Abstract
In this chapter, we will discuss the most general case of geophysical inverse problem, when operator A of the forward problem is nonlinear. This case arises in electromagnetic and seismic methods, and in many other applications. In the framework of general regularization theory, the solution of the inverse problem can be reduced to minimization of the Tikhonov parametric functional. The last problem can be solved by different optimization methods. We will discuss in this chapter the most powerful optimization technique based on the gradient-type methods. They include the steepest descent method, the Newton method, and the conjugate gradient method.
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