Surface loading of a viscoelastic earth-I. General theory

Jeroen Tromp, Jerry X. Mitrovica

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54 Scopus citations


We present a new normal-mode formalism for computing the response of an aspherical, self-gravitating, linear viscoelastic earth model to an arbitrary surface load. The formalism makes use of recent advances in the theory of the Earth's free oscillations, and is based upon an eigenfunction expansion methodology, rather than the traditional Love-number approach to surface-loading problems. We introduce a surface-load representation theorem analogous to Betti's reciprocity relation in seismology. Taking advantage of this theorem and the biorthogonality of the viscoelastic modes, we determine the complete response to a surface load in the form of a Green's function. We also demonstrate that each viscoelastic mode has its own unique energy partitioning, which can be used to characterize it. In subsequent papers, we apply the theory to spherically symmetric and aspherical earth models.

Original languageEnglish (US)
Pages (from-to)847-855
Number of pages9
JournalGeophysical Journal International
Issue number3
StatePublished - Jun 1999

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Geochemistry and Petrology


  • Glacial rebound
  • Mantle viscosity
  • Normal modes
  • Viscoelasticity


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