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| Titel |
Vector-valued spherical Slepian functions for lithospheric-field analysis |
| VerfasserIn |
A. Plattner, F. J. Simons |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250064655
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| Zusammenfassung |
| One of the mission objectives of Swarm is to resolve and model the lithospheric magnetic
field with maximal resolution and accuracy, even in the presence of contaminating signals
from secondary sources. In addition, and more generally, lithospheric-field data analysis will
have to successfully merge information from the global to the regional scale. In
the past decade or so, a variety of global-to-regional modeling techniques have
come of age that have, however, been met with mixed feelings by the geomagnetics
community. In particular, the theory of scalar Slepian functions has been developed for
applications mostly in geodesy, but support from within geomagnetism has been
tepid. In the Proceedings of the First Swarm International Science Meeting, now six
years ago, it was written with reference to Slepian localization analysis that these
methods are theoretically powerful but still need to find their way from the applied
mathematician’s desk to the geophysicist practitioners’. In the intervening six years
"these methods" have done just that, and thereby enjoyed much use in a variety of
fields: but the root cause of their slow adoption for lithospheric-field analysis had
not been remediated. To this date, only the theory of scalar Slepian functions on
the sphere has been completely worked out. In this contribution we report on the
development, at last, of a complete vectorial spherical Slepian basis, suited for applications
specifically of geomagnetic data analysis, representation, and model inversion. We
have designed a basis of vector functions on the sphere that are simultaneously
bandlimited to a chosen maximum spherical harmonic degree, while optimally
focused on an arbitrarily shaped region of interest. The construction of these bases
of vector functions is achieved by solving Slepian’s spatiospectral optimization
problem in the vector case, as has been done before for scalar functions on the sphere.
Scalar Slepian functions have proven to be very useful in fields as wide as geodesy,
geomagnetism, gravimetry, geodynamics, biomedical science, planetary science and
cosmology. We expect the same benefits from our newly designed vector Slepian bases
for example in the inversion for crustal magnetization. In this presentation, we
discuss our construction in detail, including a treatment of numerical efficiency for a
variety of specific scenarios, and discuss the first examples of fully vectorial-field
representation and approximation tailored to problems in lithospheric-field analysis. |
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