Mathematics – Logic
Scientific paper
Dec 1984
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984sses.nasa...49g&link_type=abstract
In JPL Solar Seismology from Space. p 49-78 (SEE N85-25060 14-92)
Mathematics
Logic
7
Equilibrium Equations, Helioseismology, Mathematical Models, Solar Oscillations, Stellar Structure, Eigenvalues, Equations Of State, Series Expansion, Sun, Vibration, Weighting Functions
Scientific paper
Helioseismological inversion, as with the inversion of any other data, is divided into three phases. The first is the solution of the so-called forward problem: namely, the calculation of the eigenfrequencies of a theoretical equilibrium state. The second is an attempt to understand the results, either empirically by determining how those frequencies vary as chosen parameters defining the equilibrium model are varied, or analytically from asymptotic expansions in limiting cases of high order or degree. The third phase is to pose and solve an inverse problem, which seeks to find a plausible equilibrium model of the Sun whose eigenfrequencies are consistent with observation. The three phases are briefly discussed in this review, and the third, which is not yet widely used in helioseismology, is illustrated with some selected inversions of artificial solar data.
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