Combination of integral transforms by spectral weighting – an overview   Article Swipe
Martin Pitoňák
,
Michal Šprlák
,
Pavel Novák
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.5194/egusphere-egu22-9610
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.5194/egusphere-egu22-9610
<p>Geodetic boundary-value problems (BVPs) and their solutions represent an important tool for describing and modelling potential fields such as the Earth’s gravitational field. Solutions to spherical geodetic BVPs lead to spherical harmonic series or surface convolution integrals with Green’s kernel functions. New BVPs have recently been formulated reflecting development of sensors. BVPs have been also developed for observables measured by kinematic sensors on moving platforms, i.e., airplanes and satellites. Solutions to BVPs for higher-order derivatives of the gravitational potential as boundary conditions are represented by multiple integral transforms. For example, solutions to gravimetric, gradiometric and gravitational curvature BVPs are represented by two, three and four integral transforms, respectively. Theoretically, each of the nine transforms provides an identical value of the gravitational potential, but practically, when discrete noisy observations are exploited, they provide different estimates. Combination of solutions to the above mentioned geodetic BVPs in terms of surface integrals with Green’s kernel functions by a spectral method is investigated in this contribution. It is assumed that the first-, second- and third-order directional derivatives of the Earth’s gravitational potential can be measured at the satellite altitude. They are downward continued to the Earth’s surface and converted into height anomalies. Thus, the spectral combination method serves in our numerical procedure also as the downward continuation technique. The spectral combination method requires deriving corresponding spectral weights for all nine estimators. A generalized formula for evaluation of spectral weights for the estimators is formulated. Properties of spectral combinations are investigated in both spatial and spectral domains.</p>
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- en
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- https://doi.org/10.5194/egusphere-egu22-9610
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https://openalex.org/W4220725096Canonical identifier for this work in OpenAlex
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https://doi.org/10.5194/egusphere-egu22-9610Digital Object Identifier
- Title
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Combination of integral transforms by spectral weighting – an overview  Work title
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preprintOpenAlex work type
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enPrimary language
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2022Year of publication
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2022-03-28Full publication date if available
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Martin Pitoňák, Michal Šprlák, Pavel NovákList of authors in order
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https://doi.org/10.5194/egusphere-egu22-9610Publisher landing page
- Open access
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YesWhether a free full text is available
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goldOpen access status per OpenAlex
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https://doi.org/10.5194/egusphere-egu22-9610Direct OA link when available
- Concepts
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Gravitational field, Mathematical analysis, Mathematics, Kernel (algebra), Boundary value problem, Applied mathematics, Physics, Classical mechanics, Pure mathematicsTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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