Spatial Variation in Late Ordovician Glacioeustatic Sea-Level Change ∗ Jessica R

Earth and Planetary Science Letters 496 (2018) 1–9

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Earth and Planetary Science Letters

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Spatial variation in Late Ordovician glacioeustatic sea-level change ∗ Jessica R. Creveling a, , Seth Finnegan b, Jerry X. Mitrovica c, Kristin D. Bergmann d a College of Earth, Ocean, and Atmospheric Sciences, Oregon State University, Corvallis, OR 97330, USA b Department of Integrative Biology, University of California, Berkeley, CA 94720, USA c Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138, USA d Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA a r t i c l e i n f o a b s t r a c t

Article history: Mass extinction of Late Ordovician marine fauna closely coincided with southern hemisphere glaciation. Received 26 September 2017 The sequence stratigraphic architecture of shallow marine deposits informs estimates of glacioeustatic Received in revised form 1 May 2018 sea-level change at sites both proximal and distal to the reconstructed Ordovician ice sheet(s) Accepted 6 May 2018 and contemporaneous changes in ice volume. A recent correlation framework for the stratigraphic Available online 24 May 2018 architectures of one near and one far field Late Ordovician margin concluded that the Late Ordovician Editor: B. Buffett glaciation encompassed multiple long-term cycles of ice volume growth and retreat with superimposed Keywords: higher frequency cycles. Here we posit that—similar to Cenozoic glacial cycles—glacial isostatic adjustment Ordovician can preclude synchronous and similar magnitude (or directional) changes in Late Ordovician sea glaciation level between ice proximal and ice distal locations and, hence, distort a globally correlative sequence sea level stratigraphy. We explored whether long-duration (i.e., million year) Late Ordovician glacial cycles should glacial isostatic adjustment produce a globally coherent, eustatic record of sea-level change between ice proximal and ice distal stratigraphy margins using a gravitationally self-consistent theory that accounts for the deformational, gravitational and rotational perturbations to sea level on a viscoelastic Earth model. We adopted a Late Ordovician paleogeography and a synthetic continental ice-sheet distribution and volume informed by the areal extent of glaciogenic deposits and geochemical records, respectively. We demonstrate that modeled million year Late Ordovician glacial cycles produce sea-level histories on near and far field margins that differ from eustasy, and from one another, due primarily to elastic flexure and associated gravitational effects. While predicted far-field sea-level histories faithfully preserve the temporal structure of modeled glacioeustasy, their amplitude may differ from eustasy by as much as 30–40%. The impact of glacial isostatic adjustment is largest at the margins of glaciated continents, and these effects can be of the same order of magnitude as the eustatic, and even induce a local sea-level rise during an episode of ice growth and eustatic sea-level fall, and vice versa. In this regard, stratal surfaces of maximum regression and flooding expressed at near-field margins need not reflect global (‘eustatic’) trends in ice sheet growth and decay, respectively, and thus may not provide chronostratigraphic horizons for correlation with far- field sequence stratigraphic architectures. © 2018 Elsevier B.V. All rights reserved.

1. Introduction cian ice centers, yet these local records produce contrasting and, at times, conflicting reconstructions of the duration, areal extent, and Continental ice sheets expanded across southern Gondwana volume of the Ordovician glaciation (Brenchley, 1994). during the Late Ordovician, and the attendant ocean–atmosphere The absence of pre-Hirnantian glaciogenic deposits contributes cooling and glacioeustatic sea-level fall likely initiated the Late to the view that a short-lived glaciation began and ended within ± ± Ordovician Mass Extinction (Hallam and Wignall, 1999; Sheehan, the Hirnantian Stage (445.2 1.4–443.8 1.5Ma; Brenchley, 1994; 2001; Finnegan et al., 2012). Compelling sedimentological, strati- Finney et al., 1999; Sutcliffe et al., 2000, 2001; Loi et al., 2010), or graphic and geochemical evidence for glaciation appears in sedi- persisted locally into the Silurian Period (Landovery Stage: 443.8 ± mentary basins both proximal and distal to reconstructed Ordovi- 1.5–433.4 ± 0.8Ma; Hambrey, 1985; Grahn and Caputo, 1992; Díaz-Martínez and Grahn, 2007;Le Heron and Craig, 2008). Nested surfaces of glacial erosion intercalated with peri-Gondwana ma- * Corresponding author. rine strata evidence dynamic intra-glacial ice advance and retreat E-mail address: jcreveling @ceoas .oregonstate .edu (J.R. Creveling). and delimit the maximum areal extent of Gondwanan ice, reveal- https://doi.org/10.1016/j.epsl.2018.05.008 0012-821X/© 2018 Elsevier B.V. All rights reserved. 2 J.R. Creveling et al. / Earth and Planetary Science Letters 496 (2018) 1–9 ing that, locally, the grounding line reached the continental shelf– imal and ice distal stratigraphies provide a unified and accurate slope break (Hambrey, 1985;Sutcliffe et al., 2000; Ghienne, 2003; reconstruction of Late Ordovician glacioeustasy. Le Heron et al., 2007;Le Heron and Craig, 2008). Determining whether and how stratigraphic inferences of Late In contrast to the short-lived glaciation deduced from ice- Ordovician local sea level differ from eustasy depends on robust proximal, glaciogenic strata, hierarchical stratigraphic cycles that constraints on numerous factors, including the temporal history of extend across non-glaciated, ice proximal and far-field continen- the volume and location of Ordovician ice; the rheological proper- tal margins of Darriwilian–Hirnantian age (467.3 ± 1.1–443.8 ± ties of the solid Earth; the location of paleocontinents; the shelf 1.5Ma) most parsimoniously reflect glacioeustatic sea-level change bathymetry, shoreline geometry, and topography of these conti- induced by frequent expansions and contractions of Gondwanan nents; and the temporal changes in sediment supply to each mar- ice sheets with inferred Milankovitch frequencies (e.g., Saltzman gin. Uncertainties in the Ordovician-relevant values for these pa- and Young, 2005; Desrochers et al., 2010;Loi et al., 2010;Turner rameters preclude numerical predictions of site-specific sea-level et al., 2012;Elrick et al., 2013; Ghienne et al., 2014; Dabard et change of sufficient accuracy to fit inferences determined from al., 2015). The characteristically condensed Hirnantian stratigraphic careful sequence stratigraphic analysis. Such models can, how- records from far-field successions typically encompass an erosion ever, provide qualitative, physical insight into questions about an- surface (sequence boundary) onlapped by transgressive lithofacies; cient ice configuration, volume, and melt history (e.g., Creveling ostensibly, these features reflect a single episode of glacial advance, and Mitrovica, 2014). To this end, this study explores the spa- maximum, and retreat, though these surfaces could conceal a more tial and temporal variation in sea level induced by the glacia- nuanced glacioeustatic history during glacial maximum (Ghienne tion and deglaciation of a modeled Late Ordovician ice sheet cov- et al., 2014). ering southern Gondwana using a theory that accounts for the Recently revised, high-resolution sequence stratigraphic frame- deformational, gravitational and rotational perturbations to sea works for archetypal near-field (glaciated) and far-field (non- level on a viscoelastic Earth model (Mitrovica and Milne, 2003; glaciated) locations in the Anti-Atlas Mountains of Morocco and Kendall et al., 2005). Here we demonstrate that (i) the histories Anticosti Island, Canada, respectively, appear to resolve discrep- of sea-level change along continental margins both near- and far ancies between ice proximal and ice distal stratigraphies and afield of the Late Ordovician ice sheet can differ substantially be- instead reveal a coherent, global glacioeustatic sea-level history tween locations, as well as deviate from the glacioeustatic curve; (Desrochers et al., 2010; Ghienne et al., 2014). Ghienne et al. (ii) reconstructions of glacioeustasy from far-field margins may not (2014)sequentially correlated the bounding surfaces of three latest faithfully reflect the magnitude of glacioeustasy; and, (iii) by infer- Katian–Hirnantian low-order genetic stratigraphic sequences—and ence, the stratal surfaces of transgression and regression developed a handful of subordinate, higher order and lower significance max- at near-field margins may, counter-intuitively, result from ice sheet imum regressive and maximum flooding surfaces—between the growth and melt, respectively, and thus may not serve as chronos- two locations. While this method allows for diachroneity on sur- tratigraphic horizons for correlation to far-field stratigraphies. faces at a temporal resolution below that afforded by biostratig- raphy, it assumes that fluctuations in global ice volume produce 2. A model Late Ordovician glaciation glacioeustatic sea-level rise or fall everywhere the same on the Ordovician paleoglobe, unless modulated by tectonic/geodynamic 2.1. Paleogeography and ice volume history changes in base level and/or local sediment supply. For sites unaf- fected or similarly affected by these confounding factors, or for Paleomagnetic reconstructions of Late Ordovician paleogeog- sites in which backstripping procedures removed these signals, raphy similarly place Gondwana in a south polar position and the (glacio)eustatic conceptual model only considers correlation distribute three large landmasses—Laurentia, Baltica, and Siberia— of equivalent stratal surfaces valid; for instance, under no circum- across the equatorial latitudinal band (Killian et al., 2016;Torsvik stance would a maximum flooding surface at a near field location and Cocks, 2017;Blakey, 2008), though models differ in the exact correspond temporally to the maximum regressive surface at a far paleolatitude and the position of minor landmasses and island arc field site because that would imply that global ice-volume change terranes. Here we adapt the 450 Ma paleogeography of Torsvik and ◦ could simultaneously produce glacioeustatic sea-level rise at one Cocks (2017)with a revised ∼10 northeastward shift of Laurentia location and glacioeustatic sea-level fall at the other. following Swanson-Hysell and Macdonald (2017)(Fig.1A). However, a variety of physical markers for past sea level during In detail, the paleotopography and paleobathymetry of Ordovi- Cenozoic glaciations and ongoing geodetic observations demon- cian continents are not well resolved. Coupled climate–ice sheet strate that viscoelastic deformation and local ice gravitation— models parameterized for the Ordovician reveal an insensitivity of physical processes collectively described as glacial isostatic ad- the areal extent of ice to modeled continental topography (Pohl justment (GIA)—produce site-specific time-histories of sea-level et al., 2016). Thus, we followed Creveling and Mitrovica (2014) change that may differ substantially from the eustatic, or global and prescribed an initial paleotopography consistent with modern mean, sea-level curve produced by the melting of ice sheets mean elevations. Modeled continental interiors have an elevation (e.g., Milne and Mitrovica, 2008;Raymo et al., 2011; Stocchi et of 850 m that linearly tapers to sea level (0 m) within 350 km al., 2013). For instance, the post-glacial uplift and emergence of of any shoreline; oceanward of the shoreline, the modeled conti- shelves surrounding formerly glaciated regions, like Hudson Bay nental shelf deepens to −150 m across a distance of 80 km, then (Andrews, 1970), contrasts with the prolonged submergence of far- to −2000 m over the next 30 km (the continental slope), and to field sites like Barbados (Peltier and Fairbanks, 2006), though both −3800 m over the next 300 km (the continental rise) to the depth occurred during late Pleistocene–Holocene ‘glacioeustatic’ sea-level of the modeled abyssal plain (Fig. 1B). rise. Hence, local differences in relative sea level, and concomitant The time history of Ordovician–Silurian ice volume adopted opposing trends in the creation and destruction of accommoda- here follows the reconstruction of Finnegan et al. (2011) who tion space, can characterize glacioeustasy. Thus, for certain Ceno- leveraged clumped isotope paleothermometry to deconvolve the 18 zoic glacial scenarios, corresponding stratal surfaces at near and trend in Ordovician δ Ocarb imparted by continental ice growth far field locations—for instance, sequence boundaries or maximum from the signal of coeval seawater temperature change. This ice flooding surfaces—neither correlate globally nor carry chronostrati- history, expressed in units of globally uniform sea level equiva- graphic significance. Could this also be true for the Late Ordovi- lent (SLE), expands from ice free conditions (0 m SLE) at 449 Ma cian? We sought to explore the circumstances in which ice prox- to a Hirnantian glacial maximum (henceforth, HGM) at 444.5 Ma J.R. Creveling et al. / Earth and Planetary Science Letters 496 (2018) 1–9 3

Given these areal and volumetric constraints, modeled ice height at HGM peaked at 2780 m (Fig. 3B).

2.2. Sea level theory

Our model predictions adopt the gravitationally self-consistent ice age sea-level theory developed by Mitrovica and Milne (2003) and Kendall et al. (2005)to account for the migration of shorelines due to local transgression/regression and the advance or retreat of ice from marine sectors. The latter occurs when the modeled Gondwanan ice sheet transits the continental shelf as ice volume expands and contracts around the HGM. The sea level theory also incorporates the rotational stability theory of Mitrovica et al. (2005) that accounts for the feedback into sea level of surface ice and ocean water load-induced perturbations to the Earth’s rotation vector. We note that in Pleistocene ice age calculations, the figure of the Earth adopted in computing perturbations in rotation gen- erally incorporates the known present-day excess ellipticity of the Earth (Mitrovica et al., 2005;Mitrovica and Wahr, 2011). In the absence of constraints on the figure of the Late Ordovician Earth, we set excess ellipticity to zero; we note that rotational feedback is a minor contributor to these sea level predictions and the associated uncertainty does not impact our conclusions. Fig. 1. (A) Late Ordovician paleogeography adopted from Torsvik and Cocks (2017) with a northward re-positioning of Laurentia following Swanson-Hysell and Mac- In the following, we adopt a one-dimensional, Maxwell vis- donald (2017). Ba = Baltica; Si = Siberia; AT = Armorican Terrane. (B) Modeled coelastic Earth model as is standard in the Pleistocene ice-age initial global topography and bathymetry (see text for discussion of values). (For in- literature (Peltier, 2004). We base our sea level predictions on terpretation of the colors in the figure(s), the reader is referred to the web version a pseudo-spectral algorithm (Kendall et al., 2005)with a trun- of this article.) cation at spherical harmonic degree and order 256. The elastic structure of the Earth model is taken from the seismic model PREM (Dziewonski and Anderson, 1981). We consider a ‘standard’ viscosity profile defined by an elastic (essentially infinite viscosity) lithosphere of 120 km thickness, an upper mantle viscosity of 5 × 1020 Pa s, and a lower mantle viscosity of 5 × 1021 Pa s. The boundary between the latter regions is set to 670 km depth. This profile falls within the class of viscosity models preferred in most Pleistocene ice age calculations (e.g., Lambeck et al., 1998; Mitrovica and Forte, 2004). However, in the results below, we test the sensitivity of the results to changes in the Earth model. We adopt the definition in ice-age sea level literature of ‘sea level’ as the difference between the height of the equipotential that defines the sea surface (which varies globally) and the height of the solid Earth surface. Thus, at any location on the Earth’s sur- Fig. 2. Modeled Late Ordovician ice volume in units of meters of global-average sea face, sea level may change due to a perturbation to the elevation level equivalent (SLE) as a function of time following Finnegan et al. (2011) assuming a Hirnantian age for the Ellis Bay Formation (see the conservative reconstruction of either (or both) of these bounding surfaces. We express symbol- in their Fig. S12). Modeled peak ice volume at 444.5 Ma = 130 m SLE. The sea level ically the decomposition of sea level (SL) at a site of colatitude θ predictions described in the text involve 100 time steps across this time interval. and east longitude Φ at time t, as:

SL(θ, ϕ,t) = G(θ, ϕ,t) − R(θ, ϕ,t), (1) (Fig. 2). Following a conservative estimate of Hirnantian mean 18 δ Oice composition (Finnegan et al., 2011), we adopted a eustatic where G refers to the sea surface height and R to the elevation of ice volume at HGM similar to the Last Glacial Maximum, or 130 m the solid Earth surface, and we write the change () in sea level SLE. The model is characterized by a relatively rapid ice growth in since the initiation of glaciation as: the ∼2Myr preceding the HGM and an equally rapid deglaciation in the subsequent 1Myr, followed by a gradual decrease in vol- SL(θ, ϕ,t) = G(θ, ϕ,t) − R(θ, ϕ,t). (2) ume that extends to the disappearance of the ice sheet at 437 Ma In this expression, G is the change in sea surface height and R (Fig. 2). Inasmuch, this model ice history aims to simulate the is the radial displacement of the crust. higher-order, lower frequency (i.e., Myr) cycles of Late Ordovician To elucidate the physics underlying predictions for Late Or- ice volume inferred from the stratigraphic record. dovician sea-level change at the various sites described below, we We model a single ice sheet nucleated atop southern Gondwana further decompose the sea surface height change, G, into glob- (Pohl et al., 2016)with a plastic (parabolic) equilibrium proﬁle ally uniform (G ) and geographically variable (G ) terms (e.g., (Cuffey and Paterson, 2010) whose geometry during the deglacia- Φ ψ Kendall et al., 2005): tion phase matches that of the glaciation phase whenever ice vol- umes are the same (Fig. 3A). We assume that the ice sheet reached SL(θ, ϕ,t) = GΦ (t) + Gψ (θ, ϕ,t) − R(θ, ϕ,t). (3) the edge of the southern Gondwana continental shelf at glacial maximum (Le Heron et al., 2007;Le Heron and Craig, 2008) and The term GΦ differs from the eustatic sea level change largely ◦ prescribe a northern latitudinal limit of 45 S (Pohl et al., 2016). because the mean crustal elevation of the ocean changes with 4 J.R. Creveling et al. / Earth and Planetary Science Letters 496 (2018) 1–9

Fig. 3. Modeled Late Ordovician ice geometry and the superimposed locations of three profiles across Laurentia, Armorica, and Arabia selected to illustrate the time history of RSL through the model Late Ordovician glacial cycle (see Fig. 2). The map of paleogeography is a stereographic projection centered at the South Pole and extending to the equator. (A) The perimeter of the model ice sheet at glacial maximum (444.5 Ma; see Fig. 2) and at 80%, 60%, 40% and 20% of this maximum ice volume. (B) Model ice thickness at glacial maximum in increments of 500 m, with a peak thickness of 2780 m. The number next to each profile represents the number of sites along each: Armorican profile, sites 1–8 (see Fig. 5A); Arabian profile, sites 1–7 (see Fig. 5B), Laurentian profile, sites 1–5 (see Fig. 5C). time in a GIA simulation. Finally, we refer below to predictions Predicted post-glacial rebound of the formerly ice-covered re- of relative sea level (RSL), which we define as the elevation of any gion of southern Gondwana produces a net sea-level fall that shoreline marker of age t relative to sea level at the end of the peaks at ∼700 m (relative to the eustatic curve) at the center of the model ice sheet (Fig. 4B). The predicted departures from eu- simulation (t f , 437 Ma; see Fig. 2): stasy distant from the perimeter of the ice sheet, and throughout the global ocean, are of smaller amplitude, typically varying from RSL(θ, ϕ,t) = SL(θ, ϕ,t) − SL(θ, ϕ,t ). (4) f ∼+50 to −25 m (Fig. 4A). The spatial pattern of these departures The question remains how numerical predictions of sea level re- reveals that they arise largely from flexure of the elastic litho- late to inferences of glacioeustasy determined from shelf strati- sphere, which results because the modeled duration of ice sheet graphic architectures. Since the aforementioned definition of sea volume changes (i.e., Myr) exceeds the dominant decay times that level is synonymous with the stratigraphic concept of ‘accom- govern GIA (i.e., kyrs). (Henceforth we will use the term ‘flexure’ modation space’ (e.g., Posamentier et al., 1981), and sequence to describe the ice and ocean load-induced crustal deformation al- stratigraphic architectural units and their bounding surfaces re- though, even on the protracted time scale considered here, viscous flect the interplay between accommodation and sedimentation effects, while relatively small, are non-zero.) The contribution of (Catuneanu et al., 2009), our numerical predictions accord with lithospheric flexure is evident on these maps in two ways. First, sequence stratigraphic architectural units that: (i) are deemed to in marine areas surrounding the region of model ice cover, a lo- calized (short wavelength) peripheral zone of subsidence predicted reflect glacioeustatic sea-level change, and do not, or only min- across the interval from HGM to 437 Ma leads to sea-level rise imally, reflect accommodation change related to sedimentation ∼25 m in excess of the eustatic rise. By comparison, in predic- and/or tectonism, or (ii) have been corrected for the mechanisms tions of Pleistocene relative sea level, viscous effects produce a far that increase or decrease accommodation via a method such as more extensive zone of peripheral subsidence (e.g., Creveling et al., backstripping. 2017). Elastic flexure, however, has a spatial scale governed by the thickness of the elastic lithosphere which, for the model predic- 3. Results tion in Fig. 4, is 120 km. The hinge point of the ice-load-induced tilting extends slightly oceanward of the shoreline (Fig. 4B, where We begin with a global prediction of RSL (equation (4)) at HGM, the 0–90 m yellow contour extends into the ocean surrounding though to isolate the predicted departures from eustasy arising the ice sheet.) Second, far-afield from the ice sheet, ocean load- from glacial isostatic adjustment, we have removed from this RSL ing leads to continental uplift (and sea-level fall) and subsidence prediction the modeled eustatic sea-level rise between the HGM of the oceanic crust (sea-level rise). The interface between these and the end of glaciation (i.e., SLEHGM–SLE437 Ma = 130 m; Fig. 4). regions is characterized by a flexural tilting of the crust over a spa- The global map (Fig. 4A) and the stereographic southern hemi- tial scale that is once again a function of the lithospheric thickness. sphere projection (Fig. 4B) allow us to explore the distinct mag- This flexural tilting is manifest as a gradient in eustatic departures nitudes of departure from eustasy for various regions on the Late (Fig. 4A) where, closer to the continent, uplift-induced sea-level Ordovician paleo-globe. fall attenuates the eustatic rise (cool colors) and, more oceanward, J.R. Creveling et al. / Earth and Planetary Science Letters 496 (2018) 1–9 5

Fig. 4. Predicted relative sea level (RSL; see equation (4)) at the model Hirnantian Glacial Maximum (444.5 Ma; see Figs. 2 and 3) as (A) a global map and (B) a stereographic projection centered at the South Pole and extending to the equator. In both maps the eustatic sea-level change from HGM to the end of the simulation (130 m; see Fig. 2) has been removed from the prediction to emphasize the spatial deviations from eustasy. Note that the right scale bar—RSL in meters, from −360 to 720 m—corresponds to the amplitude of RSL change at near-field locations emphasized in frame (B) and the left scale bar—RSL from −24 to 48 m—corresponds to the amplitude of RSL at far-field locations emphasized in frame (A). The entirety of the far-field (left) scale is encompassed within the yellow and orange colorbar divisions of the near-field (right) scale; for this reason, for instance, the red-colored, negative RSL values around southern Gondwana (Frame A, −6 to −24 m) appear in orange in Frame B. subsidence of the crust produces a magnified sea-level rise (warm colors). This modeling exercise demonstrates that GIA induces spatially variable departures from eustasy that are largest in regions surrounding far field continental shorelines and in the near field of the model Gondwana ice sheet, which at HGM extended to the edge of the continental shelf. To explore these regional departures from eustasy in greater detail, we computed time-histories of RSL for 20 sites along three profiles representing: (1) a near-field region, from the Armorica Terrane to the southern margin of Gond- wana; (2) a transect across the inundated, shallow marine Arabian crustal block, distal from the southern Gondwana ice sheet; and (3) a far-field transect orthogonal to the southern margin of Lauren- tia (Fig. 3). Comparisons of the time histories of predicted RSL at all 20 sites for the full glacial–deglacial simulation (black lines) to the eustatic sea-level change associated with the model ice volume (red lines) reveal local departures from eustasy along a profile, and differences in sea-level histories between profiles (Fig. 5). The predicted RSL histories along the Laurentian profile, in the far field of the Late Ordovician ice sheet, show the same temporal structure and directional trend as the eustatic curve; however, the amplitude of the departure from eustasy increases landward along the profile (Fig. 5C). The largest departure coincides with the HGM, and it reaches ∼40 m at the northernmost site along the profile. This trend can be seen spatially in Fig. 4. During the model deglaciation, for example, the eustatic sea-level rise increases the ocean load (on oceanic crust and continental shelves), but does not load the remaining continent. This causes a tilting of the crust downward towards the ocean and upward towards the continent (as discussed in the context of the far-field flexure signal in Fig. 4A). Therefore, as one moves landward along the profile, GIA will drive a progressively more pronounced crustal uplift during the deglaciation that acts in opposition to—and ef- fectively attenuates—the glacioeustatic rise (Fig. 5C). In this region, the RSL prediction at the most oceanward site (site 1) most closely matches the eustatic. Fig. 5. RSL predictions for the model simulation at sites along (A) the Armorican profile, 8 sites; (B) the Arabian profile, 7 sites; and (C) the Laurentian profile, 5 We next explore the two profiles whose constituent sites sat sites. See Fig. 3 for the location of these profiles. Note that dashed sections of the close to and under the model ice sheet at its maximum extent RSL histories in frames (A) and (B) depict the interval over which ice covered the during the HGM (Figs. 5A, B). (Note that dashed sections of the site and will not have a marine sedimentary record that preserves relative sea level. RSL histories in Figs. 5A and 5B indicate the interval over which The red line on each frame is the modeled eustatic (globally averaged) sea-level ice covered the site.) The general trend in the Armorican (sites change for the adopted ice history (see Fig. 2). The profiles in frames (A)–(C) extend 1250 km, 2250 km, and 1100 km, respectively. The numbered sites are not evenly 2–8) and Arabian (sites 1–7) profiles shows the dramatic impact distributed along these profiles. of GIA on predictions of relative sea level as one moves landward 6 J.R. Creveling et al. / Earth and Planetary Science Letters 496 (2018) 1–9

Fig. 6. The time history of RSL predictions at (A) Armorica site 6 and (B) Laurentia site 4 (solid black lines reproduced from Fig. 5A) decomposed into contributions from the perturbation to the sea surface height (solid blue line) and crustal displacement (dotted green line). The former is further decomposed (see equation (3)in the text) into a geographically uniform (dotted blue line) and geographically variable (dashed blue line) perturbation. Line colors apply to both frames (A) and (B). along the profiles toward the model Late Ordovician ice sheet. For the system were in perfect isostatic equilibrium, then these two instance, while we modeled 65 m of eustatic sea-level rise in the signals would have canceled; however, strength in the elastic litho- 1 Myr after the HGM, we predict a coeval 35 m sea-level fall at sphere ensures that, even over such long time scales (order Myr), Armorica site 7, a differential amplitude of ∼100 m and one of the gravitational effect of crustal displacement does not cancel the opposite trend to the eustatic history (Fig. 5A). We note that the direct gravitational effect, such that the system remains in isostatic non-monotonicity in the sea level histories along the Armorican disequilibrium. In this case, the sum of the two signals (the geo- profile results from this profile initiating near the eastern mar- graphically variable component of the sea surface height) leads to gin of the Armorican Terrane (site 1), transiting the shallow sea an elevation of the sea surface during glaciation and a lowering of to the east (site 2), and continuing a landward transect up south- this surface during deglaciation (Fig. 6A, dashed blue line). ern Gondwana (sites 3–8). Thus, the profile trends landward as one Next, we examine the temporal history of crustal displacement moves from site 2 to site 1 and from site 2 to site 8, and in this (R(θ, ϕ, t); Fig. 6A, dotted green line). Following equations (2) regard the trend in RSL predictions from sites 2–8 (Fig. 5A) closely and (3), the total sea-level change (Fig. 6A, solid black line) equals matches that of the Arabian profile (Fig. 5B). G(θ, φ, t) (solid blue line) minus R(θ, ϕ, t) (the dotted green Clearly post-glacial rebound of near-field sites contributes to line). Over most of the simulation, this site remained at the pe- these departures from eustasy and, as discussed above, this ef- riphery of the ice sheet and the crust was deflected upward as fect extends beyond the margin of the ice sheet at HGM (e.g., see the ice sheet grew and downward as the ice sheet waned. The Armorican profile, sites 4 and 5; Fig. 5A). But is the GIA signal exception is the ∼1Myr interval around the HGM, when the ice along the Armorican and Arabian profiles entirely a consequence sheet was sufficiently close to the site that it experienced a rapid of crustal rebound? To answer this question, we decomposed the subsidence during the last phase of glaciation and uplift during sea level prediction at Armorica site 6 into the various contribut- the initial phase of deglaciation. Note that this trend occurs even ing terms summarized in equations (2) and (3)(Fig.6A). We first when the site is outside the ice sheet perimeter because, as we focus on the net deflection of the sea surface (G(θ, φ, t), solid noted above, flexure acts to smooth the crustal displacement field blue line), which is a sum of the contributions from geographi- (i.e., the hinge point on the crustal displacement is pushed out- cally uniform (GΦ (t), dotted blue line) and geographically vari- ward from the ice sheet margin). In summary, while one would able (Gφ(θ, φ, t), dashed blue line) perturbations to sea surface anticipate that the large departures from eustasy seen at near-field height. The latter represents the local gravitational effect of the GIA sites result from crustal displacements alone (Fig. 6A), these re- process on the sea surface elevation. As the model ice sheet grew sults demonstrate that the relative sea level histories at sites close toward HGM (prior to 444.5 Ma), it exerted a direct gravitational to the ice sheet margin have significant contributions from both pull on the ocean and raised the sea surface. This was countered crustal elevation changes and perturbations to the gravity field. by subsidence beneath the ice sheet, which acted to weaken the We performed an analogous decomposition of the sea level his- gravitational pull and lower the local sea surface equipotential. If tory at Laurentia site 4 (Fig. 6B; see also Figs. 3 and 5C). The site J.R. Creveling et al. / Earth and Planetary Science Letters 496 (2018) 1–9 7

regard, our singular focus on the background state—or long-term history—of the ice sheet; any more rapid changes in ice sheet volume, such as those produced by Milankovitch forcing, would be superimposed on this background state and would show a more significant sensitivity to mantle viscosity.) In contrast, the near field (Armorican and Arabian profiles) predictions do show sensitivity to lithospheric thickness (Fig. 7, solid versus dashed lines). As indicated above, sea level predictions near the margin of the ice sheet at HGM will show significant discrepancies with the eustatic sea-level curve due to crustal deformation, and the associated local gravitational perturbation, resulting from flexure. The geometry and magnitude of this flexure is a strong function of the thickness of the lithosphere.

4. Discussion

Robust inferences of Late Ordovician glacioeustasy require a deliberate selection of field sites. For the case of the Myr- duration Late Ordovician glacial cycles modeled here, far-field localities preserve a robust temporal history of Late Ordovician ice-volume change, but flexure arising from these changes can progressively attenuate the amplitude of glacioeustasy landward along a continental shelf (Figs. 4A, 5C). For this reason, inferences of glacioeustasy at sites that represent shallow environments on far-field paleo-margins could misrepresent the amplitude of glacioeustatic fluctuation. For far field localities that preserve a transverse cross-section of a continental shelf or ramp, the applica- tion of backstripping methods (e.g., Loi et al., 2010) to facies-based inferences of water depth from the site(s) situated furthest down depositional dip will most closely approximate the magnitude of glacioeustasy, but the site-specific departure from eustasy will depend on how the geometry of the coastline maps on to the relatively smooth pattern of ocean-load–induced flexural deformation. However, the most distal depositional environment preserved Fig. 7. RSL predictions for the model simulation at (A) Armorica site 6; (B) Arabia (or exposed) at a given field area need not have been situated site 4, and (C) Laurentia site 4. The solid black line on each frame reproduces the outboard of the zone of flexure, and thus stratigraphic-based infer- result in Fig. 5. The dashed lines are predictions from a simulation in which the ences of local sea level could differ from eustasy by up to 30–40%. lithospheric thickness of the Earth model was reduced to 72 km, while the dotted lines are generated using a model in which the lower mantle viscosity is increased As we have noted, the spatial-scale of flexure depends largely to 3 × 1022 Pa s. The identical red line on each frame is the eustatic (globally aver- on the thickness of the underlying elastic lithosphere, although aged) sea-level change for the ice history (see Fig. 2). gravitational effects associated with the departure from isostatic equilibrium will have a larger spatial scale; while lithospheric sits on the landward side of the ocean-load induced tilting evident thickness can be estimated for paleo-continents (Grotzinger and in Fig. 4A and so it experiences local subsidence during glaciation Royden, 1990), it is not known precisely for the Late Ordovician. and uplift during deglaciation. This deformation is accompanied by Indeed, quantitative constraints on the down-dip attenuation of a similar trend in the geographically variable (i.e., local) compo- the amplitude of relative sea-level change arising from a single nent of the sea surface elevation. Since these trends follow the cycle of glacioeustatic change could provide a novel estimate of general time history of the eustatic curve, the net effect is that the the flexural rigidity (or, equivalently, the effective elastic litho- (total) relative sea level change (Fig. 6B solid black line) also tracks sphere thickness) of Late Ordovician paleocontinents. Moreover, the eustatic curve, albeit at a reduced amplitude. For instance the the higher fidelity of the glacioeustaic signal at down-dip loca- HGM low stand of 100 m at Laurentia site 4 is not as large as the tions presents a possible paradox for stratigraphic-based inferences modeled eustatic value of −130 m (Fig. 5C). of glacioeustatic sea-level change in that a site located sufficiently The results presented in Figs. 4 and 5 are based on a single offshore so as to minimize elastic flexure may also be character- viscoelastic Earth model with a viscosity profile consistent with ized by facies belts rather insensitive to the depth change of the analyses of various Holocene geologic and geodetic observations typical glacioeustatic amplitude (i.e., order 101–102 m). related to the GIA process. We evaluated the sensitivity of the re- Our model simulations also demonstrate that Late Ordovician sults to this choice by running two additional simulations. In the ice sheet growth and decay can simultaneously produce divergent first, we reduced the lithospheric thickness from 120 km to 72 km, and even opposing sea-level histories across ice proximal continen- and in the second we increased the lower mantle viscosity by a tal shelves (Figs. 5A, B) and between near- and far-field locations factor of six, from 5 × 1021 Pa s to 3 × 1022 Pa s. Fig. 7 shows the (Fig. 5A, B and C). For long-duration glacial cycles, those sites prox- predicted RSL curves for an illustrative site on all three profiles. imal to, and overlain by, the ice sheet will display a sea-level rise The RSL predictions are relatively insensitive to the adopted man- leading into and during the glacial maximum as a result of litho- tle viscosity (Fig. 7, solid versus dotted lines) because the mod- spheric deformation and gravitational attraction in response to the eled loading history has a time scale that is much longer than ice load; these same sites will experience a sea-level fall in the ini- the dominant viscous decay times associated with any realistic tial stages of the deglaciation as the crust rebounds elastically and Earth model. That is, viscous effects have largely relaxed in cal- the gravitational attraction relaxes in response to a diminished ice culations of sea-level change over this time scale. (We note, in this volume. In this regard, ice proximal settings experience a direc- 8 J.R. Creveling et al. / Earth and Planetary Science Letters 496 (2018) 1–9 tional change in the creation and destruction of accommodation level is rapidly falling, and vice versa, when the site is close to space counter to that predicted by contemporaneous, ‘glacioeustat- the evolving ice margin. In this regard, near-field stratal surfaces ic’ ice volume growth; for the model duration of ice volume fluctu- of maximum regression and flooding need not reflect global (‘eu- ation considered here, these changes may persist for 100–500 kyr static’) trends in ice sheet growth and decay, respectively, and thus (Fig. 5A, B). Thus, an episode of glacioeustatic sea-level fall as- may not provide chronostratigraphic horizons for correlation with sociated with ice volume growth may appear as a transgressive far-field sequence architectures. At continental margins in the far surface (or retrogradational stratal package) at ice-proximal sites field of the glaciation, local sea level variations preserve the tem- (e.g., Fig. 5A, Armorican profile, sites 4–8)—including those sites poral structure of the eustatic trend, but the amplitude can depart not directly overlain by the ice sheet (e.g., Fig. 5A, Armorican pro- from this trend by as much as 30–40%. file, sites 4 and 5)—and temporally correlate to a regressive surface Our predictions adopt a synthetic Hirnantian glacial maximum (or progradational/degradational stratal package) at ice-distal sites (444.5 Ma) ice volume that is equivalent to a 130 m SLE drawdown located further down depositional dip of the glaciated margin (e.g., relative to the end of the glaciation (437 Ma) (Fig. 2). However, Fig. 5A, Armorican profile, sites 1–3) or at far-field margins (e.g., the HGM ice volume may have been larger or smaller (Pohl et al., Fig. 5C, Laurentian profile, sites 1–5), assuming, of course, that 2016). Importantly, our modeling predictions scale quasi-linearly the latter sequence architectures reflect glacioeustasy and not dy- with the excess ice volume between HGM and end glaciation. If namics related to tectonism or local sedimentation. Likewise, at the excess ice volume at HGM were, for example, 260 m, then the ice-proximal margins, regressive surfaces may evidence and coin- amplitudes in Fig. 4 would scale up by a factor of 2 and the spa- cide with global ‘glacioeustatic’ rise and episodes of ice volume tial patterns would remain relatively unaltered. For instance, while melt, and hence correlate with transgressive surfaces developed the details of site-specific sea level histories near coastlines would across far-field continental margins. change (e.g., Fig. 5)—since a larger ice volume change causes a Here we modeled a long-duration Late Ordovician cycle of ice larger migration of shorelines, and this impacts predicted depar- volume growth and decay (Fig. 2), but numerous stratigraphic tures from eustasy—the percent departure in the amplitude relative studies have concluded that the Late Ordovician glaciation was to the eustatic trend would be relatively robust. comprised of a hierarchy of higher-order, lower-significance depo- The predictions presented here are sensitive to lithospheric sitional cycles analogous to Cenozoic glaciation (e.g., Ghienne et thickness, but not to mantle viscosity; the latter insensitivity is a al., 2014), and some ascribe Milankovitch periodicities—specifically consequence of the long-duration modeled Late Ordovician glacia- a 400-kyr eccentricity cycle and subordinate ∼100 and ∼20 kyr tion adopted here, and reflects the fact that on the time scale orbital cycles—to these constituent depositional sequences (e.g., associated with this ice/ocean loading, relaxation associated with Loi et al., 2010; Dabard et al., 2015). If robust, then future nu- viscous effects in the mantle will be complete. Thus, any depar- merical modeling should incorporate these superimposed, smaller- ture from isostatic equilibrium largely results from the presence of amplitude fluctuations in global ice volume. While stratigraphic the elastic (high viscosity) lithosphere, and the gravitational effects inferences need necessarily inform the amplitude of these higher- associated with this disequilibrium. The same would not be true order fluctuations, we caution that the viscous deformation arising for the sea level response to shorter time-scale ice mass fluctua- from more rapid glacial–interglacial cycles will combine with the tions superimposed onto the long time scale trends, where viscous aforementioned effects dominated by elastic deformation to pro- effects would drive departures from eustasy with a distinct geom- duce local relative sea-level histories that, like the Plio–Pleistocene, etry and amplitude. Future modeling efforts should focus on these substantially differ from glacioeustasy (e.g., Raymo et al., 2011). oscillations. In this regard, our model predictions serve to caution stratig- raphers of the potential pitfalls of correlating near- and far field Acknowledgements stratigraphic successions in attempts to refine chronostratigraphic frameworks of Late Ordovician (or other) glaciation. Our approach We gratefully acknowledge the constructive review by Steven has been intentionally broad, and we have not undertaken a rigor- Holland and the editorial work of Bruce Buffett. We thank Jacque- ous analysis to predict site-specific histories of relative sea level line Austermann for discussion and Francis J. Sousa for assistance around the Late Ordovician paleoglobe. Future efforts to do so with figures. This research was supported in part by a donation could leverage any contemporaneous and contrasting records of from the G. 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