Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009agufmsh13a1509s&link_type=abstract
American Geophysical Union, Fall Meeting 2009, abstract #SH13A-1509
Astronomy and Astrophysics
Astrophysics
[3200] Mathematical Geophysics, [7260] Seismology / Theory, [7522] Solar Physics, Astrophysics, And Astronomy / Helioseismology
Scientific paper
Fréchet kernels, an emerging tool in helioseismic data analysis, describe the first-order (linear) relationship between medium properties affecting helioseismic wave propagation and measured wave traveltimes. Although many treatments of these kernels exist in the literature, we believe a need exists to provide a consistent, systematic method of deriving them. We present an approach using some basic tools and concepts of functional analysis, such as functional derivatives and functional Taylor series. Although no fundamentally new results are obtained from this approach, it clarifies the approximations used and provides a nice organizing principle for the theory. In addition to the theoretical apparatus, we also provide general formulas for any desired medium property that can affect helioseismic wave propagation. We also supply specific formulas for some properties, such as wave speed and density, and calculate some sample kernels.
Kosovichev Aleksandr G.
Schlottmann R.
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