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Aims. To describe the theory of surface layer independent model fitting byphase matching and to apply this to the stars HD49933 observed by CoRoT, andHD177153 (aka Perky), observed by Kepler Methods. We use theoretical analysis,phase shifts, and model fitting. Results. We define the inner and outer phaseshifts of a frequency set of a model star and show that the outer phase shiftsare (almost) independent of degree $\ell$, and that a function of the innerphase shifts (the phase function) collapses to an $\ell$ independent functionof frequency in the outer layers. We then show how to use this result in amodel fitting technique to find a best fit model to an observed frequency setby calculating the inner phase shifts of a model using the observed frequenciesand determining the extent to which the phase function collapses to a singlefunction of frequency in the outer layers. We give two examples applying thistechnique to the frequency sets of HD49933 observed by CoRoT and HD177153 (akaPerky) observed by Kepler, and compare our results with those of previousstudies and show that they are compatible with those obtained using differenttechniques. We show that there can be many different models that fit the datawithin the errors and that better precision on the frequencies is needed todiscriminate between the models. We compare this technique to that using theratios of small to large separations, showing that in principle it is moreaccurate and avoids the problem of correlated errors in separation ratiofitting.

Surface layer independent model fitting by phase matching: theory and application to HD49933 an HD177153 (aka Perky)