On the analysis of physical wave trains

When a wave train whose constituent frequencies and wave numbers are unresolved by observation propagates through an inhomogeneous medium, beating between the components can contaminate deductions one might naively draw about the inhomogeneous background. This is a severe problem to anyone confronted with analysing helioseismic data with a view to determining the structure of giant convective cells. We propose a procedure for analysing wave trains, based on approximating a packet as a single representative pure wave. We present some preliminary results of analysing artificial data. For simplicity, we have deliberately excluded some of the effects of wave interference, which must be faced by any means of analysis. Therefore we do not claim to have found a complete procedure for analysing real data.