Smith & Bailey (2017a) have criticized the methods applied for time series analysis in our study of a late Campanian chalk core in the North Sea (Perdiou et al. 2016). These critics rely essentially on two points: (1) the resolution spacing that can be applied to our gamma-ray data; (2) the use of the autoregressive order 1 (‘AR1’) noise model, which allows calculation of significance thresholds.
With respect to point (1), in their comment and re-analysis of our gamma-ray signal, Smith & Bailey recall our methods section where we correctly report that gamma-ray probes used by Schlumberger have a cone of influence of c. 40 cm, and therefore that gamma-ray values must be smoothed over a complex running mean over an interval between 40 and 60 cm, which alters the record of potential high-frequency Milankovitch cycles. Smith & Bailey rely on our assertion to justify that our gamma-ray data series based on 457 data points with an average vertical spacing of c. 15 cm should actually be re-interpolated at 45 cm (thus with a significant lower resolution) without any loss of spectral information. Then they calculate a new multi-taper method (MTM) periodogram based on this re-interpolated time series and claim that no frequency peaks appear as significant in the dataset. We profoundly disagree that the re-interpolation they apply does not result in a loss of spectral information. Indeed, a cone of influence of c. 40 cm for a probe does not mean that the gamma-ray values received from the measured rock in the alignment of the probe have equal power throughout the cone of influence. In fact, the term ‘cone’ describes with accuracy how the gamma-ray of the measured rock is integrated by the probe as shown on Figure 1. Although we could not find any proper technical description of the Schlumberger probe used at the time when gamma-ray was measured for the Adda-3 core, such probes are generally supplemented by a collimator, which narrows the cone of influence, ensuring maximal power of gamma-ray values in the alignment of the probe and rapidly decreasing power at lateral distances (Fig. 1). An example of the effect of a collimator has been given by Silva et al. (2006) for a gamma probe used in radioguided surgery. Figure 1a shows a theoretical power received by a probe with a collimator as a function of distance with a cone of influence of c. 40 cm. As shown in Figure 1b, when measurements are taken every 15 cm, the three cones of influence at t − 1, t and t + 1 overlap but the overlapping area between two consecutive measurements is 
50%, ensuring overall gamma-ray values that can potentially be significantly different between the three distinct measurements. Therefore, although the actual rock signal is smoothed by the probe over the width of the cone of influence, it is still valuable to have a narrow vertical spacing between two distinct measurements and it is erroneous to consider that a dataset with a spacing of 45 cm and 152 values should not differ from the actual dataset of 15 cm spacing and 457 values.
(a) Theoretical, 40 cm wide cone of influence for a gamma-ray probe with use of a collimator showing the power (in counts per seconds) as a function of the lateral distance from the probe. (b) Overlap between the cones of influence of three distinct measurements taken at 15 cm steps.
With respect to point (2), similar concerns by the same group of authors have been raised on multiple occasions for cyclostratigraphic studies of various sediment facies and ages (Bailey et al. 2009 on Kemp & Coe 2007; Smith & Bailey 2017b on Howe et al. 2016; Smith & Bailey 2017c on Andrews et al. 2016; Smith et al. 2016 on Fang et al. 2015; Smith & Bailey 2018 on Ruhl et al. 2016). In several of these comments, the same critics essentially point at the use of the AR1 noise model, nowadays commonly used in cyclostratigraphy as a suitable spectral ‘null’ model for climate processes (e.g. Gilman et al. 1963). This AR1 model allows calculation of significance thresholds (generally 99, 95 and 90%) above which spectral peaks of the analysed signal have a high probability of originating from nonrandom processes. Two in-depth and technically robust rebuttals to similar previous comments by the same authors (Smith et al. 2016; Smith & Bailey 2018) have recently been published by Hinnov et al. (2016) and Hinnov et al. (2018). Both rebuttals negate the concerns raised by Smith & Bailey on the use of the AR1 model. Similarly to Andrews et al. (2017), we consider that repetition of this debate is sterile. As recalled by Hinnov et al. (2016), citing Hays et al. (1977), ‘questions about orbital control of climate will be answered through the repetition of results rather than the outcome of a fiducial test’. Ages adopted for the Plio-Pleistocene timescale that originally derived from the astronomical calibration of Hilgen (1991) have remained nearly unchanged since then in the last generations of the geological timescales, apart from minor changes resulting from the adoption of different astronomical solutions over time. The age of the Cretaceous–Paleogene boundary derived from the Paleogene astronomical timescale now converges with the most recent radiometric datings (Westerhold et al. 2015; Renne et al. 2013, 2015; Dinarès-Turell et al. 2014; Schoene et al. 2015). A recent Late Cretaceous astronomical calibration in chalk deposits of southern England appears to match radiometric anchors of the Coniacian–Santonian and Santonian–Campanian boundaries in the Western Interior (Thibault et al. 2016). In a similar fashion, astronomical controls derived from cyclostratigraphic studies of the Paleozoic and Mesozoic will be confirmed only through the repetition of results on multiple deep-sea sites and sections, and through inter-calibration with radiometric dating, rather than through debates on the accurate use of AR1 and subsequent statistical significance of power spectra frequency peaks.
Scientific editing by Stuart Jones
- © 2018 The Author(s)
References
Reply to the discussion on ‘Orbital calibration of the late Campanian carbon isotope event in the North Sea’, Journal of the Geological Society, London, 173, 504–517
