The main goal of modern seismic imaging is to find the best representation of the subsurface that sticks better to the data recorded during acquisition campaigns. The first oil exploration has been conducted in the early 20s and one well-known example is the salt dome of Orchard, Texas (USA) which was discovered in 1924 by the seismic reflection method. The mathematical model that is the most suitable is the wave equation and the imaging technique that uses its solution is called the Reverse Time Migration (RTM). The wave equation is the reference model for seismic imaging because its solution is reversible in time. By applying the backpropagation of the reflected waves, one can thus, relocate the information recorded by the receivers on the reflectors. The RTM is an iterative process of imaging, therefore based on solving a series of wave equations. In a pioneering work, Hemon showed that solving the wave equation is an effective tool for seismic migration. It is amusing to note that Hemon thought his theory had no practical interest and it took more than 5 years to see that the RTM was effective for imaging salt domes.

Depth imaging thus constitutes a major challenge for exploration and oil production. The complex environments to consider involves a very high level research activity providing new techniques for solving three-dimensional wave equations. This research is based on advanced methods combining mathematics, geophysics and scientific computing and this pluri-disciplinar collaboration is essential to the design of numerical simulation codes capable of delivering a clear picture of the subsurface.

The aim of the strategic action DIP (Depth Imaging Partnership) is to contribute significantly to the numerical simulation of wave propagation in complex media. The dedicated application is seismic imaging via the migration technique but also the resolution of the inverse problem. By bringing together researchers covering a broad spectrum of activities, DIP aims to develop new methods for numerical depth imaging, focusing both on the mathematical modelling and high-performance computing.

Generally speaking, the identified issues concern the design of new numerical methods for wave equations which must be developed in such a way they can be used in modern computing architectures. Topics could be

- 1. Advanced numerical methods for wave equations including for instance discontinuous Galerkin methods, local-time stepping, upscaling, optimized absorbing conditions
- 2. Construction of optimized solvers for Helmholtz problems
- 3. Use of accelerator technology
- 4. Mesh generation

This is just a non exhaustive list of topics. We encourage any INRIA team which believes it can contribute to the advancement of depth imaging using wave equations.