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An introduction to scattering and multiple scattering.

Energy scattering:

Scattering description is especially useful when waves travel a long distance in heterogeneous media. Whether the effects of velocity heterogeneities are regarded as scattering or not depends on the ratio of the heterogeneity size to the wavelength and the distance travelled by the wave through the heterogeneous zone. When the heterogeneity is large compared to the wavelength, we regard the wave as following a distinct ray path that is distorted by multipathing. Otherwise, we think of scattered energy.

Unscattered waves travel the shortest distance and arrive first (direct travel). The ellipsoid shown in Fig. 1 b) defines the possible scatterers for energy that arrives later.

Fig. 1: The principle of energy scattering.

Single scattering:

3D isotropic or anisotropic structures often contain heterogeneities. Scattering is a way to model them and to understand them in a better way. We can model scattering of body waves and surface waves.

We have developed methods for surface wave scattering, which uses the property of mode coupling: the incident wavefield is decomposed on several Rayleigh and Love modes of a reference structure. The heterogeneities act as secundary sources that couple the modes and diffract energy in all directions, as shown on the figure below.

Fig. 2: The principle of scattering: a wavefield scattered by a local heterogeneity. R0: Rayleigh fundamental mode, L0: Love fundamental mode, R1: first overtone of the Rayleigh wave.

Multiple scattering iterates this method.

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