Open AccessSpherical‐earth Fréchet sensitivity kernels
Author(s) -
NissenMeyer Tarje,
Dahlen F. A.,
Fournier Alexandre
Publication year - 2007
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2006.03123.x
Subject(s) - sensitivity (control systems) , magnetic monopole , moment (physics) , mathematical analysis , dipole , physics , quadrupole , tensor (intrinsic definition) , kernel (algebra) , diffraction , computation , geometry , mathematics , algorithm , classical mechanics , optics , electronic engineering , engineering , quantum mechanics , atomic physics , combinatorics
SUMMARY We outline a method that enables the efficient computation of exact Fréchet sensitivity kernels for a non‐gravitating 3‐D spherical earth model. The crux of the method is a 2‐D weak formulation for determining the 3‐D elastodynamic response of the earth model to both a moment‐tensor and a point‐force source. The sources are decomposed into their monopole, dipole and quadrupole constituents, with known azimuthal radiation patterns. The full 3‐D response and, therefore, the 3‐D waveform sensitivity kernel for an arbitrary source–receiver geometry, can be reconstructed from a series of six independent 2‐D solutions, which may be obtained using a spectral‐element or other mesh‐based numerical method on a 2‐D, planar, semicircular domain. This divide‐and‐conquer, 3‐D to 2‐D reduction strategy can be used to compute sensitivity kernels for any seismic phase, including grazing and diffracted waves, at relatively low computational cost.