Pushing limits of the 3D acoustic waveform inversion in the frequency domain

We present a 3-D acoustic full waveform tomography (FWT) based on a forward problem suited for<br>multisource simulations. This forward problem based on the wave equation is solved in the frequency<br>domain using a direct solver technique, leading to an impressive request of core memory. The imaging<br>problem (Tarantola, 1987) is built through a local minimization of the mis t function between recorded<br>and synthetic data. The frequency-domain (FD) formulation of FWT was originally developed for 2D<br>cross-hole acquisition surveys which involve wide-aperture propagations (Pratt and Worthington, 1990).<br>Only few discrete frequencies are required to develop a reliable image of the medium thanks to the<br>wavenumber redundancy provided by multifold wide-aperture geometries. The lowest frequency and<br>the starting model both play a critical role in the convergence of the minimization. Since the full wave<br>propagation modeling is a critical issue in FWT methods, a 3D optimal nite-difference stencil has been<br>designed by Operto et al. (2007) that leads to 4 grid points per wavelength for an accurate modelling,<br>reducing the memory request when solving the large sparse linear system for each frequencywe consider.<br>Although present hardware con gurations limit the domain dimensions, it remains unclear where are the<br>different bottlenecks of the approach as the degrading conditioning of the impedance matrix or the poor<br>scalability when we increase the number of nodes. In this presentation, we shall provide some insights on<br>the feasibility and relevance of 3D frequency-domain FWT for building high-resolution velocity models<br>of isotropic acoustic media with one application related to the SEG/EAGE Overthrustmodel and we shall<br>provide an analysis for isotropic elastic media.