A 3D Parsimonious Finite-volume Frequency-domain Method for Elastic Wave Modelling

We present the finite-volume (FV or P0 Galerkin Discontinuous) formulation applied to the 3D visco-elastic wave equation in the frequency domain. This work is motivated within the framework of global offset seismic imaging by full waveform inversion. Concerning the direct problem, the FV formulation leads to the resolution of a large and sparse system of linear equations. This system can be solved with a direct solver particuraly suitable to tomographic applications since only one matrix factorization is performed per frequency for all the right hand terms (i.e. the sources). On the other hand, direct solvers require large amount of RAM and therefore restrict the possible field of realistic applications. The memory complexity of the proposed method implies reduced size models spanning over several wavelengths. In order to push back this limitation, the use of a higher order of interpolation, as Pk Galerkin Discontinuous, should decrease the discretization step allowing coarser meshes leading to a possible managing situation. Furthermore, the use of a domain decomposition method might reduce significantly the memory requirements of the FV frequency domain approach.