The Backus--Gilbert theory for piecewise continuous structures with variable discontinuity levels and its application to the magnetotelluric inverse problem

The Backus-Gilbert theory is extended to the case when the models are piecewise continuous vector functions of depth with variable discontinuity locations. In addition, some of the layers may be represented by linear combinations of known functions. For such layers only a finite number of discrete parameters is to be determined. The iterative process for obtaining a model satisfying the data is convergent, the numerical procedure by which the iterations are performed being equivalent to the method of spectral decomposition for continuous structures. The method of obtaining the Fréchet kernels by using the first perturbation of the differential system satisfied by the corresponding functionals is shown to be valid. The theory is applied to the magnetotelluric problem, Fréchet kernels being calculated for isotropic and non-isotropic structures. A few numerical examples are described.