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Vol. 60, n.3, September 2019
pp. 457-474

On the relations between signal spectral range and noise variance in least-squares collocation and simple kriging: example of gravity reduced by EGM2008 signal

W. Jarmolowski

Received: 24 April 2018; accepted: 23 December 2018

Abstract

The study investigates the problem of uncorrelated noise variance in least-squares spatial prediction of geophysical phenomena. This issue is commonly solved by the regularisation or variance-component estimation, however, the attempts at physical explanations of the issue are scarce or very cautious. In this study, an equivalent procedure to the regularisation is performed numerically, but the meaning of noise variance level is explained, and the source of the noise is more carefully examined. The presented numerical test uses spatial prediction technique i.e. least-squares collocation and reveals its relationships with the spectral signal properties. The numerical test is based on terrestrial Bouguer anomalies, which have a large variance at higher signal frequencies, i.e. their power spectral density decreases slowly when the spatial resolution increases. The same quantity is calculated from the EGM2008 model using various maximum degrees of the harmonic expansion. The different degrees of applied harmonics remove some spectral part of the signal from the data, which leads to the observations of the suspected relation of the estimated values of noise variance with medium and high-frequency signal parts. The observed statistical quantities prove that the noise has some relations with signal spectral range and data spatial resolution. The paper provides a relevant proof that the noise is not solely dependent on the survey error and introduces some physical interpretations of the regularisation requirement.



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