Open AccessA variational approach to whole‐Earth dynamics
Author(s) -
Johnson I. M.,
Smylie D. E.
Publication year - 1977
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.1977.tb01323.x
Subject(s) - classical mechanics , coupling (piping) , physics , hermite polynomials , displacement (psychology) , piecewise , oscillation (cell signaling) , computation , inertial frame of reference , mathematical analysis , mechanics , mathematics , quantum mechanics , algorithm , mechanical engineering , psychology , biology , engineering , psychotherapist , genetics
Summary A variational approach to whole‐Earth dynamics is formulated and implemented with piecewise Hermite cubic splines as trial functions. A fast computational algorithm is developed which allows rotational Coriolis coupling to be taken fully into account for the first time. The method can be generalized to include ellipticity and centrifugal coupling, making the full Earth oscillation problem tractable in a single calculation. This permits the investigation of free elastic modes, fluid core inertial modes and undertone modes associated with any stable regions of the outer core, as well as modes involving wobble, fluctuations in spin rate and displacement of the solid inner core. The present paper expounds the method and illustrafes its application to the computation of undertone modes previously estimated by direct integration of the equations of motion.