## Abstract

In Paper I of this series we developed a generalized normal-mode formalism for computing the response of an aspherical, self-gravitating, linear viscoelastic earth model to a surface load. In the present article we introduce an expansion for the normal modes of an aspherical earth model, using as basis functions the normal modes of a spherically symmetric reference model. This expansion leads to a non-linear eigenvalue problem for the expansion coefficients and decay rates. We develop a linearization of this problem using perturbation theory, which incorporates arbitrary levels of coupling between normal-mode multiplets. As an illustration, we consider the special case of radial perturbations to a spherically symmetric model, and compare predictions based upon perturbation theory with those based upon the usual non-perturbative forward theory. We demonstrate that including overtone coupling is necessary for the accurate prediction of perturbations to the normal-mode decay times and eigenfunctions. These calculations suggest that our theory can accurately accommodate order of magnitude lateral variations in mantle viscosity and significant changes in lithospheric thickness.

Original language | English (US) |
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Pages (from-to) | 425-441 |

Number of pages | 17 |

Journal | Geophysical Journal International |

Volume | 140 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2000 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Geophysics
- Geochemistry and Petrology

## Keywords

- Glacial rebound
- Lateral heterogeneity
- Mantle viscosity
- Normal modes
- Viscoelasticity