Discretization of the model parameters

We assume that the model parameters, anomalous conductivity distribution. Ad (r), belong to some complex Hilbert space Mp of the functions 7(r), 7 6 My, defined in domain D and integrable in D with the inner product  

We can discretize the model, in this case the anomalous conductivity distribution, Ad (r), by introducing a set of basis functions, V l (r), V 2 (r), / /v (r) in the finite dimensional Hilbert space M, which is a subspace of the complex Hilbert space Mo M/v C Mo- Let us approximate the anomalous conductivity by its projection over the basis functions  

The choice of the basis functions, 0 , is important in both forward and inverse electromagnetic problems. It depends on the specific geophysical problem and the required accuracy of discretization. 

Let us divide the domain D into elementary cells, Z , formed by some rec- 

we have the following representation for the anomalous conductivity distribution  

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