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Formulation of the elastic field inverse problem

Consider a 3-D elastic medium. The propagation of elastic waves in the frequency domain can be described by the Lame equation (13.34) [Pg.518]

We also assume that the elastic field satisfies the radiation conditions (13.202) - (13.204) at infinity. [Pg.519]

We will consider a general nonlinear elastic inverse problem  [Pg.519]

Operator Al denotes the nonlinear forward modeling operator, given by the Lame equation (15.230) and radiation conditions (13.202) - (13.204). This operator can be calculated, for example, from the general integral representation of the elastic field in the frequency domain (13.97), which we write here in the form [Pg.519]

Following our standard approach to regularized solution of the inverse problem, we substitute for the solution of the inverse problem (15.231) a minimization of the corresponding parametric functional with, for example, a minimum norm stabilizer  [Pg.519]


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