Open AccessImproved resolution of complex eigenfrequencies in analytically continued seismic spectra
Author(s) -
Buland Ray,
Gilbert Freeman
Publication year - 1978
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.1978.tb04243.x
Subject(s) - spectrum (functional analysis) , fourier transform , amplitude , function (biology) , zero (linguistics) , transient (computer programming) , resolution (logic) , mathematical analysis , spectral line , frequency spectrum , event (particle physics) , physics , mathematics , computational physics , optics , computer science , quantum mechanics , linguistics , philosophy , evolutionary biology , artificial intelligence , spectrum analyzer , biology , operating system
Summary. The response of the Earth to an earthquake is a transient that is effectively zero several days after the event. A recording of the event, of finite duration in time, has a Fourier spectrum that is an entire, or integral, analytic function of frequency. We present a very simple procedure for computing the Fourier spectrum as a function of complex frequency; the analytically continued spectrum. By investigating the properties of the analytically continued spectrum we show how to extract high‐ Q modes, how to estimate Q either from the amplitude or from the width of a resonance function, and how to improve the resolution of splitting to the theoretical maximum. Examples of these procedures, using observed data, are presented.