MIDDLE EAST GEOLOGIC TIME SCALE 2013: Antarctica′s glacio-eustatic signature in the Aptian and late Miocene– Holocene: Implications for what drives sequence stratigraphy

The Middle East Geologic Time Scale was launched in 2008 with the objective of correlating transgressive-regressive (T-R) depositional sequences across the Arabian Plate (Al-Husseini, 2008). In this ongoing project precedence is given to those sequences that have been extensively documented and are important for understanding the petroleum systems of the Middle East. This objective could not be achieved for the hydrocarbon-bearing Lower Cretaceous Aptian sequences of the Shu’aiba and equivalent formations, mainly because the lowermost Aptian and most of the Upper Aptian rocks are not represented in many parts of the Arabian Plate (see review in Sharland et al., 2001; van Buchem et al., 2002). Another reason was that where the Aptian rocks are present in the Arabian Plate, they could not be correlated because their lithostratigraphic definitions and sequence-stratigraphic interpretations are local, and biostratigraphic and chemostratigraphic age control was poor. These limitations were resolved in 2010 by the documentation and correlation of the Barremian, Aptian and Early Albian T-R sequences in the eastern part of the Arabian Plate in GeoArabia Special Publication 4 – “GeoArabia SP4” (van Buchem et al., 2010a, b, and papers therein).

One paper in GeoArabia SP4 by Yose et al. (2010) presented correlations between the Arabian Plate’s Aptian T-R sequences and the global sequences of Hardenbol et al. (1998, Figure 1). These correlations were based on biostratigraphic and chemostratigraphic data, and allowed the 18 other papers in GeoArabia SP4 to calibrate the Arabian Plate’s and global Aptian sequences in the Geologic Time Scale 2004 (GTS 2004) of the International Commission on Stratigraphy (ICS, Ogg et al., 2004; Gradstein et al., 2004). Also in GeoArabia SP4, Al-Husseini and Matthews (2010) compared the dating of the Arabian Plate’s and global sequences in GTS 2004 to a time scale that is entirely based on orbital-forcing of glacio-eustasy, abbreviated “M&H-2010” (Matthews and Al-Husseini, 2010; Figure 2). The estimated ages of the Aptian sequences differed by about + 1.0 million years (Myr), or less, between GTS 2004 and the M&H-2010 scale. This result was independently confirmed by an astronomical-geochronological study by Huang et al. (2010; Figure 3), as discussed in this paper (Tables 1–4).

Another result that emerged from GeoArabia SP4 was the documentation of two major box-like drops in relative sea level in the Arabian Plate (Figure 2). Similar drops occur in other regions of the world such as in the Russian Platform (Sahagian et al., 1996; see discussion in Maurer et al., 2012). In the Arabian Plate the older drop of ca. 40 m (Droste, 2010) lasted about one million years in the earliest Aptian (Hillgärtner, 2010), and the younger one of 40–50 m lasted about 5.0 Myr in the late Aptian (Pierson et al., 2010; Maurer et al., 2010, 2012; Raven et al., 2010). These two events were interpreted as glacio-eustatic in origin (van Buchem et al., 2010b; Al-Husseini and Matthews, 2010), which contradicts the widely held view of an ice-free Greenhouse World in the Aptian (e.g. Larson et al., 1993; Larson and Erba, 1999; Jenkyns et al., 2011).

This paper has three main sections. The opening section, “Age Calibration of the Aptian Sequences”, compares the results of Huang et al. (2010) and Al-Husseini and Matthews (2010) in relation to previous calibrations and correlations of the global and Arabian Plate’s T-R sequences (Tables 1–4; Figures 1–3). The next section, “Antarctica’s Glacio-eustatic Signature”, interprets the late Miocene– Holocene sea-level curve of Miller et al. (2005; abbreviated Metal-05; Enclosures 1 and 2; Table 5). It shows that long-period sea-level cycles, corresponding to the volume of ice on Antarctica, the Northern Hemisphere and Greenland, can be correlated to the Earth’s eccentricity by the amplitude envelope of the 41-Kyr obliquity signal. The final section, “What Drives Sequence Stratigraphy?” argues that eccentricity is the modulating signal that contains the message of glacio-eustasy. Obliquity is compared to a carrier signal, that is modulated by eccentricity, and which, on its own, is insufficient to drive glacio-eustasy.

The technique used by Huang et al. (2010) to date the Aptian Stage combines cyclostratigraphy and geochronology to build an Astronomical Time Scale (Hinnov and Ogg, 2007). The first step involved a cyclo-stratigraphic analysis of a deep-marine reference section to estimate the durations of the Albian (Grippo et al., 2004) and Aptian stages (Huang et al., 2010; Figure 3). The Aptian–Albian section is represented in the Piobicco core, which was extracted from a borehole drilled in 1982 in central Italy (Larson et al., 1993). The Milankovitch cyclicity in the core is seen as high-resolution grayscale and lithology rhythms that reflect carbon content. These rhythms are interpreted as the long-eccentricity 405,000 year (E = 405 Kyr) and short-eccentricity (e = ca. 100 Kyr) orbital cycles (La04 of Laskar et al., 2004).

A total of 62.5 long-eccentricity 405-Kyr cycles were identified between the top Albian and top of Chron M0r, which occupies the earliest ca. 500 Kyr of the Aptian (Huang et al., 2010; Figure 3). The upper 30.75 cycles (E1 to upper part of E31) are Albian implying the Albian Stage lasted 12.45 Myr. The lower 31.75 cycles (lower part of E31 to upper part of E63) are Aptian, and adding 500 Kyr for the duration of the M0r Chron, calibrate its duration as 13.35 Myr. To estimate the age of the top Aptian, the Albian’s duration is added to the radiometric dating for top Albian: either (1) 99.6 Ma (GTS 2004, Figure 3), or (2) 100.62 Ma (Renne et al., 2009). Ogg et al. (2012) discussed the accuracy of these age estimates and adopt 100.5 + 0.4 Ma for top Albian in GTS 2012 (Ogg et al., 2012).

Huang et al. (2010) attributed the biostratigraphic zones, geopolarity, color, oceanic anoxic events (OAE, black shales) and chrons, as repeated here in Figure 3, to several studies (Larson et al., 1993; Erba, 1996; Bralower et al., 1999; Leckie et al., 2002). In GTS 2012, these events are shown based on the calibration of Huang et al. (2010), and in particular the foraminiferal events are related to the Aptian ammonite zones according to Leckie-Huber’s correlations. J. Ogg (written communication, 2012) provided age estimates for the sequences of Hardenbol et al. (1998, see Table 1). He cautioned, however, that these are not exact because J. Hardenbol did not publish his reference sections and actual biostratigraphic constraints for those sequences.

Huang et al. (2010) correlated the black shale unit in the E59 to E62 cycles in the Piobicco core to the oceanic anoxic event OAE1a (Selli Interval, Figure 3). In GTS 2012, the Selli Interval is correlated to the planktonic foraminiferal Laupoldina cabri Zone and Deshayesites deshayesi ammonite Zone. They tentatively identified the Fallot, Jacob and Kilian OAEs (Figure 3) but the reliability of these black shale intervals as correlation markers is uncertain. For example, the Fallot Interval is tentatively picked in the E45 cycle (ca. 117.8–117.4 Ma) in the Hedbergella trocoidea planktonic foraminiferal Zone (Huang et al., 2010). However, in France’s Vocontian Basin, Friedrich et al. (2003) defined the (Niveau) Fallot Interval in terms of four thin black shale beds that straddle the boundary between the Globigerinelloides ferreolensis and Globigerinelloides algerianus zones. In the Piobicco core this boundary is picked in the E54 cycle (ca. 121.4–121.0 Ma in GTS 2004), nearly 4.0 Myr older than the age suggested by Huang et al. (2010).

According to Wang et al. (2011) the black shale intervals (OAEs) and Oceanic Red Beds (ORBs) in the Piobicco core may be proxies for Aptian warming and cooling. They interpreted the OAEs as periods of extreme warm climate, ocean circulation, high bioproductivity and organic-carbon preservation. In contrast they interpreted the red beds, which are associated with very low organic-carbon content and oxic depositional environments, as suggestive of cold periods and oscillating climate shifts. They concluded that the presence of ORBs sandwiched between OAEs may reflect major climatic and paleoceanographic changes.

An assessment of the reliability of the biostratigraphic zones, black shale and red bed intervals given in the Piobicco core indicates that the Selli Interval is the most reliable correlative marker (Figure 3). This conclusion is important for tying the Italian reference section to the Arabian Plates’s stratigraphy, as will be discussed below.

In the Arabian Plate (AP), third-order Barremian (abbreviated Bar), Aptian (Apt) and Early Albian (Alb) T-R sequences, maximum flooding surfaces (MFS) and sequence boundaries (SB) have been interpreted and dated in GTS 2004 using biostratigraphy and chemostratigraphy (van Buchem et al., 2010a, b) (Figures 1 and 2). Table 1 shows the names of key surfaces and their ages, including several Cretaceous (K) global MFS as interpreted in the Arabian Plate (MFS K60, K70, K80 and K90; Sharland et al., 2001; van Buchem et al., 2010a, b). The Arabian Plate T-R sequences have been dated using strontium-isotope data calibrated according to GTS 2004 (Vahrenkamp, 2010; Strohmenger et al., 2010; Table 4).

Matthews and Frohlich (1998, 2002) modeled Antarctica’s ice sheet during the Mesozoic and Cenozoic as an ice cylinder that interacts with a warm saline bottom-water (WSBW) ocean current that originates from mid to low latitudes (reverse thermo-haline ocean circulation). The interaction is driven by orbital forcing (precession, obliquity and eccentricity) of solar insolation at 30°N in July (source of the WSBW) and 70°S in January (coast of Antarctica). They showed that the cylinder grows (snow gun) and shrinks (rain gun) causing glacio-eustatic cycles with amplitudes of several 10s of meters and periods of ca. 400 Kyr and 2.0, 2.4 and 2.8 Myr. They proposed the corresponding depositional sequences as the “fourth-order” and “third-order” sequences.

The definition of orders by Matthews and Frohlich (2002) were not adopted in GeoArabia SP4 or in the literature. For example, Boulila et al. (2011) suggest that the duration of “third-order” depositional sequences may change from 1.2 Myr in the Icehouse World to 2.4 Myr in the Greenhouse World. They state that the “fourth-order” stratigraphic cycle could be linked to 405-Kyr eccentricity, as well as the ca. 160–200 Kyr obliquity cycle. In order to avoid confusion involving the duration of orders, the term ”straton” is given to the transgressive-regressive (T-R) sequence that tracks the 405-Kyr cycle in the M&H-2010 scale. The adjectives “short”, “nominal” and “long” are added for the third-order orbital sequences corresponding to 2.025, 2.43 and 2.835 Myr. All of these sequences are attributed to glacio-eustasy, which is believed to have driven sequence stratigraphy throughout the Phanerozoic.

In 2005 R.K. Matthews, based on a minor tune-up of the Fourier periods of the Earth’s eccentricity (Laskar et al., 2004), predicted that Antarctica’s ice cylinder should have grown to a maximum size every 14.58 million years (Myr), and oftentimes every 4.86 Myr (Matthews and Al-Husseini, 2010). These times correspond to major glacio-eustatic drops manifested as regional sequence boundaries (SB) or unconformities. The time-rock units between these major sequence boundaries are named “orbitons” (36 stratons, 14.58 Myr), which consist of three “dozons” (12 stratons, 4.86 Myr) in the M&H-2010 scale. The age of SB 0 is 1.586 Ma, and older SBs (N = 1, 2, etc.) can be dated as follows:

SB N = 1.586 + N × 14.58 Ma

The Barremian–Aptian time interval spans 130–112 Ma in GTS 2004, and contains just one orbiton sequence boundary, SB 8, predicted to occur in the late Aptian at 118.2 Ma:

SB 8 = 1.586 + 8 × 14.58 = 118.226 Ma = ca. 118.2 Ma

The first step in using the M&H-2010 scale is to correlate SB 8, at the base of Straton 292 (292 × 0.405 = 118.2 Ma), to a global sequence boundary and/or its correlative in the Arabian Plate (Figures 1 and 2). The only candidate is mid-Aptian Global SB Apt 5 of Hardenbol et al. (1998), which was correlated to Arabian Plate SB Apt 5 (Yose et al., 2010; Strohmenger et al., 2010; Table 1, Figure 1). The estimated age of Global SB Apt 5 is 117.85 Ma in GTS 2004 and unchanged in GTS 2012 if taken just above the top of the E. martinoides ammonite Zone (J. Ogg, written communication, 2012). The three-way correlation, SB 8 = AP SB Apt 5 = Global SB Apt 5 is unique because: (1) an alternative correlation with the next-older Global SB Apt 4 (121.3 Ma in GTS 2004, 123.0 Ma in GTS 2012) would mistie by more than 3.0 Myr, and (2) an alternative correlation with the next-younger Global SB Apt 6 (112.4 Ma in GTS 2004, 114.2 Ma in GTS 2012) would mistie by more than 4.0 Myr (Figure 1).

The three-way correlation is also supported by the estimated sea-level drop that occurred at these boundaries (Figures 1 and 2): ca. 50 m in the global sea-level curve (Haq et al., 1988; Hardenbol et al., 1998; compilation in Snedden and Liu, 2011), and ca. 40–50 m at AP SB Apt 5, between third-order Arabian Plate sequences Apt 4 and Apt 5.

The second step in applying the M&H-2010 scale involves finding stratons to represent time units of 405 Kyr and using SB 8 at 118.2 Ma as a datum from which to determine their age (Figure 2).

Working down from SB 8, Al-Husseini and Matthews (2010) counted 17 candidate stratons that appear to represent continuous deposition between 118.2 and 125.1 Ma. Eight stratons (293–300) are broad clinoforms that are controlled by borehole data and imaged in a 3-D seismic survey recorded in the intra-shelf Bab Basin in Abu Dhabi (Yose et al., 2010, named AP Apt 4.8 to Apt 4.1, Figure 2). These form Arabian Plate Sequence AP Apt 4, which correlates closely to Global Sequence Apt 4 of Hardenbol et al. (1998) with a GTS age of 117.85–121.0 Ma and orbital age of 118.2–121.4 Ma (Table 1).

Nine more stratons (301–309) are correlated to nine fourth-order platform sequences in Wadi Mu’aydin, Oman, denoted WM16 to WM8 (van Buchem et al., 2002, 2010b). The uppermost four (WM16–WM13) form third-order Arabian Plate Sequence Apt 3. Dozon 9C consists of 12 stratons (304–293, 9C1–9C12; Figure 2) grouped into two third-order sequences: AP Apt 3 consisting of the four aggradational fourth-order sequences (WM13–WM16, stratons 9C1–9C4, ca. 1.6 Myr), and the eight progradational clinoforms (AP4.1 to AP4.8, stratons 9C5–9C12, 3.2 Myr). The break-up into 1.6 and 3.2 Myr sequences was due to the switch from aggradation to progradation, and is unrelated to orbital tuning.

The other five fourth-order platform sequences in Wadi Mu’aydin, denoted WM12 to WM8 (van Buchem et al., 2002) form Apt 2 and Apt 1 (Table 1, Figure 2) and together correlate to Global sequences Apt 2 and possibly Apt 1 of Hardenbol et al. (1998).

The earliest Aptian is represented by a hiatus over most of the Arabian Plate except along the margin of the Neo-Tethys Ocean at Wadi Baraka in eastern Oman (Figure 2). At this locality a 70-m thick section forms part of a wedge that pinches out to the west, i.e. towards the Arabian Plate. The boundaries of the wedge merge into a sequence boundary that separates, over the rest of the Arabian Plate, two layer-cake sequences: Upper Barremian Sequence AP Bar 2 from Lower Aptian Sequence AP Apt 1 (Hillgärtner et al., 2003; Hillgärtner 2010). H. Hillgärtner (written communication, 2010) estimated the duration of the hiatus as ca. 1.0 Myr suggesting it corresponds to the two stratons 311 and 310 (125.9–125.1 Ma). In Oman, this boundary is interpreted as an exposure surface and the amplitude of relative sea-level fall is estimated as ca. 40 m (Droste, 2010). The base of the wedge is near the Barremian/Aptian boundary at ca. 125.9 Ma in the orbital calibration (Figure 2), comparable to the estimate of Huang et al. (2010) at ca. 125.45 Ma and 125.0 + 1.0 Ma in GTS 2004 (Table 3, Figure 3).

Upper Barremian third-order Sequence AP Bar 2 extends over the eastern Arabian Plate (van Buchem et al., 2002, 2010b, Table 1 and Figure 2). It is characterized in Wadi Mu’aydin by five fourth-order aggradational sequences WM3 to WM7. They were correlated by Al-Husseini and Matthews (2010) to stratons 316–312 (127.9–125.9 Ma) and to Global sequences Bar 5 and Bar 6 of Hardenbol et al. (1998) dated between 127.75–125.0 Ma in GTS 2004.

The earliest Aptian 40 m drop with a duration of ca. 1.0 Myr is related to how the stratons of the late Barremian–Aptian group together into Dozon 9B (stratons 316–305, 9B1–9B12, Figure 2). It consists of the short (ca. 2.0 Myr) and then long (ca. 2.8 Myr) third-order sequences (Matthews and Frohlich, 2002). The short one is the late Barremian Sequence AP Bar 2 formed by the five fourth-order sequence WM3–WM7 (stratons 9B1–9B5). The long one starts with the lowstand Wadi Baraka Wedge (9B6 and 9B7), and continues with the five fourth-order sequence WM8–WM12 (9B8–9B12) that form early Aptian sequences AP Apt 1 and Apt 2. Drops between the 5^th, 6^th and 7^th stratons of a dozon are predicted in the M&H-2010 scale.

Counting upwards from SB 8 (AP SB Apt 5), Al-Husseini and Matthews (2010) correlated the nine stratons 292–284 to nine more regional clinoforms in the Bab Basin (AP Apt 5.1 to Apt 5.9 that form AP Apt 5; Pierson et al., 2010; Maurer et al., 2010, 2012; Table 1, Figure 2). The top of the clinoforms is 40–50 m lower than that of the AP Apt 4 Sequence (Pierson et al., 2010; Raven et al., 2010; Maurer et al., 2012). This second drop occurred in a time interval that is less than 405 Kyr because the bounding clinoforms do not show any break in continuity. It is not associated with any structural movements as evident from the seismic and well control. Because only nine clinoforms are assigned to Dozon 8A, it is assumed that the three stratons 283–281 (C10–C12) are not recognized in the central part of the Bab Basin. Alternatively a 1.2-Myr hiatus of non-deposition, possibly due to silling of the Bab Basin, may have followed the deposition of AP Apt 5.9. It is also assumed that the deposition of the uppermost Aptian part of the Nahr Umr Formation started at AP SB Apt 6 corresponding to the base of the Dozon 8B, and consists of stratons 280–278 Ma, with the Aptian/Albian taken at ca. 112.1 Ma.

Coincidently, the only orbiton-level sequence boundary SB 8 at 118.2 Ma that was predicted in the studied interval coincides precisely with the start of the late Aptian 40–50 m drop (Figure 2). Orbiton-level glacio-eustatic events that repeat every 14.58 Myr are the basis for the M&H-2010 scale.

The age of the top Aptian is estimated by adding the astronomically determined duration of the Albian Stage (12.45 Myr) to the radiometric dating of the top Albian (99.6 Ma or 100.6 Ma; Huang et al., 2010, Table 2). In this paper the age of the top Aptian is found to be more consistent with 112.0 Ma in GTS 2004, rather than 113.0 Ma in GTS 2012 (Table 2), based on the dating of the Selli Interval (OAE1a). In the Piobicco core the Selli Interval occurs in cycles E62 to E59 between 124.55–123.16 Ma, assuming the 99.6 Ma age for the top Albian (Huang et al., 2001; Figure 3). In GTS 2012 its age is 125.55–124.16 Ma. In the Arabian Plate the equivalent of the Selli Interval was recognized by several authors by correlating the δ¹³C curve to global curves (Droste, 2010; Strohmenger et al., 2010; Vahrenkamp, 2010; Yose et al., 2010). It occurs in third-order AP Apt 2 (124.3–123.1 Ma), and upper part of AP Apt 1 (124.7–124.3 Ma, Figure 2). Thus the age of the Selli Interval in the core (124.55–123.16 Ma) assuming top Aptian at 112.0 Ma, differs by no more than 150 Kyr from that obtained by the M&H-2010 scale in the Arabian Plate (124.7–123.1 Ma).

The previous section described how the Aptian stratigraphy can be equivalently represented by: (1) deep-marine sedimentary rhythms that are tuned by the 405-Kyr long-eccentricity orbital cycle in central Italy (Huang et al., 2010), as well as (2) shallow-marine T-R sequences, named stratons, in the Arabian Plate (Al-Husseini and Matthews, 2010). The similar count of Italian rhythms and Arabian Plate’s stratons, and nearly coincident position and age of the Selli Interval, implies that both successions were tuned by the 405-Kyr signal (Figure 3).

Maurer et al. (2010, 2012) estimated the amplitude of the regular fluctuations in relative sea level that controlled the deposition of the stratons as ca. 10–20 m in the Arabian Plate’s late Aptian Sequence AP Apt 5, and ca. 5–10 m in other Aptian and Barremian sequences (Figure 2). Their estimates lead to the second implication: the 405-Kyr eccentricity signal played a leading role in forcing the regular ca. 5–20 m sea-level fluctuations, whether through the waxing and waning of ice sheets on continents (mainly Antarctica, Figure 4), or some other climatic mechanism (e.g. water locked in lakes and ground water, thermo-eustasy, etc.).

This section of the paper argues that ice-making and melting during the Aptian time, mainly in Antarctica, caused the 5–20 m fluctuations and the longer-period 40–50 m sea-level changes recorded in the Arabian Plate (Figure 2). To support this argument, aspects of Antarctica’s late Miocene–Holocene (9.25–0.0 Ma) glacio-eustatic signature are interpreted and compared to those of the Aptian Arabian Plate. The signature is interpreted from the sea-level curve of Miller et al. (2005, abbreviated “Metal-2005”, Enclosures 1 and 2), which is available as a spreadsheet in the supplement of the journal Science. It is based on benthic foraminiferal δ¹⁸O data, which reflect global ice volume and deep-ocean temperature and provides a proxy for glacio-eustasy.

In Enclosure 1 a second sea-level curve is shown between 5.3–0.0 Ma that is based on the stack of 57 globally distributed benthic foraminiferal δ¹⁸O records, known as “LR04” after Lisiecki and Raymo (2005; see review in Walker and Lowe, 2007). The δ¹⁸O values in LR04 are here linearly converted to sea level by setting the present-day level to 0.0 m and Lowstand 2 to -122 m. In contrast to the linear conversion, the δ¹⁸O values in Metal-2005 are converted by Miller et al. (2005) to sea level by accounting for cooling of the oceans between 3.3–2.5 Ma. The two curves show a similar number of marine isotope stages (MIS) but differ by about 20 m before 3.3 Ma. A third sea-level curve, Metal-2011, was calculated by Miller et al. (2011) using the LR04 δ¹⁸O values between 5.3–0.0 Ma and Metal-2005 between 9.25–5.3 Ma. For the purpose of interpreting Antarctica’s glacio-eustatic signature the Metal-2005 curve is used because it is considered sufficiently similar to LR04 and Metal-2011.

In Enclosure 2, a sine wave with a period of 405 Kyr is plotted so that the ages of the minima (-1.0) coincide with minima of the 405-Kyr long-eccentricity cycles. It provides a 405-Kyr Clock for approximately dating the sequence boundaries of sea-level cycles. The two curves at the bottom of Enclosure 2 show the calculation of the Earth’s eccentricity based on the full solution by Laskar et al. (2004, between 5.0–0.0 Ma) and the tuned-eccentricity approximation between 9.25–0.0 Ma by Matthews and Al-Husseini (2010). They are comparable for the purpose of sequence stratigraphy, and the latter’s advantage is that it repeats every 14.58 Myr starting at 1.586 Ma.

The largest present-day ice sheet is located on the continent of Antarctica, situated between approximately 70°S and the South Pole (Figure 4). It holds 57–66 m sea-level equivalent (Lythe et al., 2001; Denton, 2011), or about 200 feet (USGS, 2012). Since the Last Glacial Maximum (LGM) occurred about 14,000 years ago (14 Ka), global sea level has risen by about 120 ± 5 m (Miller et al., 2005; Denton, 2011; Enclosures 1 and 2). Estimates for the contribution made by the melting of Antarctica’s ice sheet vary from about 12 m (Pollard and DeConto, 2009; Macintosh et al., 2011) to as much 35 m (Nakada and Lambeck, 1988). Ingólfsson and Hjort (1999) reviewed several studies that estimated the contribution between 12 and 26 m, and made their own estimate of between 10 and 17 m since 8–5 Ka. A model of Antarctica’s ice sheet by Naish et al. (2009, see their figure 4) showed fluctuations of 25 m (glaciations 11 and 5) and about 16 m since the Last Glacial Maximum. These various estimates indicate that since the Last Glacial Maximum the melting of Antarctica’s ice sheet raised global sea level by about 20 m in 14 Kyr – a rate that is essentially “instantaneous” in geological time.

The second largest present-day ice sheet is located over Greenland, situated between 59°N and 84°N (Figure 5). Greenland’s ice sheet holds about seven meters sea-level equivalent (Bartoli et al., 2005; USGS, 2012), and being nearly fully-ice-loaded, it may have only contributed 2–3 m sea-level equivalent since the Last Glacial Maximum (Hill et al., 2010). The remaining present-day ice sheets are located in the Arctic Ocean (Figure 5) and on mountains. The Arctic ice cap occupies approximately the same surface area (70° to Pole) as Antarctica. The ice is floating, thin (meters to 10s of meters), and mostly submerged and therefore does not alter sea level as much as ice build-ups on land. The Arctic ice cap, together with all mountain glaciers, hold a fraction of one meter sea-level equivalent (USGS, 2012).

If the contribution of Antarctica’s melted ice to the global sea-level rise since the Last Glacial Maximum is about 20 m, then most of the other 100 m sea-level rise, from the total of 120 m, was due to the melting of the Northern Hemisphere’s ice sheets. These sheets extended on land from the Arctic Circle at about 70°N to about 45°N into North America (Laurentide, Cordillerian, Innuitian and Franklin ice sheets), and higher latitudes in Eurasia (Scandinavian, Barents and Kara ice sheets) (Figure 5, after Denton and Hughes, 1981).

Matthews and Frohlich (2002) estimated that Antarctica’s ice cylinder during the Mid-Jurassic to Cretaceous time had the capacity to change global sea level by a total of about 90 m. Their estimate is consistent with the 57 to 66 m in Antarctica’s present-day ice and 20 m in its melted ice since the Last Glacial Maximum. In terms of glacio-eustasy these estimates indicate that an ice-free Greenhouse World should have a sea level of +70 m above present-day’s (+57 to 66 m from Antarctica, +7 m from Greenland and +1 m from all other ice), as consistent with the +70 m estimate of Alley et al. (2005). Therefore, if the Northern Hemisphere and Greenland were ice-free, then Antarctica’s ice sheet – on its own – could have caused sea level to fluctuate between -20 m when it was fully-ice-loaded, and +70 m when it was ice-free. Sahagian et al. (1996) estimated the relative eustatic change for the Aptian was about 60 m (Figure 2).

The sea-level curves in Enclosure 1 show the combined glacio-eustatic signatures of the Northern Hemisphere, Greenland and Antarctica ice sheets. Separating Antarctica’s is approximately possible by making the following three assumptions based on time and sea-level constraints discussed below (Enclosure 2):

• (1) Sea level above -20 m between 9.25–3.5 Ma is exclusively Antarctica’s.

• (2) Sea level above -20 m between 3.5–0.0 Ma is Antarctica’s and Greenland’s.

• (3) The Northern Hemisphere’s glacio-eustatic signature is between -20 and -120 m and started after 3.3 Ma.

Based on glaciogenic and climatic evidence (e.g. ice-rafted sediments, surface and deep-marine temperatures, etc.), the Northern Hemisphere’s Ice Age started at about 3.3–3.1 Ma and assumed to be linked to the final closure of the Central American Seaway (Panama Isthmus; see discussion in Shackleton, 1987; Raymo, 1994; Maslin et al., 1998; Bartoli et al., 2005; Molnar, 2008). The closure is interpreted to have blocked the circulation of currents between the Atlantic and Pacific oceans, thus causing a major change to the Earth’s oceanic and atmospheric systems. Besides the time coincidence, the closure of the Central American Seaway provides the most likely trigger for the initiation of Northern Hemisphere’s Ice Age (Mikolajewicz and Crowley, 1997; Philander and Fedorov, 2003). Molnar (2008), however, argues that the relationship between the closure and the Ice Age remains poorly understood.

The 3.3–3.1 Ma age for the start of the Northern Hemisphere’s Ice Age is consistent with the drop to -67.4 m at 3.315 Ma during Glaciation M2. It is 47.4 m below the -20 m level for a fully-ice-loaded Antarctica. Glaciation M2 is also evident as a drop to -40 m in the sea-level-converted δ¹⁸O stack of Lisiecki and Raymo (2005, Enclosure 1). Naish and Wilson (2009), using LR04, apportioned the M2 Lowstand as -18 m due to the expansion of Antarctica’s ice sheet, and -20 m to that of the Northern Hemisphere. Marine Isotope Stage (MIS) M2 was also analyzed by Dwyer and Chandler (2009) using a combination of ostracode Mg/Ca-based bottom-water temperatures with benthic foraminiferal δ¹⁸O at DSDP Site 607 in the North Atlantic. They estimated that sea level dropped to ca. -65 m during Glaciation M2, consistent with the estimate of -67.4 in Metal-2005. These studies confirm that Glaciation M2 is indeed a Transient Precursor Event for the Northern Hemisphere’s Ice Age (Bartoli et al., 2005).

The trend to greater and greater lowstands, which correspond to further southwards advances by the Northern Hemisphere’s glaciers, occurred after KM2 (3.145 Ma, -50.5 m). Bartoli et al. (2005) used climatic proxies to show that the build-up of Northern Hemisphere’s ice sheets occurred even later than at KM2 with Glaciation G10 at 2.82 Ma, and was followed by the Climate Crash starting with Glaciation G6 at 2.74 Ma.

Greenland’s ice sheet started to form in its southern region in the late Miocene and expanded to northern Greenland at ca. 3.5–3.3 Ma (Maslin et al., 1998; Hill et al., 2010). Its glacio-eustatic signature is between 7 to possibly 10 m, and cannot be separated from Antarctica’s after 3.5–3.3 Ma.

The curve between 9.25–3.3 Ma rarely drops below -20 m, which corresponds to a fully-ice-loaded Antarctica. It is unclear whether the few spike-like sea-level lowstands that drop below -20 m prior to 3.3 Ma are errors or short-lived glaciations in the Northern Hemisphere. K. Miller (written communication, 2012) indicated that ice sheets developed in the Northern Hemisphere by 14 Ma, if not earlier.

In this paper the values of sea level and their ages are quoted precisely as given by Miller et al. (2005). This practice is not intended to imply such accuracies but is adopted so that glacio-eustatic events can be correlated to the marine isotope stages (MIS) in LR04 and other studies. K. Miller (written communication, 2012) estimated the accuracy of the sea-level values in Metal-2005 to be ± 20%; however a comparison between several studies suggests that much greater errors can occur in the Metal-2005 dataset. The mid-Pliocene (3.3–3.0 Ma) sea level has been estimated by several authors using benthic foraminiferal δ¹⁸O records from different localities and provides an opportunity to evaluate the accuracy of this technique.

Besides the Transient Precursor Event M2 (3.305 Ma, Enclosure 2), Dwyer and Chandler (2009) analyzed several other mid-Pliocene marine isotope stages (MIS). They estimated sea level for KM2 (3.145 Ma) and G22 (3.060 Ma) as both -40 m, compared to -50.6 and -11.2 m in Metal-2005, and -15 and -21 m in LR04. They obtained -60 m for G16 (2.935 Ma), compared to -40.6 m in Metal-2005 and -20 m in LR04. These comparisons indicate that the accuracy of sea-level estimates for specific MIS can be much greater than ± 20%.

Between 3.3–3.0 Ma (M2 to G20), Dwyer and Chandler (2009) estimated that mean sea level was similar to present-day’s and fluctuated between ± 20 or ± 30 m. The linearly converted sea-level curve based on LR04 similarly shows fluctuations of ± 20 m relative to present-day’s (Lisiecki and Raymo, 2005; Enclosure 1). In contrast, Rohling et al. (2009) estimated mid-Pliocene mean sea level as +25 ± 5 m.

As noted above, Miller et al. (2005) shifted sea-level downwards to account for cooling of the oceans during the time between 3.3–2.5 Ma. Their curve is lower than that derived from LR04 between 3.5–3.0 Ma (Enclosure 1). Between M2 and KM2 (3.305–3.145 Ma) it oscillates between 0 and -20 m, and -30 to +20 m between KM2 and G20 (3.145–3.015 Ma). Miller et al. (2012) estimated that the peak Pliocene sea level was ca. +22 ± 10 m (95% confidence) but then corrected this estimate to ca. 10 m (K. Miller, written communication, 2012).

In this section sea-level cycles are correlated to eccentricity and identified in terms of specific MIS in LR04 and corresponding sea-level/age data pairs in Metal-2005 (Enclosure 2, Table 5). As noted above the sea-level/age data pair is quoted precisely for ease of identification without implying such great accuracy.

Both the LR04 and Metal-2005 sea-level curves contain a persistent 41-Kyr obliquity signal, which produces “sixth-order” T-R depositional sequences. Naish and Wilson (2009) recognized these sequences in a marine basin in New Zealand. In very shallow-marine settings, like the Aptian Arabian Plate, the transgressive 41-Kyr highstands and maximum flooding interval will correspond to deposition. However, depending on accommodation space and sediment supply, the regressive 41-Kyr highstands and all the lowstands may correspond to a hiatus of non-deposition and/or erosion, or a section of reduced thickness.

The 41-Kyr fluctuations form longer-period patterns that can be recognized by their envelopes. The envelopes are bounded by prominent lowstands (sequence boundary) and the included highstands generally shows a rising sea-level trend followed by a falling one (transgression-regression). These cycles have durations of 325–545 Kyr and on average track the 405-Kyr Clock over a time span of 2.43 million years (Enclosure 2, Table 5). They correspond to the T-R depositional sequences that are named stratons, and are numbered according to the 405-Kyr Clock (E1–E23). Some of the sea-level cycles contain more than one 405-Kyr cycle and cannot be separated. They are combined and named after the correlative 405-Kyr cycles (e.g. sea-level cycles 8 and 9).

In several sea-level cycles the envelope of the 41-Kyr fluctuations forms a pattern that resembles a parallelogram (e.g. cycles 8, 6 and 5). This shape is caused by the obliquity signal melting and refreezing Antarctica’s, Greenland’s and the Northern Hemisphere’s ice sheets. Leaving Greenland’s signature aside for simplification, the schematic in Figure 6 shows how this pattern emerges by the super-position of obliquity fluctuations on an eccentricity-driven 405-Kyr glacio-eustatic cycle. Other geometric patterns formed by the envelopes of the 41-Kyr fluctuations can be interpreted in terms of ice volume changes in Antarctica and Greenland above -20 m, and the Northern Hemisphere below -20 m.

The following discussion describes aspects of each sea-level cycle starting with the eighth one, which followed the Northern Hemisphere’s Transient Precursor at Glaciation M2 (3.305 Ma). It then continues with the younger cycles 7 to 1, and concludes with Antarctica’s exclusive cycles from 20 to 9. In the interval 9.25–8.105 Ma the sea-level curve does not show patterns that can be interpreted in terms of cycles 21 to 23. Boulila et al. (2011) similarly noted that from 9.25–7.5 Ma the “δ¹⁸O inferred eustatic amplitudes are weak.”

The older sequence boundary of Cycle 8 is picked at Lowstand KM2 at 3.145 Ma for several reasons: (1) it is a prominent sea-level drop reaching -50.6 m in Metal-2005 or -40 m in Dwyer and Chandler (2009); (2) across KM2, sea level rises from -4.4 m at Highstand KM3 (3.16 Ma) of Cycle 9, to +20.2 m at Highstand K1 (3.075 Ma) of Cycle 8. Dwyer and Chandler (2009) estimated sea level at K1 as +15 m, i.e. within 25% of the estimate in Metal-2005 (+20.2 m). (3) Lowstand KM2 (3.145 Ma) correlates by age to Pliocene Piacenzian SB Pia1 (3.18 Ma) in the compilation of Snedden and Liu (2011, Table 5).

The maximum flooding interval (MFI) is picked in Highstand K1 because it marks the end of the transgression KM2–K1 and the start of the regression K1–G11. The younger sequence boundary of Cycle 8 is picked at Lowstand G10 (2.82 Ma, -43.2 m), and correlates within 100 Kyr to SB Pia2 (2.72 Ma; compilation of Snedden and Liu, 2011, Table 5). The age of Cycle 8 using the 405-Kyr Clock is 3.206–2.801 Ma, compared with 3.145–2.82 Ma. In the eccentricity curve KM2 correlates to the third eccentricity low at 3.1 Ma (between EC8c and EC8d) rather than the one at 3.21 Ma.

Cycle 8 lasted 325 Kyr and contains eight high-frequency fluctuations implying their average duration is 40.6 Kyr, thus confirming they are the 41-Kyr obliquity signal. Their amplitude averages 40 m and forms the parallelogram pattern discussed above (Figure 6). The lowstands G20–G10 form a decreasing trend below -20 m implying successively greater advances by the Northern Hemisphere’s ice sheets. The fluctuations above -20 m are attributed to the ice sheets of Antarctica and Greenland.

Cycle 7 is picked between Lowstands G10 (2.820 Ma, -43.2 m) and 96 (2.445 Ma, -54.4 m). The sea-level rise from G10 to G7 is the transgression, and the drop from +21.8 m at G7 to +10.8 m at 97, the regression. Cycle 7 has a duration of 375 Kyr between 2.820–2.445, and its age closely matches Cycle E7 in the 405-Kyr Clock (2.801–2.396 Ma), and eccentricity cycle EC7 (2.82–2.45 Ma). The lowstands level off at about -60 m indicating the Northern Hemisphere’s ice front reached the same latitude as at M2 and KM2.

Matthews and Frohlich (2002, see figure 2 in Matthews and Al-Husseini, 2010) referred to this eccentricity cycle (EC7) as a “simple straton” because it has a shape that approximately repeats every 2.0, 2.4 or 2.8 Myr. In Enclosure 2 simple stratons occur between 2.82–2.45, 4.82–4.38 and 7.695–7.31 Ma.

This cycle is picked between lowstands 96 (2.445 Ma, -54.4 m) and 78 (2.085 Ma, -69.6 m), and lasted 360 Kyr. The nine 41-Kyr fluctuations form a regressive parallelogram similar to that of Cycle 8. The amplitude of the 41-Kyr cycles is about 60–70 m, comparable to that of Cycle 7, but much greater than the 40 m of Cycle 8. Cycle 6 (2.445–2.085 Ma) correlates closely to eccentricity Cycle EC6 (2.45– 2.062 Ma) and Pleistocene Gelasian Sequence Ge1 (2.5–2.08 Ma; compilation in Snedden and Liu, 2011).

Cycle 5 resembles Cycle 6 by its parallelogram-shaped pattern, but differs in three significant ways. (1) It lasted much longer: 545 Kyr between lowstands 78 (2.085 Ma) and 52 (1.54 Ma). (2) The amplitude of the 41-Kyr envelope is about 40–50 m compared to 60–70 m in cycles 6 and 7. (3) Sea level between highstands 57 to 51 remained below -20 m for a period of about 100 Kyr. This interval is interpreted as an Antarctican Deep Freeze corresponding to its ice sheet holding its full capacity of 90 m sea-level equivalent. Lowstand 52 correlates precisely with Pleistocene Calabrian SB Cala1 (1.54 Ma, compilation in Snedden and Liu, 2011).

In the M&H-2010 scale the youngest orbiton sequence boundary SB 0 is predicted to occur at 1.586 Ma. Orbiton sequence boundaries occur because Antarctica’s ice cylinder reaches maximum ice-making in the final part of the long-cold EC5 eccentricity cycle between 1.68–1.52 Ma (Enclosure 2). SB 0 is similar to mid-Aptian SB 8 (118.2 Ma), which triggered the 40–50 m sea-level drop discussed in the first part of this paper (Figure 2).

Following Antarcica’s Deep Freeze at the end of Cycle 5, Cycle 4 started with a major sea-level rise reaching +10.1 m at Highstand 47 (1.45 Ma), compared to -27.5 m at Highstand 53 (1.57 Ma). The highstands rose above -20 m at interglacials 49, 47, 45, 43, and 37, implying Antarctica’s and Greenland’s ice sheets were melting. The lowstands decrease in amplitude from -78.4 to -60.4 m between glaciations 52 and 36, implying the Northern Hemisphere’s ice sheets were in overall retreat. Cycle 4 lasted 415 Kyr and contains ten 41-Kyr obliquity fluctuations with maximum amplitude of 100 m. It stands out visually as the final cycle with the distinct 41-Kyr obliquity signal.

These three cycles mark a great increase in the amplitude of sea-level fluctuations to ca. 100–120 m with sea level dropping to a maximum of about -125 m during Glaciation 16. During this time interval it becomes possible, for the first time, to visually correlate the ca. 100 Kyr eccentricity signal to specific sea-level highstands and lowstands (see numbering in Enclosure 2). Obliquity’s 41-Kyr appear as splits in the highstands of the 100-Kyr cycles (e.g. 5, 7, 9, 15, etc.). They have fluctuations with amplitudes of about 40–60 m, similar to that of the older Cycles 5 and 8. The reason for the dominance of the ca. 100-Kyr signal during these three cycles is discussed in the following section.

Sea level rose above -20 m just a few times after Glaciation 34 (1.125 Ma) at interglacials 1, 5, 7, 9, 11, 25 and 31, each lasting about 10–20 Kyr (Tzedakis et al., 2009). This pattern is seen in both Metal-2005 and LR04 (Enclosure 1). It suggests Antarctica was fully-ice-loaded during most of this time. This interpretation, however, is not consistent with the models of Antarctica’s ice sheet that show it melted about 15 m sea-level equivalent at interglaciers 13, 15, 17 and about 8 m at 19 and 21 (Pollard and DeConto, 2009; Naish et al., 2009). This discrepancy may be due to the contribution of 7–10 m by the melting of Greenland’s ice sheet.

Highstand 17 stands out because it only attains a level of -53.8 m, whereas other highstands generally cross above -20 m. At first this might suggest that the Northern Hemisphere’s ice sheets did not completely retreat during Interglacial 17. However, in the δ¹⁸O curve of Lisiecki and Raymo (2005, Enclosure 1) Highstand 17 has the same amplitude as highstands 15 and 19, suggesting an error in Metal-2005.

These five cycles may be typical of Antarctica’s glacio-eustatic signature. Sea level was at about present-day level and shows several transgressive-regressive patterns that resemble the tuned eccentricity curve of Matthews and Al-Husseini (2010). Lowstands that suggest a correlation to eccentricity minima occur at 8.105, 7.645, 6.90 6.45 and 6.045 Ma (Table 5). The older bounding lowstand at 8.105 Ma may correspond to sequence boundary Kw-Ch6 with an estimated age of 8.045–8.23 Ma (De Verteuil, 1997). The younger one at 6.045 Ma approximately correlates to the globally recognized Messinian sequence boundary or unconformity in the late Miocene at 5.83 Ma (SB Me2; compilation of Snedden and Liu, 2011). The magnitude of several lowstands are close to -20 m suggesting that Antarctica was briefly fully-ice-loaded at these times.

Cycle 15 corresponds to a sustained lowstand between 6.045 and 5.570 Ma in which sea level generally fluctuated between 0 and -20 m, with a few drops to -30 m or lower. These levels suggest that Antarctica was fully-ice-loaded during much of this interval. The sustained lowstand approximately coincides with E15 (6.041–5.636 Ma) and EC15 (5.99–5.61 Ma) and possibly EC16a. During this time interval the high-frequency sea-level fluctuations have typical periods of ca. 20 Kyr. Krijgsman et al. (1999) interpreted them as climate changes driven by precession, rather than obliquity-driven glacio-eustasy. The interval also coincides with the late Miocene Messinian Salinity Crisis (MSC) of the Mediterranean Sea. During the crisis, the Strait of Gibraltar formed a sill resulting in the isolation of the Mediterranean Sea from the Atlantic Ocean. As a result massive evaporites, up to 3 km thick, were deposited throughout the Mediterranean Basin (Ryan, 2008).

Estimates for the starting age for the basin’s isolation vary from 5.59 Ma (Krijgsman et al., 1999) to 6.13 Ma (Butler et al., 1999). Based on radiometric dating and astronomical tuning of sedimentary cycles and benthic foraminiferal oxygen-isotope records, Hilgen et al. (2007) estimated the isolation started at 5.96 Ma. They concluded that the onset of the crises is not related to glacio-eustatic sea-level lowering, but “its timing can best be attributed to the influence of the 400-Kyr eccentricity cycle on regional climate superimposed on a tectonic trend”. They estimated the duration of the crisis using two Messinian evaporite units in the classical section of Sicily. The evaporite cycles of the “Lower Evaporite” unit were converted to time using the period of the precession cycle (21.7 Kyr) for a total of 350–370 Kyr. The duration of the “Upper Evaporite” was tentatively estimated between 5.59–5.50 Ma. These estimates place the isolation of the basin between 5.96–5.50 Ma.

The study by Butler et al. (1999) used a combination of high-resolution magneto-stratigraphy and astro-stratigraphy to calibrate the crisis in the Caltanissetta Basin in central Sicily. They concluded that the oldest evaporites began to accumulate in the basin no later than 6.88 Ma, nearly the age of the start of long-cold eccentricity cycle EC17 (6.93 Ma). This was followed by a regression in the basin that lasted about 800 Kyr (from pre-6.88 Ma to post-6.0 Ma), which coincides closely with eccentricity cycles EC17 and EC16 (6.93–5.99 Ma). They estimated the Mediterranean Basin became isolated at 6.13 Ma and the greatest lowstand between 5.8–5.5 Ma. The lowstand in Metal-2005 ended at about 5.57 Ma corresponding to the final eccentricity low at 5.61 Ma. Butler et al. (1999) calibrated the rapid post-crises transgression between 5.5–5.3 Ma, as approximately consistent with Metal-2005.

Cycles 14 and 13 cannot be separated. The combined cycle occurs between 5.57 Ma (TG14?, -35.2 m) and 4.83 Ma (Si4, -45.6 m). Spike-like highstands occur at 5.475 Ma (+38.4 m) and 5.33 Ma (+48.8 m); the latter is the Miocene/Pliocene Boundary in GTS 2004. The spikes seem spurious and excessively high and could be errors in the data. Cycle 14 and 13 lasted 740 Kyr (5.57–4.830 Ma) and correlates with the eccentricity cycles EC14 and EC13 between 5.61–4.82 Ma.

Joined cycles 12 and 11 occur between Si4 (4.83 Ma, -45.6 m) and Gi20 (3.995 Ma, -56.4 m). They correlate closely to cycles EC12 and EC11 (4.82–3.99 Ma) and can be precisely dated with the 405-Kyr Clock (4.826–4.016 Ma).

Joined cycles 10 and 9 occur between Gi20 (3.995 Ma, -56.4 m) and KM2 (3.145 Ma, -50.6 m). The Metal-2005 sea-level curve shows good correlations to eccentricity between 3.3–3.1 Ma, with lowstands M2 (3.305 Ma) and KM2 (3.145 Ma) coinciding with local eccentricity minima. As discussed above, Lowstand M2 attains a level of about -60 m and is interpreted as a Transient Precursor Event for the Northern Hemisphere’s Ice Age. The main eccentricity minimum occurs at 3.21 Ma and is centered at the low sea level between M2 and KM2. The interval 3.5–3.3 Ma coincides with the first full glaciation of Greenland resulting in a possible 7–10 m drop (Maslin et al., 1998; Hill et al., 2010).

Most studies of the Pliocene to Holocene (5.33–0.0 Ma) glacio-eustasic pattern divide it into the 41-Kyr obliquity segment prior to about 1.1 Ma, and the 100-Kyr short-eccentricity segment since then (see review in Walker and Lowe, 2007; Enclosures 1 and 2). The reason for the switch from 41 to 100 Kyr is not understood and is known as the “100 Kyr problem” in the literature (e.g. Hinnov, 2000; Lisiecki, 2010). Another unanswered question is why the 100 Kyr is so prominent after 1.1 Ma but not the 405 Kyr cycle – the “400 Kyr problem” (e.g. Elkibbi and Rial, 2001). Some authors suggest that eccentricity does not play a role in glacio-eustasy – the “eccentricity myth” according to Maslin and Ridgewell (2005). Wikipedia gives a contemporary summary of some of these problems under the title “Milankovitch cycles”.

In this paper, the LR04 and Metal-2005 sea-level curves are displayed as large enclosures so that some of these problems can be examined in detail. The Metal-2005 curve of Miller et al. (2005), in particular, covers a longer time span and is rich in details that are visually obscured in the tiny displays and huge spreadsheet of the journal Science. Enclosure 2 is colored in a manner that shows how the glacio-eustatic cycles track the eccentricity signal. They lag, lead and eventually synchronize with the 405-Kyr Clock. The 41-Kyr-obliquity signal forms a pattern that rides on the longer-period, eccentricity-driven, glacio-eustatic signal.

Rial (2004) analyzed the significance of the riding pattern by applying signal-processing techniques used in telecommunications to a deep-sea δ¹⁸O time series that spans 2.0–0.0 Ma. He described his study as “teasing out the concealed pacemaker” – the 405-Kyr cycle. He used the estimate of 413 instead of 405 Kyr, but this does not change his conclusion. The 405 Kyr cycle is the modulator or modulating signal that contains the information or message (glacio-eustasy), while the 41-Kyr and 100-Kyr cycles are the carriers. This is a similar message to the one proposed by Matthews and Frohlich (1998, 2002) and Matthews and Al-Husseini (2010).

The distinction between the modulating and carrier signals is a useful way to understanding what drives glacio-eustasy and sequence stratigraphy. A simple analogy is how the eccentricity of the Earth’s orbit changes the average temperature from season to season, and the Earth’s rotation changes it from day to night. Eccentricity is the modulating signal because the season is the required information to predict when snow will fall on a specific location. Rotation is the carrier signal because knowing whether it is day or night at a certain location, without knowing the season, is not relevant to predicting the temperature or likelihood of snowfall.

The distinction is also implied in the schematic in Figure 6, which seeks to explain the parallelogram-shaped envelopes of sea-level cycles 8, 6 and 5. The parallelogram is constructed by superposing two independent 405-Kyr sea-level cycles to represent the glacio-eustatic contributions of Antarctica’s and the Northern Hemisphere’s ice sheets, above and below -20 m respectively (leaving Greenland aside for simplification). The amplitudes of the 41-Kyr obliquity fluctuations are completely different because they are modulated by the differently shaped 405-Kyr triangular-like envelopes. The 405-Kyr envelopes determine how much ice is sitting on the continents, like the seasons, and obliquity melts and refreezes it, like day and night. Without the 405-Kyr cycle’s power in making and melting ice, the obliquity signal would be turned off.

Again setting aside Greenland’s smaller contribution to glacio-eustasy, the reason why the envelopes of cycles 8, 6 and 5 look like parallelograms is because Antarctica and the Northern Hemisphere were making ice at the same rate during their regressions. This coincidence is not seen in other cycles. For example, in Cycle 7 Antarctica’s highstands form a triangular-like shape, but the Northern Hemisphere’s fluctuate within a rectangle between -20 and -55 m. Antarctica’s highstands also form a triangular-like shape in Cycle 4, but the Northern Hemisphere’s lowstands are in retreat from glaciations 52 to 36. In Cycles 2 and 3 Antarctica’s obliquity signature may have been subdued or turned off when it went into deep freeze, and the Northern Hemisphere’s ice sheets responded to this cold spell by making their greatest advances. In all of these cycles eccentricity determined the shape of the envelope of each ice sheet’s glacio-eustatic signal and the obliquity signal carried it, not vice versa.

In their recent paper Boulila et al. (2011) argued that during Icehouse times obliquity drives glacio-eustasy with periods of 41 Kyr and 1.2 Myr. Both S. Boulila and K. Miller (written communication, 2012) noted that they did not find a strong imprint of the 405 Kyr cycle in the Metal-2005 dataset. In Table 5 the minima of their predicted 1.2 cycle (see their figures 1 to 3) do not correlate with global sequence boundaries (Snedden and Liu, 2011) or those of the sea-level cycles in Enclosure 2. Moreover obliquity-forcing does not explain why the 100–120 m sea-level fluctuations after 1.1 Ma have periods of about 100 Kyr rather than 41 Kyr. This is the “100-Kyr Problem”. Its solution may have to do with the size of the ice sheets and at what latitude their ice fronts were located.

The Earth’s obliquity angle changes from low (21.2°) to high (24.5°) every 41 Kyr, which causes annual mean insolation to vary at high latitudes (Figure 7, modified after Mantsis, 2011). A small ice sheet centered at the poles is sensitive to obliquity because annual mean insolation changes by about 9% between high and low obliquity. In contrast an ice sheet that covers the entire continent of Antarctica will experience a 5% difference in annual mean insolation at its ice front along the coastline (70°S). The implication is that the more Antarctica’s ice cylinder grows, the less significant obliquity-forcing becomes. This pattern may be manifested by the apparent weakening of the obliquity signal during the Messinian Salinity Crisis (ca. 6.045–5.57 Ma; Enclosure 2). During the crisis, Antarctica may have been fully-ice-loaded with precession taking over as the carrier of the eccentricity-driven, glacio-eustatic modulating signal.

The weakening of the obliquity signal is also suggested by the amplitude of the envelopes of sea-level cycles 7 to 4. The amplitude is about 40–50 m in Cycle 5, compared to 60–80 m in cycles 7, 6 and 4. This amplitude anomaly may be related to Antarctica’s ice sheet approaching its maximum capacity in long-cold eccentricity cycle EC5.

The relationship between obliquity and the size of continental ice sheets is more evident in the Northern Hemisphere’s case. They started advancing on continents from much further south (70°N at the Arctic Circle) at ca. 3.3–3.1 Ma, and the greatest advances reached 45°N in North America (Last Glacial Maximum at 14 Ka, Figures 5 and 7, Enclosure 2). The maximum sea-level fluctuations caused by the Northern Hemisphere’s ice sheets swing between -20 and -120 m, corresponding to the North American ice front advancing 25° from 70°N to 45°N. This approximate relationship implies, for example, that between glaciations M2 and 36 (3.305–1.190 Ma) when sea-level lowstands were about -60 m the North American ice sheet was between 70°N and 60°N. At the 65°N mid-point, annual mean insolation varies by 3.0% between high and low obliquity, and its signal is remarkable in Sea-level Cycle 4 – The Last of the Distinct 41-Kyr Obliquity Cycles.

At Glaciation 34 (1.125 Ma) sea level dropped to about -80 m implying the North American ice front crossed 55°N where insolation does not appreciably vary with obliquity. The interval 1.125–0.875 Ma is the transition from 41-Kyr to 100 Kyr. For most glaciations between 22 (875 Ka) and 2 (14 Ka) more than half of the North American ice sheet was situated between 60°N and its front at 45°N. As a result the 41-Kyr obliquity carrier signal was turned off during these glaciations because it could not melt the ice front during high obliquity. It took the power of high eccentricity to force the ice front to retreat from 45° to 60°N, north of which the obliquity signal reappeared. This pattern occurs after 1.1 Ma as obliquity splits in the highstands starting above about -80 m.

The latitudinal sensitivity of insolation to obliquity could explain why Greenland’s ice sheet counter-intuitively started to form in its southern region in the late Miocene and then expanded northwards at ca. 3.5–3.3 Ma (Maslin et al., 1998; Hill et al., 2010). Southernmost Greenland is situated at 60°N where obliquity does not appreciably affect insolation (Figures 5 and 7). Southern Greenland could therefore hold its ice for longer periods than 41 Kyr. The rest of Greenland is located at higher latitudes reaching 84°N, and would have had difficulty maintaining an ice sheet from one 41-kyr cycle to the next. It was not until the Earth became sufficiently cold after the Central American Seaway closed at 3.3–3.1 Ma that eccentricity forced all of Greenland to be glaciated.

The M&H-2010 scale is constructed by stratons (405 Kyr), dozons (12 stratons, 4.86 Myr) and orbitons (36 stratons, 14.58 Ma) with the age for the base of Orbiton 0, Sequence Boundary SB 0, predicted at 1.586 Ma. It is here picked at 1.54 Ma at Glaciation 52 corresponding to Global Calabrian SB Cala1 (Enclosure 2, Table 5). The age of the next-older SB 1 is predicted at 16.166 Ma by adding 14.58 Myr to 1.586 Ma. This boundary correlates to Miocene SB Kw2c (16.48–16.06 Ma, De Verteuil, 1997) and Marine Isotope Stage Mi2 at 16.1 Ma (Miller et al., 1991; see table 1 of Boulila et al., 2011).

The Metal-2005 curve offers the opportunity to look for only one dozon, Dozon 1C, predicted at the terminations of long-cold eccentricity cycles EC5 (SB 0 at 1.586 Ma) and EC17 (SB 1C at 6.446 Ma) (Enclosure 2). The younger boundary, SB 0, is picked at 1.54 Ma (Glaciation 52), and the older SB 1C correlates to the lowstand at 6.450 Ma. The age of Dozon 1C is 6.45–1.54 Ma in Metal-2005, and compares closely to 6.446–1.586 Ma in the M&H-2010 scale.

The sea-level cycles between 6.45–1.54 Ma can be grouped into various sequence-stratigraphic schemes (Table 5). A preferred choice for the M&H-2010 scale is to divide Dozon 1C into two “nominal third-order sequences” each lasting 2.43 Myr, as predicted by Matthews and Frohlich (2002). This is possible by picking Glaciation Gi20 (3.995 Ma) as the third-order sequence boundary such that two sequences with durations of 2.455 Myr occur between 6.45–3.995 Ma and 3.995–1.54 Ma. The difference of 25 Kyr between 2.455 and 2.43 Myr is not an error that accumulates with time because the 405-Kyr cycle is a stable clock to at least 250 Ma (Laskar et al., 2004).

In 2010, an extensive geological dataset from GeoArabia Special Publication 4 (van Buchem et al., 2010a) was used to determine if the Arabian Plate’s Aptian T-R sequences can be cast in a time scale that is entirely based on orbital-forcing of glacio-eustasy (Figures 1 and 2, M&H-2010 scale for Matthews and Al-Husseini, 2010). Testing of this model-based approach to chrono-stratigraphy and sequence stratigraphy raised many important questions, some of which are addressed in this paper.

How do we know that the Arabian Plate’s Aptian fourth-order sequences tracked the 405-Kyr eccentricity signal and can be dated with the M&H-2010 time scale?

This study correlated the Arabian Plate’s Aptian stratons to the 405-Kyr cycles in the Piobicco core reference section in central Italy (Figure 3). Both the Italian and Arabian calibrations are consistent with the Geological Time Scales 2004 and its 2012 update, and the M&H-2010 scale (Tables 1–4). The combination of astronomical and radiometric time scales shows good promise for age-calibrating and better understanding sequence stratigraphy.

How can the Aptian T-R sequences be glacio-eustatic when there is no evidence of an ice sheet in Antarctica at that time, and the mid-Cretaceous was not only ice-free but also one of the warmest times of the Greenhouse World?

Figure 4 shows that Antarctica and Australia occupied about half of the southernmost 50° including the South Pole during the Aptian. A major expansion of the ice sheet was predicted at 118.2 Ma (SB 8) in the Southern Hemisphere by the M&H-2010 time scale, and this is consistent with the sea-level drop of ca. 50 m in the global, Russian Platform and Arabian Plate sea-level curves (Figures 1 and 2). Today Antarctica’s ice sheet holds 57 to 66 m sea-level equivalent, a similar level to that implied for the Aptian. Finding additional proof-of-ice (glaciogenic rocks beneath three kilometers of ice, ice-rafted deposits, isotopic data, etc.) may be possible but requires firstly dropping the Greenhouse-Icehouse Worldview (see review in Price, 1999; Immenhauser and Matthews, 2004; Maurer et al., 2012).

How can eccentricity, particularly the 405-Kyr cycle, drive glacio-eustasy when the 41-Kyr obliquity and 100-Kyr short-eccentricity cycles clearly dominate the late Miocene to present-day sea-level curve?

To answer this question the sea-level curve of Miller et al. (2005; Enclosure 2, Table 5) was interpreted. The glacio-eustatic signatures of three major ice sheets can be approximately separated in time and absolute sea level. Antarctica’s signature before 3.3 Ma is expressed by fluctuations of 20–40 m above -20 m, the level at which it is fully-ice-loaded and holds about 90 m sea-level equivalent. The Northern Hemisphere’s ice sheets started advancing at about 3.3–3.1 Ma and their signature is expressed by sea-level fluctuations between ca. -20 to -120 m after 3.3 Ma. Greenland’s signature fluctuates by about 7–10 m starting after 3.5–3.3 Ma, and cannot be clearly separated. The signatures of the three ice sheets consist of synchronized cycles with durations of 325–545 Kyr that are modulated by the Earth’s eccentricity (not just 405 and 100 Kyr) and carried by the 41-Kyr obliquity signal. The cycles tracked the 405-Kyr Clock and were on time every few million years.

The author thanks Slah Boulila, Linda Hinnov, Chunju Huang, Joerg Mattner, Florian Maurer, Ken Miller, James Ogg and Frans van Buchem for their important comments and suggestions that have helped in clarifying aspects of the interpretations given in this paper. The interpretations in this paper, particularly those shown in Enclosure 2, do not necessarily reflect those of the above named colleagues. The author thanks GeoArabia’s Assistant Editor, Kathy Breining, for proofreading the manuscript, and Designer Arnold Egdane for interesting discussions and preparing the graphics for press.

Moujahed I. Al-Husseini founded Gulf PetroLink in 1993 in Manama, Bahrain. Gulf PetroLink is a consultancy aimed at promoting technology in the Middle East petroleum industry. Moujahed received his BSc in Engineering Science from King Fahd University of Petroleum and Minerals in Dhahran (1971), MSc in Operations Research from Stanford University, California (1972), PhD in Earth Sciences from Brown University, Rhode Island (1975) and Program for Management Development from Harvard University, Boston (1987). Moujahed joined Saudi Aramco in 1976 and was the Exploration Manager from 1989 to 1992. In 1996, Gulf PetroLink launched the journal of Middle East Petroleum Geosciences, GeoArabia, for which Moujahed is Editor-in-Chief. Moujahed also represented the GEO Conference Secretariat, Gulf PetroLink-GeoArabia in Bahrain from 1999–2004.

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