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Previous studies of deep-sea sediment cores have found evidence for Milankovitch cycles, climatic cyclicity due to the periodicity of the Earth's orbital parameters. Many of the cores recovered on Leg 114 of the Ocean Drilling Program showed outward signs of cyclicity, especially at Site 704. We have analyzed the GRAPE density, carbonate content, and magnetic susceptibility using both standard and nonstandard spectral analysis techniques. One of the nonstandard techniques used was the Lomb-Scargle spectral estimation method, which is designed for unequally spaced data and which yields as part of the process the statistical significance of any observed spectral peaks. Pairs of spectra were compared for statistical similarity using the Kolmogorov-Smirnov method. All of the data sets contain some spectral peaks, including both the expected Milankovitch cycles as well as other peaks. Upon further investigation, we have found that the other peaks could be explained as the nonlinear climate system response to the Milankovitch orbital forcing functions, because the extra peaks appear to be simple linear combinations, harmonics and subharmonics of the Milankovitch peaks. At Site 704, there is a marked change in the response at the Brunhes/Matuyama boundary (0.73 Ma B.P.) from strong long-period cyclicity in the Brunhes to more prevalent shorter period cyclicity in the Matuyama. INTRODUCTION The hydrosphere of the Earth is complex and inherently nonlinear. The Navier-Stokes equations and the associated thermodynamic equations form a coupled highly nonlinear set of governing equations for atmospheric and oceanic flow. The climate of the Earth represents a long-term average of the parameters of the nonlinear system and thus should also exhibit nonlinearity. Nonetheless, numerous researchers have sought simple (linear) mechanisms to explain major climatic variations. The most prominent such mechanism recently proposed for driving climatic variations has been the effect of the periodicity in the Earth's orbital parameters, Milankovitch cycles (see, for example, Berger et al., 1984). The analysis of deep-sea drill core and logging data has naturally expanded to include spectral analysis for the purposes of identifying Milankovitch cycle peaks, and numerous papers have found evidence for such peaks (see Berger et al. 1984; Ruddiman et al., 1986). In many cases extraneous peaks have been found, for example, by Pestiaux and Berger (1984) and Ruddiman et al., (1986). Figure 1 (from Borehole Research Group, 1986) shows results from Ocean Drilling Program (ODP) Site 646; Milankovitch peaks are identified at 19,000-23,000, 41,000, 95,000, and 410,000 yr. The presence of other peaks, however, can be explained as linear combinations of the main peaks. We 1 Ciesielski, P. F., Kristoffersen, Y., et al., 1991. Proc. ODP, Sci. Results, 114: College Station, TX (Ocean Drilling Program). 2 Department of Earth Sciences, Department of Physics, and Quaternary Sciences Institute, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. 3 Department of Physics and Quaternary Sciences Institute, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. GEOMAR, Forschungszentrum der Christian-Albrechts-Universitàt zu Kiel D-2300 Kiel, FRG. Alfred Wegener Institut für Polar und Meeresforschung, Postfach 120161, D-2850 Bremerhaven (Present address: Université de Nantes, Laboratoire de Sédimentologie Sciences de la Terre, 2 Rue de la Houssiniere, 44072 Nantes Cedex, France). believe that these extraneous peaks are evidence for the nonlinear nature, of the climatic system (Bloomer and Nobes, 1989; Bloomer, 1989). The prominent spectral power at 100,000 yr found in most ocean core and logging data spectra is another compelling piece of evidence for the nonlinear nature of climatic response. Because there is no primary power at the eccentricity (100,000 yr) cycle in the expansions of theoretical solar insolation (the eccentricity term acts only to modulate the precessional cycles), the high power in paleoclimatic spectra associated with the 100,000-yr cycle has been attributed to the effect of ice sheets (Pollard, 1982; Le Treut and Ghü, 1983) or some other nonlinear mechanism. To demonstrate how 100,000-yr power can arise in paleoclimatic spectra, Wigley (1976) considered an amplitudemodulated periodic signal of the form F(t) = ßsin{2f2i))sin{2fλt), (1) where fλ is the frequency of the basic signal and f2 is the modulator frequency. This is analogous to the insolation signal, where the 100,000-yr cycle acts as a modulator of the precessional cycles at 23,000 and 19,000 yr. In the plot of F(i) in Figure 2A,/i = 1/20,000 cycles/yr,/2 = 1/100,000 cycles/yr, and ß = 0.4. Spectral analysis of this signal yields a major peak at/i, minor peaks/j ± f2 (16,000 and 25,000 yr), and no peak at the modulator frequency, f2 (Fig. 2B). If the output is related to the input by the simple nonlinear response model Z{t) = (F(t)), (2) the spectrum of Z(i) has a dominant peak at the modulator frequency, with a series of peaks centered at 2/t (10,000 yr) and a peak at 2/2 (50,000 yr) (Fig. 2C). This demonstrates how primary output power can arise from relatively minor input power and how combination tones can arise. We have analyzed data from sediment cores of Quaternary age recovered on ODP Leg 114. The Leg 114 sites form a transect across the South Atlantic (Figs. 3 and 4; Shipboard

Milankovitch Cycles and Nonlinear Response in the Quaternary Record in the Atlantic Sector of the Southern Oceans