A uniformly valid asymptotic representation of normal mode multiplet spectra on a laterally heterogeneous Earth

Abstract

Summary. A new asymptotic formula is obtained for the spectrum of an isolated normal mode multiplet nSl or nTl, with n≪l, on a laterally heterogeneous Earth. The principal feature of this formula is that it is uniformly valid on the Earth's surface, including near the epicentre and its antipode. The formal conditions for its validity are that |δm/m0|≪ 1 and smax≪l≪smin|δm/m0|–1, where |δm/m0| is the relative magnitude of the lateral heterogeneity, and smin and smax are the minimum and maximum significant degrees in its spherical harmonic expansion. As well as providing a basis for the geographical interpretation of near‐epicentral or near‐antipodal long‐period recordings, the new formula also unifies the asymptotic theory and adds insight into the phenomena which govern the details of multiplet spectra in general. Copyright © 1980, Wiley Blackwell. All rights reserved