Multiplet - multiplet coupling due to lateral heterogeneity : asymptotic effects on the amplitude and frequency of the Earth ’ s normal modes

We show that, to order zero, these coupling terms introduce a small shift in epicentral distance into the expression for the long period seismogram obtained by normal mode summation. This shift depends on the difference between the great circle and the minor arc averages of the local frequency. The coupling terms thus permit us to reconcile results obtained by normalmode summation and by a propagating wave approach, as far as the dependence on structure of the phase of surface waves is concerned. To order 1 / 1 , the coupling terms result in a perturbation in the amplitude of the mode considered, which depends on spatial derivatives of the local frequency and thus on the structure in the vicinity of the s.ource station great circle path. We show that this term is equivalent to that which is found using ray perturbation methods for propagating surface waves. We compare and discuss the assumptions underlying both approaches and illustrate, by an example, the potential of the asymptotic normal-mode formulation for improved modelling of lateral heterogeneity in the earth. (I, 1).