Developments in the implementation and use of least-squares collocation

TY - GEN

T1 - Developments in the implementation and use of least-squares collocation

AU - Tscherning, Carl Christian

PY - 2015

Y1 - 2015

N2 - The method of Least-Squares Collocation (LSC) was developed in the 1960s based on theoretical advances by T. Krarup and H. Moritz. The method may be used for the determination of approximations to the anomalous gravity potential (T) and associated parameters like biases or tilts. All gravity field observabels which may be related to T through a linear functional may be predicted and error-estimates computed. The method has primarily been used in local or regional applications, due to the fact that a system of equations with as many unknowns as the number of observations need to be established and solved. The problem has been solved due to the use of multiprocessing in the current GRAVSOFT implementation of GEOCOL. The method has been implemented using isotropic reproducing kernels fitted to empirical covariance functions. The Kernels are harmonic outside a so-called Bjerhammar-sphere, which must be inside the volume bounded by the location of the used data. This problem has been overcome by initially lifting the data in Polar areas 20 km, thereby enabling global LSC solutions in the form of spherical harmonic expansions. The theoretical possibility of computing error-estimates does not give good results due to the isotropy of the kernels used. The error estimates primarily shows where good data are located or where data are missing. However due to the advent of global gravity gradients from the ESA Gravity and Ocean Circulation Explorer (GOCE) mission it is possible to compute nearly everywhere local signal variances which can be used to tune the otherwise uniform estimates.

AB - The method of Least-Squares Collocation (LSC) was developed in the 1960s based on theoretical advances by T. Krarup and H. Moritz. The method may be used for the determination of approximations to the anomalous gravity potential (T) and associated parameters like biases or tilts. All gravity field observabels which may be related to T through a linear functional may be predicted and error-estimates computed. The method has primarily been used in local or regional applications, due to the fact that a system of equations with as many unknowns as the number of observations need to be established and solved. The problem has been solved due to the use of multiprocessing in the current GRAVSOFT implementation of GEOCOL. The method has been implemented using isotropic reproducing kernels fitted to empirical covariance functions. The Kernels are harmonic outside a so-called Bjerhammar-sphere, which must be inside the volume bounded by the location of the used data. This problem has been overcome by initially lifting the data in Polar areas 20 km, thereby enabling global LSC solutions in the form of spherical harmonic expansions. The theoretical possibility of computing error-estimates does not give good results due to the isotropy of the kernels used. The error estimates primarily shows where good data are located or where data are missing. However due to the advent of global gravity gradients from the ESA Gravity and Ocean Circulation Explorer (GOCE) mission it is possible to compute nearly everywhere local signal variances which can be used to tune the otherwise uniform estimates.

KW - Error-estimates

KW - GEOCOL program

KW - Gravity

KW - GRAVSOFT package

KW - Least-squares collocation

KW - Reproducing kernels

U2 - 10.1007/1345_2015_54

DO - 10.1007/1345_2015_54

M3 - Article in proceedings

AN - SCOPUS:84984876260

SN - 9783319246031

SP - 199

EP - 204

BT - IAG 150 Years - Proceedings of the 2013 IAG Scientific Assembly

PB - Springer

T2 - 150th Anniversary with a Scientific Assembly, IAG 2013

Y2 - 2 September 2013 through 6 September 2013

ER -