Hilbert transform of unequally sampled data: Application to dispersion relations in magnetotellurics

What is it about?

A numerical method has been developed to calculate the Hilbert transform of the frequency normalized impedance. The real and imaginary parts of the FNI data can be calculated from each other. The outcomes of the computation can be used to check the data validity in the magnetotelluric method. The method involves the reconstruction of the measured data by a linear combination of an analytic interpolation function distributed along the horizontal axis. Then, the decomposition coefficients that provide a fit between the measured and the reconstructed data are solved by the linear least-squares method with singular value decomposition. Finally, the discrete Hilbert transformed data are constructed at any desired abscissa values by the sum of the analytic Hilbert transform of the interpolation function using the decomposition coefficients solved in

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Why is it important?

A numerical method is presented to calculate the real and imaginary parts of the frequency-normalized impedance from one another using the Hilbert transform. It is valid for 3D earth, while the former methods based on the apparent resistivity data are valid only for 1D earth. The suggested approach provides a tool to verify the magnetotelluric data.

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