Optimal experimental design for full waveform inversion using a wavenumber sampling criterion—Part 2: 3-D extension and practical application

SUMMARY In a companion paper, we have proposed an optimal experimental design (OED) strategy for seismic imaging. Using the theory of diffraction tomography, for a specified target, given an acquisition geometry and a prior information on the subsurface velocity, we characterize the wavenumber space of the image that would result at the image point from such an acquisition. Our strategy relies on optimizing the sources and receivers positions so as to guarantee a regular sampling of the wavenumber space within the pre-computed envelope. The regularity of a given sampling is assessed through the use of Voronoi tessellations, associated with the wavenumber points cloud. Computing a centroidal Voronoi tessellation, which can be formulated as an optimization problem, guarantees a regular tessellation, which in turns provides a regularly spaced wavenumber points cloud. We have introduced this method in a 2-D context, in relatively simple settings. In this second paper, we present the extension of this method to a more realistic framework and investigate its application to synthetic case studies. This extension consists in considering now a fully 3-D geometry, as well as specific deployment constraints with polygonal shaped deployment 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 OED algorithm. We investigate on simple velocity models the feasibility and limitations of our method for target-oriented seismic imaging using full waveform inversion.