Reservoir Offset Models for Radiocarbon Calibration

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Abstract
The purpose of a reservoir offset is to enable the application of calibration data (μ(θ), e.g. Stuiver et al. 1998) developed for one reservoir (primary reservoir) to CRAs from another (secondary reservoir), for example the use of a hemispheric offset for terrestrial samples (Barbetti et al. 1995; McCormac et al. 1998; Sparks et al. 1995; Vogel et al. 1986, 1993). The usual approach has been to define the activity of the secondary reservoir as some form of constant offset (with error) from the primary reservoir (e.g. Higham and Hogg 1985; McFadgen and Manning 1990). In this case, all CRAs from a secondary reservoir are given the same offset. The value of this common offset is not known exactly, but any uncertainty in the measured value of the offset corresponds to uncertainty in the common offset for all CRAs. However, the standard procedure for incorporating offset error into CRAs incorrectly allows a different offset for each CRA. The offset for each CRA is incorrectly allowed to vary by the measurement error reported for the offset value. Technically, the offset is incorrectly treated as varying independently from one CRA to the next, when in fact it is a single parameter for the secondary reservoir in question. In light of this, the calibrated date distributions will be incorrect for CRAs where an offset has been applied and the standard approach to offset error treatment has been used. In many cases, the differences between correct and incorrect calibrated date distributions will be insignificant. However, in some cases significant differences may arise and other approaches to treating the error associated with offsets need to be adopted.