Surface wave tomography: Global membrane waves and adjoint methods

D. Peter*, C. Tape, L. Boschi, J. H. Woodhouse

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


We implement the wave equation on a spherical membrane, with a finite-difference algorithm that accounts for finite-frequency effects in the smooth-Earth approximation, and use the resulting 'membrane waves' as an analogue for surface wave propagation in the Earth. In this formulation, we derive fully numerical 2-D sensitivity kernels for phase anomaly measurements, and employ them in a preliminary tomographic application. To speed up the computation of kernels, so that it is practical to formulate the inverse problem also with respect to a laterally heterogeneous starting model, we calculate them via the adjoint method, based on backpropagation, and parallelize our software on a Linux cluster. Our method is a step forward from ray theory, as it surpasses the inherent infinite-frequency approximation. It differs from analytical Born theory in that it does not involve a far-field approximation, and accounts, in principle, for non-linear effects like multiple scattering and wave front healing. It is much cheaper than the more accurate, fully 3-D numerical solution of the Earth's equations of motion, which has not yet been applied to large-scale tomography. Our tomographic results and trade-off analysis are compatible with those found in the ray- and analytical-Born-theory approaches.

Original languageEnglish (US)
Pages (from-to)1098-1117
Number of pages20
JournalGeophysical Journal International
Issue number3
StatePublished - Dec 2007
Externally publishedYes


  • Adjoint methods
  • Born approximation
  • Membrane waves
  • Scattering theory
  • Seismic tomography
  • Surface waves

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


Dive into the research topics of 'Surface wave tomography: Global membrane waves and adjoint methods'. Together they form a unique fingerprint.

Cite this