Finite-frequency sensitivity of body waves to anisotropy based upon adjoint methods

Anne Sieminski, Qinya Liu, Jeannot Trampert, Jeroen Tromp

Research output: Contribution to journalArticlepeer-review

51 Scopus citations


We investigate the sensitivity of finite-frequency body-wave observables to mantle anisotropy based upon kernels calculated by combining adjoint methods and spectral-element modelling of seismic wave propagation. Anisotropy is described by 21 density-normalized elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. In a 1-D reference model, body-wave sensitivity to anisotropy is characterized by 'banana-doughnut' kernels which exhibit large, path-dependent variations and even sign changes. P-wave traveltimes appear much more sensitive to certain azimuthally anisotropic parameters than to the usual isotropic parameters, suggesting that isotropic P-wave tomography could be significantly biased by coherent anisotropic structures, such as slabs. Because of shear-wave splitting, the common cross-correlation traveltime anomaly is not an appropriate observable for S waves propagating in anisotropic media. We propose two new observables for shear waves. The first observable is a generalized cross-correlation traveltime anomaly, and the second a generalized 'splitting intensity'. Like P waves, S waves analysed based upon these observables are generally sensitive to a large number of the 21 anisotropic parameters and show significant path-dependent variations. The specific path-geometry of SKS waves results in favourable properties for imaging based upon the splitting intensity, because it is sensitive to a smaller number of anisotropic parameters, and the region which is sampled is mainly limited to the upper mantle beneath the receiver.

Original languageEnglish (US)
Pages (from-to)368-389
Number of pages22
JournalGeophysical Journal International
Issue number1
StatePublished - Oct 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geophysics
  • Geochemistry and Petrology


  • Adjoint methods
  • Body waves
  • Fréchet derivatives
  • Seismic anisotropy
  • Sensitivity
  • Shear-wave splitting


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