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On the elimination of bias averaging-errors in proxy records
Beelaerts, V.; De Ridder, F.; Schmitz, N.; Bauwens, M.; Dehairs, F.; Schoukens, J.; Pintelon, R. (2009). On the elimination of bias averaging-errors in proxy records. Math. Geosc. 41(2): 129-144. dx.doi.org/10.1007/s11004-008-9193-1
In: Mathematical Geosciences. Springer: Dordrecht. ISSN 1874-8961, more
Peer reviewed article  

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Author keywords
    Averaging; Signal processing; Calibration; Environmental proxies

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Abstract
    Knowledge of and insight into past environmental conditions can be obtained by processing and analyzing proxies. The proxies need to be processed as precisely and accurately as possible, otherwise the conclusion of the analysis will be biased. A calibration method which reduces bias errors in the proxy measurements due to averaging is presented. Sampling with nonzero sample sizes causes an averaging of the true proxy signal over the volume of the sample. The method is applied on a linear synthetic record which results in an optimal correction for frequency components ranging from the dc-frequency (DC) to one half of the sample frequency (f s /2). Next, the method is tested on non-linear synthetic data where the signal is reconstructed reasonably well. Finally, the method is applied to a real vessel density record of R. mucronata from Makongeni, Kenya, and to a real delta deuterium record of ice core EDC from dome C, Antarctica. The method discussed in this paper is a valuable tool for the calibration of proxy measurements; it can be applied as a correction for low resolution measurements and expanded to other types of samples and proxies. Working with small sample sizes (high resolution) amounts to working near the detection limit, where the signal-to-noise-ratio is low. This correction method provides an alternative in which low resolution measurements can be upgraded to minimize the loss of information due to larger sample sizes.

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