Summation of the Born series for the normal modes of the Earth

Jeroen Tromp, F. A. Dahlen

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We derive an explicit formula for the response of a laterally heterogeneous, self‐gravitating, rotating, dissipative, and physically dispersive earth to an earthquake. The long‐period spectrum at a single station is given by u(ω) =RH0 [V(ω) +ωW−ω2T]−1·S0(ω) where R0 and S0(ω) are the unperturbed source and receiver vectors and H denotes the Hermitian transpose. The quantities V(ω), W, and T are the potential energy, Coriolis, and relative kinetic energy matrices, and V(ω) +ωW−ω2T is the Lagrangian matrix whose eigenvalues are the perturbed complex eigenfrequencies. This simple result is obtained by formal summation of the Born series.

Original languageEnglish (US)
Pages (from-to)527-533
Number of pages7
JournalGeophysical Journal International
Issue number3
StatePublished - Mar 1990

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Geochemistry and Petrology


  • Born approximation
  • free oscillations
  • lateral heterogeneity
  • normal modes
  • synthetic seismograms


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