  A method is derived for the quantitative analysis of signals that are
composed of superpositions of isolated, time-localized "events". Here these
events are taken to be well represented as rescaled and phase-rotated versions
of generalized Morse wavelets, a broad family of continuous analytic functions.
Analyzing a signal composed of replicates of such a function using another
Morse wavelet allows one to directly estimate the properties of events from the
values of the wavelet transform at its own maxima. The distribution of events
in general power-law noise is determined in order to establish significance
based on an expected false detection rate. Finally, an expression for an
event's "region of influence" within the wavelet transform permits the
formation of a criterion for rejecting spurious maxima due to numerical
artifacts or other unsuitable events. Signals can then be reconstructed based
on a small number of isolated points on the time/scale plane. This method,
termed element analysis, is applied to the identification of long-lived eddy
structures in ocean currents as observed by along-track measurements of sea
surface elevation from satellite altimetry
