TAILIEUCHUNG - SEISMIC WAVES, RESEARCH AND ANALYSIS_2

Low-frequency acoustic energy released within the Earth's crust and mantle mostly propagates - depending on the density and elasticity of the medium - through several types of seismic waves categorized as body waves (longitudinal P and transverse S) or surface waves (long L and ground roll R). The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity | 8 Coupling Modeling and Migration for Seismic Imaging Hervé Chauris and Daniela Donno Centre de Geosciences Mines Paristech UMR Sisyphe 7619 France 1. Introduction Seismic imaging consists of retrieving the Earth s properties typically velocity and density models from seismic measurements at the surface. It can be formulated as an inverse problem Bamberger et al. 1982 Beylkin 1985 Lailly 1983 Tarantola 1987 . The resolution of the inverse problem involves two seismic operators the modeling and the migration operators. The modeling operator M applies to a given velocity model m x where x denotes the spatial coordinates and indicates how to generate the corresponding shot gathers at any position in the model usually at the surface. It consists of solving the wave equation for given velocity and density parameters. Fig. 1 and 2 illustrate the acoustic wave propagation for different travel times in two different velocity models. A point source generates a roughly circular wavefront for short travel times. The wavefront is then largely distorted due to the heterogeneous aspect of the velocity model. In simple models it is easy to derive which part of the wave energy is diffracted reflected transmitted or refracted Fig. 1 . In more complex models the wave modeling is obtained by numerically solving the wave equation here with a finite difference scheme in the time domain Fig. 2 . In our definition the migration operator is the adjoint M of the modeling operator. It is related to kinematic migration in the sense that the adjoint operator does not necessarily consider proper amplitudes. Equivalently the modeling operator is also known to be the demigration operator. Both the modeling and the migration operators can be very complicated. They provide the link between the time data domain shot receiver and time and the space model domain x positions . For example a homogeneous model with a local density anomaly will create a data gather containing the direct arrival and a .

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