constraints are commonly met in survey design and it is important to be able to take them into account in an optimal design algorithm. We validate our method through numerical examples of varying complexities : when comparing optimized acquisitions with regular ones, the results show a consis- tent local improvement of the quality of the inversion with the optimized geometries. We also discuss the limitations of the method in its current implementation and we propose possible improvements. The results motivate the exploitation of the methodiii for target-oriented applications such as seismic monitoring. It also offers a tool for the optimal selection of subsets in large seismic data volumes, to be used in post- processing applications which are target-oriented.
Directors:
- Dr Ludovic Métivier
- Dr Brossier Romain
- Pr Édouard Oudet
Raporteurs:
- Dr Bruno Lévy
- Dr Hansruedi Maurer
Examinators:
- Dr Stéphane Operto
- Pr Boris Thibert
- Dr Thibaut Allemand