DQA approximation in magnetotelluric inverse problem

2 DQA approximation in magnetotelluric inverse problem The DQA approximation is particularly suitable for constructing massive 3-D magnetotelluric inversion schemes, because of the low cost and simplicity of the expressions for forward modeling. In this section I discuss the implementation of the DQA approximation in MT inversion, following the paper by Hursan and Zhdanov, 2001. The main advantage of the QA method over the iterative Born method is that now 

Substituting the QA approximations (9.238) into the anomalous field components in (10.133), we obtain the QA approximation for the data containing the log anomalous apparent resistivities and phases  

the MT inverse problem is reduced to the solution of the nonlinear matrix inverse problem (10.135). 

Now let us consider the derivation of the Fr6chet derivative matrix of the forward operator (10.135). Noting that the model parameters are the anomalous conductivity values in the cells of the anomalous body, and that matrices C, A and A/f are independent of the model parameters, one can express the perturbation of the forward operator (10.135) with respect to the model parameters in the form 

Note that the terms depending on the model parameters are diagonal matrices. The full matrices A and depend only on the background conductivity distribution. Therefore, after precomputing full matrices Ae and A for the background model, the iterative updating of F (m) is relatively inexpensive during the inversion process. 

---