High Order Time Discretization Of The Wave Equation By Nabla-P Scheme. Application to the Reverse Time Migration

Abstract : Reverse Time Migration (RTM) is one of the most widely used techniques for Seismic Imaging, but it in- duces very high computational cost since it is based on many successive solutions to the full wave equation. High-Order Discontinuous Galerkin Methods (DGM), coupled with High Performance Computing techniques, can be used to solve accurately this equation in complex geophysic media without increasing the computational burden. However, to fully exploit the high-order space discretization, it is necessary to use a high-order time discretization. In this work, we propose a new high order time scheme, the so-called Nabla-p scheme. This scheme does not increase the storage costs since it is a single step method and does not require the storage of auxiliary unknowns. Nu- merical results show that it requires less storage than the ADER scheme for a given accuracy and that it can be efficiently implemented in an RTM algorithm.
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Hélène Barucq, Henri Calandra, Julien Diaz, Florent Ventimiglia. High Order Time Discretization Of The Wave Equation By Nabla-P Scheme. Application to the Reverse Time Migration. WAVES 2013, Jun 2013, Gammarth, Tunisia. ⟨hal-00924172⟩

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