A New Robust Inversion Method Using Cauchy-Steiner Weights – And Its Application in Data Processing
H. Szegedi, M. Dobroka and J. Somogyi Molnar
Event name: Near Surface Geoscience 2014 - 20th European Meeting of Environmental and Engineering Geophysics
Session: Modelling and Inversion
Publication date: 08 September 2014
Info: Extended abstract, PDF ( 543.42Kb )
Price: € 20
The Fourier-transform (FT) often results noisy Fourier spectrum because this operation is linear and contaminate noise in time domain dataset appear in the frequency domain also. Especially, in case of non-Gaussian nature of the noise distribution (for example outliers in the data sets) can cause appreciable distortions in the Fourier spectra. If we treat the FT as an over-determined inverse problem, the noise effect on the Fourier spectrum can be greatly reduced. The geophysical series inversion was used for the discretization. The scaled Hermite functions - note that they are eigen-functions of the FT - were chosen as basis function. During the inversion process by using the Steiner-weights we get a highly robust inversional FT method. Numerical tests show the significant noise rejection capability of the new inversion based FT algorithm.