A new isotropic covariance function on the sphere based on a self-convolving spherical cap
| العنوان: | A new isotropic covariance function on the sphere based on a self-convolving spherical cap |
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| المؤلفون: | Piretzidis, Dimitrios, Kotsakis, Christopher, Mertikas, Stelios P., Sideris, Michael G. |
| المصدر: | XXVIII General Assembly of the International Union of Geodesy and Geophysics (IUGG) |
| سنة النشر: | 2023 |
| الوصف: | Modeling the stochastic behavior of global-scale geophysical signals, such as the Earth’s external gravity field, requires the use of valid (i.e., positive-definite) covariance functions on the sphere. The construction of such functions is still a challenging task, especially when a compactly-supported (i.e., finite) covariance function is needed. A standard approach for deriving a positive definite function is by convolving any function with itself. Accounting for the convolution-multiplication duality, the spectrum of the resulting function is always positive, since it is equal to the multiplication of the spectrum of the self-convolving function with itself. The validity of the resulting function can therefore be easily established. In this study, we utilize this property and develop a new compactly-supported covariance function on the sphere based on the self-convolution of a spherical cap. The shape of this new covariance function resembles other models developed using the self-convolution property. Two representative examples are the spherical covariance function, which is based on the self-convolution of a two-dimensional ball, and the more generalized “Euclid’s hat” function, which is described by the self-convolution of an n-dimensional ball. Although the spatial representation of our newly-developed covariance function is given by a somewhat involved mathematical expression, its spectral representation is rather simple and only requires the calculation of spherical harmonic coefficients of a spherical cap. The latter are also known as Pellinen smoothing coefficients and are commonly evaluated by a well-known recurrence relation for local gravity field modeling applications. The 28th IUGG General Assembly (IUGG2023) (Berlin 2023) |
| اللغة: | English |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::021ebf978e2ad04a2628a9e09a7e6ccaTest https://gfzpublic.gfz-potsdam.de/pubman/item/item_5018758Test |
| حقوق: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....021ebf978e2ad04a2628a9e09a7e6cca |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |