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I present a matched-wave asymptotic analysis of the driving of solaroscillations by a general localised source. The analysis provides a simplemathematical description of the asymmetric peaks in the power spectrum in termsof the relative locations of eigenmodes and troughs in the spectral response.It is suggested that the difference in measured phase function between themodes and the troughs in the spectrum will provide a key diagnostic of thesource of the oscillations. I also suggest a form for the asymmetric lineprofiles to be used in the fitting of solar power spectra.  Finally I present a comparison between the numerical and asymptoticdescriptions of the oscillations. The numerical results bear out thequalitative features suggested by the asymptotic analysis but suggest thatnumerical calculations of the locations of the troughs will be necessary for aquantitative comparison with the observations.Comment: 18 pages + 8 separate figures. To appear in Ap

Peaks and Troughs in Helioseismology: The Power Spectrum of Solar Oscillations