Ressource pédagogique : Seismic tomography : A giiant inverse problem

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Description (résumé)

In this talk I shall give an overview of the development of seismic tomography: constructing images of elastic properties in the Earth's interior from seismic observations at its surface. The use of ray-theoretical approximations allows us to image long-wavelength structure. To increase resolution, however, we cannot escape using the wave equation. Modeling the waveforms themselves is highly nonlinear, but the nonlinearity of the problem can be kept under control by using secondary observables such as delays of time- and frequency windowed waveforms. The resulting problem is a giant linear inverse problem that is at the same time under- and overdetermined. Regularization techniques include total variation minimization and compressed sensing. The estimation of accuracy and resolution of a solution poses a number of unsolved questions of mathematical nature.

"Domaine(s)" et indice(s) Dewey

• Modélisation mathématique (511.8)
• Volcans, tremblement de terre, eaux thermales et gaz (551.2)
• Reconnaissance des formes par ordinateur (006.4)

Thème(s)