Open AccessThe effect of data windows on the estimation of free oscillation parameters
Author(s) -
Dahlenb F. A.
Publication year - 1982
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1982.tb04964.x
Subject(s) - amplitude , oscillation (cell signaling) , window (computing) , mode (computer interface) , term (time) , mathematics , variance (accounting) , computational physics , statistics , geology , geodesy , optics , physics , computer science , chemistry , biochemistry , accounting , quantum mechanics , business , operating system
Summary In seeking to estimate the frequencies, decay rates, amplitudes and phases of the free oscillations of the Earth using observed seismic spectra, data windows are required to reduce the effects of mode—mode interference. Formal expressions for the variances and covariances of these estimated parameters are derived here, for the case of a single isolated mode and an arbitrary data window. Explicit results are given for a Hann and Blackman—Harris minimum four‐term window as well as for a boxcar. The optimum or minimum variance record length for measuring frequencies and decay rates using a Hann window is 1.1 Q ‐cycles, and that for determining amplitudes and phases is 0.5 Q ‐cycles.