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#### A minimal cost function method for optimizing the age‐depth relation of deep‐sea sediment cores

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Paleoceanography-1992-Brueggemann.pdf

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##### Citation

Brueggemann, W. (1992). A minimal cost function method for optimizing the age‐depth
relation of deep‐sea sediment cores.* Paleoceanography,* *7*,
467-487. doi:10.1029/92PA01235.

Cite as: http://hdl.handle.net/21.11116/0000-0001-2BDD-7

##### Abstract

The question of an optimal age-depth relation for deep-sea sediment cores has been raised frequently. The data from such cores (e. g., delta O-18 values) are used to test the astronomical theory of ice ages as established by Milankovitch in 1938. In this work, we use a, minimal cost function approach to find simultaneously an optimal age-depth relation and a linear model that optimally links solar insolation or other model input with global ice volume. Thus a genera. tool for the calibration of deep-sea cores to arbitrary tuning targets is presented. In this inverse modeling type approach, an objective function is minimized that penalizes: (1) the deviation of the data. from the theoretical linear model (whose transfer function can be computed analytically for a given age-depth relation) and (2) the violation of a set of plausible assumptions about the model, the data and the obtained correction of a first guess age-depth function. These assmnptions have been suggested before but are now quantified and incorporated explicitly into the objective function as penalty terms. We formulate an optimization problem that is solved numerically by conjugate gradient type methods. Using this direct. approach, we obtain high coherences in the Milankovitch frequency bands (over 90%). Not only the data time series but also the the derived correction to a first guess linear age-depth function (and therefore the sedimentation rate) itself contains significant energy in a broad frequency band around 100 kyr. The use of a sedimentation rate which varies continuously on ice age time scales results in a shift of energy from 100 kyr in the original data spectrum to 41, 23, and 19 kyr in the spectrum of the corrected data. However, a. large proportion of the data variance remains unexplained, particularly in the 100 kyr frequency band, where there is no significant input by orbital forcing. The presented method is applied to a real sediment core and to the SPECMAP stack, and results are compared with those obtained in earlier investigations.