Formulation of the nonlinear wavefield inverse problem

In this section, we consider general nonlinear acoustic and vector wavefield inverse 

The nonlinearity of the operators Aa and A with respect to the anomalous slowness As is related to the fact that the wavefields p(r, w) and u(r, o ) also depend on As.  

As usual, following the conventional Tikhonov regularization method, we substitute for the solution of the inverse problems (15.167) or (15.168) a minimization of the corresponding parametric functional with, for example, a minimum norm stabilizer  

The minimization problem (15.170) can be solved by the conjugate gradient or re-weighted conjugate gradient methods introduced in Chapter 5. 

Let us describe, for example, the algorithm based on the regularized conjugate gradient method (5.92), which we reproduce here with small modifications  

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