Details
| Original language | English |
|---|---|
| Title of host publication | VII Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium |
| Pages | 199-204 |
| Number of pages | 6 |
| Publication status | Published - 2012 |
| Externally published | Yes |
| Event | 8th Hotine-Marussi Symposium on Mathematical Geodesy - Chania, Crete, Italy Duration: 6 Jul 2009 → 10 Jul 2009 |
Publication series
| Name | International Association of Geodesy Symposia |
|---|---|
| Volume | 137 |
| ISSN (Print) | 0939-9585 |
Abstract
The recovery of local (time-variable) gravity features from satellite-to-satellite tracking missions is one of the current challenges in Geodesy. Often, a global spherical harmonic analysis is used and the area of interest is selected later on. However, this approach has deficiencies since leakage and incomplete recovery of signal are common side effects. In order to make better use of the signal content, a gravity recovery using localizing base functions can be employed. In this paper, two different techniques are compared in a case study using simulated potential observations at satellite level - namely position-optimized radial base functions and a single layer representation using a piecewise continuous density. The first one is the more common approach. Several variants exist which mainly differ in the choice of the position of the base function and the regularization method. Here, the position of each base is subject to an adjustment process. On the other hand, the chosen radial base functions are developed as a series of Legendre functions which still have a global support although they decay rapidly. The more rigorous approach is to use base functions with a strictly finite support. One possible choice is a single layer representation whereas the density is discretized by basic shapes like triangles, rectangles, or higher order elements. Each type of shape has its own number of nodes. The higher the number of nodes of a particular element, the more complicated becomes the solution strategy but at the same time the regularity of the solution increases. Here, triangles are used for the comparison. As a result, the radial base functions in the employed variant allow a modeling with a minimum number of parameters but do not achieve the same level of approximation as the discretized single layer representation. The latter do so at the cost of a higher number of parameters and regularization. This case study offers an interesting comparison of a near localizing with a strictly localizing base function. However, results can currently not be generalized as other variants of the radial base functions might perform better. Also, the extension to a GRACE-type observable is desirable.
Keywords
- Radial base function, Regional gravity field recovery, Single layer representation
ASJC Scopus subject areas
- Earth and Planetary Sciences(all)
- Computers in Earth Sciences
- Earth and Planetary Sciences(all)
- Geophysics
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VII Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium. 2012. p. 199-204 (International Association of Geodesy Symposia; Vol. 137).
Research output: Chapter in book/report/conference proceeding › Conference contribution › Research › peer review
}
TY - GEN
T1 - On the Comparison of Radial Base Functions and Single Layer Density Representations in Local Gravity Field Modelling from Simulated Satellite Observations
AU - Weigelt, M.
AU - Keller, W.
AU - Antoni, M.
PY - 2012
Y1 - 2012
N2 - The recovery of local (time-variable) gravity features from satellite-to-satellite tracking missions is one of the current challenges in Geodesy. Often, a global spherical harmonic analysis is used and the area of interest is selected later on. However, this approach has deficiencies since leakage and incomplete recovery of signal are common side effects. In order to make better use of the signal content, a gravity recovery using localizing base functions can be employed. In this paper, two different techniques are compared in a case study using simulated potential observations at satellite level - namely position-optimized radial base functions and a single layer representation using a piecewise continuous density. The first one is the more common approach. Several variants exist which mainly differ in the choice of the position of the base function and the regularization method. Here, the position of each base is subject to an adjustment process. On the other hand, the chosen radial base functions are developed as a series of Legendre functions which still have a global support although they decay rapidly. The more rigorous approach is to use base functions with a strictly finite support. One possible choice is a single layer representation whereas the density is discretized by basic shapes like triangles, rectangles, or higher order elements. Each type of shape has its own number of nodes. The higher the number of nodes of a particular element, the more complicated becomes the solution strategy but at the same time the regularity of the solution increases. Here, triangles are used for the comparison. As a result, the radial base functions in the employed variant allow a modeling with a minimum number of parameters but do not achieve the same level of approximation as the discretized single layer representation. The latter do so at the cost of a higher number of parameters and regularization. This case study offers an interesting comparison of a near localizing with a strictly localizing base function. However, results can currently not be generalized as other variants of the radial base functions might perform better. Also, the extension to a GRACE-type observable is desirable.
AB - The recovery of local (time-variable) gravity features from satellite-to-satellite tracking missions is one of the current challenges in Geodesy. Often, a global spherical harmonic analysis is used and the area of interest is selected later on. However, this approach has deficiencies since leakage and incomplete recovery of signal are common side effects. In order to make better use of the signal content, a gravity recovery using localizing base functions can be employed. In this paper, two different techniques are compared in a case study using simulated potential observations at satellite level - namely position-optimized radial base functions and a single layer representation using a piecewise continuous density. The first one is the more common approach. Several variants exist which mainly differ in the choice of the position of the base function and the regularization method. Here, the position of each base is subject to an adjustment process. On the other hand, the chosen radial base functions are developed as a series of Legendre functions which still have a global support although they decay rapidly. The more rigorous approach is to use base functions with a strictly finite support. One possible choice is a single layer representation whereas the density is discretized by basic shapes like triangles, rectangles, or higher order elements. Each type of shape has its own number of nodes. The higher the number of nodes of a particular element, the more complicated becomes the solution strategy but at the same time the regularity of the solution increases. Here, triangles are used for the comparison. As a result, the radial base functions in the employed variant allow a modeling with a minimum number of parameters but do not achieve the same level of approximation as the discretized single layer representation. The latter do so at the cost of a higher number of parameters and regularization. This case study offers an interesting comparison of a near localizing with a strictly localizing base function. However, results can currently not be generalized as other variants of the radial base functions might perform better. Also, the extension to a GRACE-type observable is desirable.
KW - Radial base function
KW - Regional gravity field recovery
KW - Single layer representation
UR - http://www.scopus.com/inward/record.url?scp=84884399891&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-22078-4_29
DO - 10.1007/978-3-642-22078-4_29
M3 - Conference contribution
AN - SCOPUS:84884399891
SN - 9783642220777
T3 - International Association of Geodesy Symposia
SP - 199
EP - 204
BT - VII Hotine-Marussi Symposium on Mathematical Geodesy - Proceedings of the Symposium
T2 - 8th Hotine-Marussi Symposium on Mathematical Geodesy
Y2 - 6 July 2009 through 10 July 2009
ER -