Homomorphic deconvolution applied to ring diagram analysis

Ring diagram analysis and homomorphic deconvolution are two techniques used independently in solar seismology. The use of homomorphic deconvolution coupled to ring analysis may improve the precision of the latter technique, as the former does for regular time series analysis. In order to compare the use of the classical Fourier Transform and the homomorphic deconvolution, ring diagram analysis using both techniques has been applied to the same data set. Results are compared at different steps in the analysis, qualitatively and quantitatively. Results from the homomorphic deconvolution are similar to those of the Fourier Transform. However, some discrepancies sometimes larger than the observed uncertainties are observed, discrepancies whose origin is still unclear. The precision of the deconvolution is in general better than that of Fourier Transform, up to a factor of two in the best cases. These preliminary results encourage us to explore the possibilities of the homomorphic deconvolution coupled to ring diagram analysis.