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Higher order accuracy in multiple filter technique

SEISMOLOGICAL OBSERVATORY INDIA METEORLOGICAL DEPARTMENT, LODI ROAD NEW DELHI 110003, India

Abstract

It is known that there are systematic errors in the determinations of group velocity and amplitude spectrum by multiple filter technique (MFT) due to change of group velocity with frequency. Here, we obtain the relation of each of these systematic errors with the variations of group velocity, amplitude spectrum, and initial phase with frequency. This is achieved by expanding (in the theory of MFT) wavenumber, amplitude spectrum, and initial phase by Taylor series and retaining some of the higher order terms. It has been seen that the above variations lead measured group velocity by MFT to the group velocity of neighboring frequency toward which amplitude spectrum is increasing. Based on the relations obtained, two methods by MFT are proposed for improved determinations of group velocity, and amplitude and phase spectra of dispersive waves. The methods are tested on a theoretical seismogram.