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) 

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

We will consider a general nonlinear elastic inverse problem  

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 

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  

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