Open AccessInverse eigenvalue problems for the mantle — II
Author(s) -
Hald Ole H.
Publication year - 1983
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1983.tb02809.x
Subject(s) - discontinuity (linguistics) , eigenvalues and eigenvectors , inverse problem , inverse , overtone , mathematical analysis , inversion (geology) , mathematics , mantle (geology) , geophysics , geology , physics , geometry , seismology , quantum mechanics , tectonics , spectral line
Summary Suppose that the density at the Mohorovičić discontinuity and the mass below this discontinuity are fixed. If the density satisfies Adams‐Williamson's equation in the lower mantle then we can reconstruct the density in the upper mantle by using the velocities of the P‐ and S‐waves and the periods of the torsional modes with a fixed angular order. The numerical method is based on an algorithm for the inverse Sturm—Liouville problem. The calculations indicate that the inverse problem is stable and that the density is more accurately determined than the index of homogeneity. Only the periods with the lowest overtone number should be used in the inversion because of the uncertainty in the periods.