Late Quaternary glacio- and hydro-isostasy, on a layered earth

QUATERNARY

RESEARCH

4,

Late Quaternary

Glacio-

and

Hydro-isostasy,

on a Layered

Earth

J. CHAPPELL~ Received

March

IB, 1974

Isostatic response of the Earth to changes in Quaternary Times of ice and water loads is partly elastic, and partly involves viscous mantle flow. The relaxation sprctrum of the Earth, crit,ical for estimation of the mantle flow component, is estimated from published determinations of Fennoscandian and Laurentide rebound, and of the nontidal acceleration of the Earth’s rotation. The spectrum is consistent with an asthenosphere viscosity around lO”P, and a viscosity around I@P below 400 km depth. Calculation of relaxation effects is done by convoluting the load history with the response function in spherical harmonics for global effects, and in rectangular or cylindrical transforms for smaller regional effects. Broad-scale deformation of the globe, resulting from the last deglaciation and sea level rise, is calculated to have involved an average depression of ocean basins of about 8 m, and mean upward movement of continents of about 16 m, relative to the center of the Earth, in the last 7000 yr. Deflection in the ocean margin “hinge zone” varies with continental shelf geometry and rigidity of the underlying lithosphere: predictions are made for different model cases. The computational methods is checked by predicting Fennoscandian and Laurentide postglacial warping, from published estimates of icecap histories, with good results. The depth variations of shorelines formed around 17,000 BP (e.g., North America, 90-130 m; Australia, 130-170 m), are largely explainable in t,erms of combined elastic and relaxation isostasy. Differences between Holocene eustatic records from oceanic islands (Micronesia, Bermuda), and continental coasts (eastern North America. Australia), are largely but not entirely explained in the same terms.

INTRODUCTION Hydroisostasy, the concept that meltwater from Pleistocene icecaps produced loadings of ocean floors such that significant global deformation followed, recently has been examined by Walcott (1972a). The earlier qualitative assessments of hydroisostasy as an important factor in glacioeustatism (e.g., Daly, 1925; Bloom, 1967; Marner, 1970) are quantitatively supported by Walcott, who also demonstrates that the effects of glacioeustatic inundation will vary with location. For example, hydroisostatic warping may introduce differences of up to 3070 between esti‘Department of Geography, School of General Studies, Australian National University Canberra, A.C.T.

mates of Flandrian transgression rates from oceanic islands, on one hand, and continental coasts, on the other. Hydroisostatic effects on the continental shelf are of particular interest, as can be illustrated by three aspects of Quaternary studies: (i) to understand fully the diffcrences between glacioeustatic records from different shelves, and from different places within shelves, hydroisostatic processes must accurately be identified; (ii) deformations of this origin will affect the distribution of sedimentary facies on shelves, and possibly the distribution of economic sedimentary deposits; (i.i) knowledge of such deformations can improve the estimation of Quaternary paleogeography in the shallow seas areas. Analysis of hydroisostasy at a level sufficiently detailed for 405

Copyright All rights

@ 1974 by University of reproduction in any

of Washington. form reserved.

406

J.

a

Elastic warping.

b

Relaxation:

CHAPPELL

(.Walcott, 1972)

flow in mantle,

downward

of ocean

uplift

floors,

movement

of landmasses.

RG. 1. Elements of isostatic deformation resulting from ice unloading and sea level rise. (a) elastic deformations after Walcott (1972a) ; (b) viscous relaxation:-tendency of mantle ilOWE.

elaboration of points (i)-(iii) must, however, include consideration of broad-scale changes in the figure of the Earth, as these cause the magnitude of glacioeustatic transgression to vary around the globe. The process of isostatic adjustment to changing water and ice loads includes instantaneous elastic deflection of the Earth’s surface, together with slow deformation involving redistribution of mass in the mantle. The elastic distortion is very broad, expressed mainly by low degree

harmonics of the Earth’s figure, and has been calculated by Walcott (1972a) whose results are reproduced in Fig. la. Estimation of the slow deformation, which may be referred to as “relaxation” and is most clearly observable in the continuing modern rebound of Fennoscandia and of the Laurentide area, is the principal topic of this paper. Especially under discussion will be movements near ocean margins, and the implications of paleo-sea level estimates within the last 17,000 yr from various parts

~~TAT~C

~EsPo~sm

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EARTH

407

of the world. A generalization of the relaxaFurther tests are outlined for the theory of tion process is shown in Fig. lb. hydroisostasy. Relaxation behavior of the Earth, espeRELAXATION OF cially in the formerly glaciated areas of SURFACE DEFORMATIONS Scandinavia and North America, is the subject of a considerable literature. Reviewed Primary data for estimating the Earth’s by Walcott (1973)) various models of the relaxation behavior come from the raised Earth’s structure have been proposed on the and tilted postglacial strandlines in Fenbasis of glacioisostatic rebound data, rangnoscandia, and from similar deformation in ing from models having uniform viscosity North America. Salient among recent analto various depths within the mantle, yses of Fennoscandian rebound is that of t,hrough those incorporating a layered visc- McConnell (1968), who uses the strandline ous structure beneath an elastic lithosphere, reconstructions given by Sauramo (1958) to layered viscoelastic models. Although the to estimate relaxation time 7(u) as a funcrange is wide of physical models, certain tion of wave number u. McConnell cornpoints are agreed upon: (i) The evidence pares the observed spectrum ~(11) w,th the of glacioisostatic rebound indicates that re- computed relaxation behaviors of several laxation rate varies with wavelength of de- rectilinear Earth models, incorporating formation or, if a spherical harmonic de- layered viscous structure beneath an elastic scription is used, the harmonic degree of de- lithosphere, and then calibrates a “best” formation; (ii) relaxation behavior of the Earth model. If this final model were actheoretical models is linear, with exponenceptable, it would provide the basis for extial relaxation of deformation at any given trapolating the relaxation spectrum to low wavelength or degree, which appears con- degree harmonics, necessary for estimating sistent with observations of glacioisostasy; global hydroisost,atic effects. However, sev(iiij flexural rigidity of the lithosphere, eral criticisms of McConnell’s empirical which varies between continental and other spectrums are listed by Walcott (1973) : he situations, filt’ers out surface deformations assumed (a) that no deformation occurred shorter than a certain wavelength. beyond 800 km from the center of rebound, There is a range of opinion about the (b) that deformation prior to complete manner in which relaxation time constant deglaciation (8500 yr BP) was solely a varies with wavelength, or degree, of deforrelaxation effect, and (c) a circular approximation. The form of the relaxation spec- mation was adequate to describe the eiliptitrum is important for estimation of hydrocal uplift pattern. Furthermore, profiles and isostatic effects, which encompass a wide ages of Fennoscandian shorelines hare I~ccn range of deformation scale, and the matter reevaluated s:nce Sauramo’s (1958) e*tiis reviewed in the first part of this paper. (1966) and Donncr mates, by Hyyppb A preferred range of relaxation spectra is (1968). As a result, the extremes are likely selected, and checked by backward calculato be in error of McConnell’s relaxation spectrum, which ranges over wave numhcrs tion of Fennoscandian and North American glacioisostatic profiles, which are compared of about 1000 km-’ to 100 km-‘. In fart, with observed profiles. In the main and McConnell’s estimate of about 4000 yr for deformation in southeast final section of the paper, calculations are the dominant Fennoscandia (at wave numbers around made of aspects of hydroisostatic deformation of the globe, and more especially of 300 km-l, or harmonics around degree 201, deformation near ocean margins. The re- appears too low when compared with modern uplift and gravity data, and Walcot,t sults are compared with relative sea level (1973) estimates 8000 yr t,o br the characdata of the last 17,000 yr from different terist’c Fennoscandian relaxation time. places, and certain discrepancies explained.

408

3.

CHAPPELL

The problem of estimating satisfactory parameters for a layered Earth model has proved to be no less difficult that interpretation of relaxation spectra from deformed shorelines. Published estimates of factors such as asthenosphere viscosity vary with the type of model chosen. A suitably comprehensive model analysed by McConnell (1965) is a system of viscous layers underlying a surface elastic layer; McConnell’s analysis of a rectilinear system cannot directly be used to estimate relaxation behavior of a similarly layered sphere, however, especially for low degree deformations. O’Connell (1971) calculates relaxation spectra for similar spherical models, showing substantially longer relaxation times for harmonics of degrees lower than about 12 than are given by the rectilinear models. Furthermore, such elastic-overviscous models do not treat mantle elasticity, and McKenzie (1967) shows that the effect of treating the mantle as viscoelastic rather than viscous is to increase relaxation times for any viscosity distribution. Walcott (1973) points out that the effect is maximal around degree 20, and that estimates of viscosity from deformations around this order (such as Fennoscandian rebound) will be too large by a factor of 2. There is considerable uncertainty attached to the direct estimation of relaxation times for low degree deformations, by extrapolating from Earth models which fit glacioisostatic rebound data, because viscosities below the asthenosphere become critical. A lead is given by nontidal acceleration of Earth’s rotation, which has been regarded as a response to isostatic adjustment to postglacial water loads (the moment of inertia decreases as the second degree zonal component of surface loading approaches compensation). O’Connell (1971) shows the relationships between secular acceleration and second degree relaxation time to vary in the manner shown in Fig. 2a. The width of the hatchured curve corresponds to uncertainty about the

precise course of postglacial sea level rise. Estimates of nontidal acceleration by Fotheringham (in Munk and MacDonald, 1960) and by Newton (1968) suggest relaxation times of either 2000 or 100,000 yr (intersections by hatchured curve and stippled band, Fig. 2a). O’Connell shows the 100,000 yr value to be very unlikely, because correlation is negligible between the geopotential and the potential which would have existed immediately after deglaciation, indicating that any large-scale anomalies resulting from deglaciation have mostly decayed. The mean mantle viscosity corresponding to the 2000-yr relaxation time is estimated by O’Connell (1971) to be around 6 X 10elP. Walcott (1973) argues that such a low value is incompatible with present uplift rates in Canada and Scandinavia. O’Connell’s result is not particularly sensitive to the sea level curve used, and resolution of the issue probably lies with the estimate for nontidal acceleration. Newton (1969) revises all prior work, concluding that nontidal acceleration is four times greater than previously thought; this result implies a second degree relaxation time of around 10,000 yr (intersection of hatchured curve with heavy line, Fig. 2a). This value is accepted in this paper, as it is consistent with a mean mantle viscosity close to 10Z3P, which in turn is compatible with glacioisostatic rebound and with the seismologybased estimate of mantle viscos:ty by Anderson and O’Connell (1967). A relaxation spectrum for calculations of hydroisostasy now can be fixed. Relaxation estimates for Fennoscandian and Northern American rebound (from McConnell, 1968, and Walcott, 1973), and for the nontidal acceleration, are plotted in a frame of relaxation time versus deformation degree/equivalent wave number in Fig. 2b. Also shown are relaxation behaviors of two Earth models (elastic lithosphere over layered viscous mantle), calculated by O’Connell (1971). These curves bound the stippled zone enveloping the empirical re-

ISOTATIC

RESPONSES

OF

409

EARTH

Result of Newton (1969) acCeh%3tiOn according to Newton (1968) c and earlier work

Non-tidal

1

...I

.(I’

b

‘

lo3

!t?

Relaxation

..,’

.((I

’

I,,’

IO4 lo5 Relaxation time lyears)

“’

IO6

Spectrum

100 Fsnnoscandian

h%iC

relaxation,

wave number Km-’

i

,. McConnell (1968) 2. Walcott (1973) Laurentide relaxation, c Walcott

(1973)

b 2nd degree relaxation,

I

,

I

I .*.*.I’

IO4

lo3

/

lo5

Relaxationtime Iyears)

C 0

102*

102’ I Elastic

10Z3

1(lz4 Vismsity poise I

p = 6.5~10”

--------5

a

Ib

1

\i viscosity

constant t0 COW

FIQ. 2. Relaxation behavior of the Earth. (a) relationship between relaxation time of second degree deformation. and nontidal acceleration resulting from postglacial sea level rise (hatchured broad curve, after O’Connell, 1971). Estimates of nontidal acceleration, shown aa horizontal bands. (b) Relaxation estimates for Fennoscandian and Laurentide rebound, and for nontidal acceleration, approximately fitted by relaxation spectra of two Earth models. Corresponding Earth model structures, calculated by O’Connell (1971), are shown in cc).

laxation data, and indicate the range of uncertainty accepted in this paper about global relaxation. The lower boundary corresponds to McConnell’s (1968) rectilinear

Earth model 62-12, recalculated by O’Connell for a spherical density-stratified Earth; and the upper boundary corresponds to an asthenosphere viscosity around 3.5 x 102’P,

410

S. CHAPPELL

FIQ. 3. Mean effects of deglaciation and sea level rise, calculated over harmonics 1-8: curve A-model course of deglaciation ; B-mean deflection of ocean floors ; C-movement of landmasses; D-sea level change relative to center of Earth.

with 10Z3P for the rest of the mantle: these structures are shown in Fig. 2~. In both cases the base of the asthenoshpere is placed at 400 km, at the pyroxene-garnet, olivene-/3 (MgFe) SiO, phase transition. O’Connell’s viscosity estimates do not take into account the effects of mantle elasticity, identified by McKenzie (1967). As a result the O’Connell values are somewhat high, especially in the upper mantle, and the viscosity values in the upper 400 km or so should be reduced by a factor of 2, in Fig. 2~. CALCULATION OF HYDROISOSTATIC DEFORMATION When a surface load is altered instantaneously upon the linear Earth models discussed in the previous section, the responding deformation at any degree n exponentially approaches equilibrium with relaxation time I. Because Late Quaternary ice and water loads vary through time, the nth degree of this load, u%(t), must be convoluted with the response function togive’ the course of deformation. The associated mass redistribution in the man-

tle can also be treated as a surface load (O’Connell, 1971), and the total uncompensated surface load s,(t) is then related to changing ice and water loads as Sdt> = unit> 1 -r/r(n) t --e u%(C)er’r(n) - d{. r(n) /0

(1)

The relative motion of ocean basins and continents resulting from a sea level rise, schematically indicated in Fig. lb, are now discussed. Mean downward deflection of the sea floor is proportional to compensation at any time, which is expressed by the righthand term of the RHS of (I). The constant of proportionality is one-t,hird, as mean deflection at full compensation is approximately one-third of the change of ocean depth. Mean upward movement of the continents, relative to the center of the Earth is twice the downward deflection of the sea floor, as oceanic area is double the land area. These points are simplified by the following simple model, illustrated in Fig. 3. Assume an icecap containing the equivalent of 100 m of ocean depth. Let melting commence at t = 0 and proceed at a constant

ISOTATIC

RESPONSESOF EARTH

rate to completion at 10,000 yr, after which no ice forms. Curve A (Fig. 3) shows the corresponding ocean depth change. The relative weight of each spherical harmonic degree in the distribution of water and ice can be determined from the coefficients (Kaula, 1967), i.e.,

After normalizing so that the sum is unity of all significant un’, the simple model of curve A (Fig. 3) is u%(t) = .OUa,‘, = 100un’,

0 < t < 10,000 t < 10,000.

Substituting in the right-hand term of (I) gives the course of net deflection of the surface at degree n as v*(1) = -.0033u,‘t - r(n)[l - exp (- t/~(n))] meters, 0 < t < 10,000 yr, = 33a,‘[l - exp( --t/T(n))] meters t > 10,000 yr.

(2)

The course of v*(t) can now be estimated for this simple model applied to the globe. As the icecap melts, so its contribution to the coefficients Cnm, 8,” changes. Limiting estimates of u,,’ correspond to the cases where the ice is fully present, and where the ice is absent and ocean load only is considered. For the latter case, u,,’ can be determined from the ocean function given by Lee and Kaula (1967), and appropriate values for the former case, at Late Wisconsin maximum, are graphed by O’Connell (1971). The course of mean deflection of the sea floor, using relaxation curves in Fig. 2b and summing v,, over degrees 1-8, is shown as hatchured curve B in Fig. 3. The width of the curve corresponds to uncertainty arising from both the relaxation data and usage of the two bases for estimating u,,‘. Curve C shows the average upward course of the continents, relative to the center of the Earth. Finally, sea level change relative to the center of the Earth is shown as

411

curve D. While these results are based on a simple “straight-lines” model of ocean dept,h change, the difference is small between curve A and Bloom’s (1971) curves of ice volume change since the Late Wisconsin maximum and the error introduced is small relative to the other uncertainties. The origins of certain important problems in eustatic studies are implicit in Fig. 3. Walcott (1972a) points out that eustatic histories will differ between oceanic islands and continental margins, and this is borne out here. An island moving with the “average” sea floor will record curve A, while points near ocean margins, lying in the hinge zone bet,ween ocean floor subsidence and continental uplift, will record sea level changes similar to curve D. Global relaxntion effects will vary in det!ail with localit#y, and records of relative sea level ehango will differ substantially, even between places unaffected by tectonism, as a result, of combined elast’ic and relaxation effects. Calculation of differential relaxation movements around the globe is con4derahly more difficult than estimation of the “mean” curves of Fig. 3. Not only of interest are relative movements of individual basins and continents, but also important are flexures in the hinge zone, which vary in detail with geometry of the continental shelf and with lot*al nature of the transit,ion from oceanic to continental lithosphere. Estimation of this level of detail is not possible via a spherical harmonic expansion, at the present time. Resolution at the scale of continental shelves ent,ails degrees beyond 100, or an order of magnitude higher than normally treated. In any case, uncertainty about the relaxation spectrum at lower degrees makes uncertain the estimation of differential movements between different ocean basins and continents. At, present, identification of Holocene movements between different landmasses, from accurate eustatic studies, is probably of as much benefit for estimating Earth rheology, as are relaxation estimates of Fig. 2 for predicting such differential movements.

412

J.

CHAPPELL

2 Cross section of circular ice-cap of variable size

radial axis

l X

CL I

Cross section of half of parallel ocean with axial symmetry, and variable depth.

to its margin. For a load varying ously through time,

A(4 z(u,t) =‘(u> r>* st0tF(u,

exp[- (t - 5)/44ld3. (3) (cf. Chappell, 1974a), where 2 (u,t) , P(u,t) are the appropriate transforms of vertical deformation x (z,t) and load g (z,t) , respectively (for coordinate axes, see Fig. 4). The transforms are the Hankel transform for the circular case, i.e., X(u)

FIG. 4. Model geometries of simple variable icecap (cylindrical coordinates), and simple variable-depth ocean, with shelf (rectangular coordinates).

=

I

and the Fourier linear case, i.e., X(u) =

The majority of studies of Late Quaternary sea levels are from coasts and continental shelves of major landmasses, i.e., within

the hinge zone where the course of

hydroisostatic deformation varies over relatively short distances. To calculate deformation here, a planar model may be used. In the following the theory is outlined and is shown to yield good reconstructions of Fennoscandian and North American glacioisostatic rebound. Calculations are then made of deformation near oceans margins, resulting from Late Quaternary sea level changes. Different shelf geometries and Kthosphere-asthenosphere parameters are considered. Analysis is for deformation resulting from loads varying spatially and temporally with relaxation behavior similar to that of Fig. 2b. Considered are waning circular icecaps, and changing sea levels over a rectilinear ocean with shelves. Model geometrles are shown in Pig. 4. The icecap is assumed to approximate a rectangular cross section and deformation is determined along any radius; the ocean is modeled initially with straight sloping shelves, and is analyzed along a traverse perpendicular

continu-

- d(x) Jo(m) dx 0

transform

/

(44

for the recti-

o” f(x) eiuz dz.

(4b)

Equation (3) implies that all wavelengths of surface deformation are transmitted equally into the Earth, which is not the case. The lithosphere acts as a low-pass filter, and hence the term A(u) in Eq. (3) is a function of wave number. Walcott (1970, and pers. cornrnun.) shows the filtering to be proportional to 1/u + DU4/(Pm - PM

(5)

where D is the flexural rigidity of the lithosphere, and pm, pc are, respectively, the densities of the asthenosphere and the load. Substitution in Eq. (3) of a time-varying load is illustrated by the following simple example. Consider an icecap of thickness c and radius a0 at t = 0, which decays at a constant rate to zero at t = lo4 yr, after which no ice forms. Assuming ice density is unity, this gives G(x,t) = cg(104 - t), 0 < x < a(t) 0 < t < lo4 yr = 0 , t > lo4 yr, with u(t) = a (lo4 - t),O
ISOTATIC

RESPONSES

OF

EARTH

418

model “b” is used. Although not ideal, this lies between Paterson’s (1972) limiting cases of steady state and stagnant icecaps. (cl from 30,000 to 20,000 uniform icecap growth is assumed, from a minimum position near Helsinki. This position estimate is a long-range interpolation, because the Substituting Eqs. (5) and (6) in Eq. (3) icecap boundary during this interstndinl gives (the Pnudorf of Woldstedt, 1967) is not t A e-t /T(u) well known. The interpolation is based on Z(U,L) = c(r) + the evidence for icecap retreat to within the du>[l + Du4/2gl I to Norwegian coast at this time (Anderson. J&(t)u] . ec’r(u) cl{. (7) 1965). (d) From 40ka to 30ka, a constant, By using the inverse counterpart of Eq. icefront near Helsinki is assumed. This (4a), the course of deformation z (z,t) can model history is shown in Fig. 5a. Calibration of the calculations is affected be determined. With methods such as this, coupled with known history of Late Qua- by uncertainty about the maximum thiekness (H) of the ice sheet at glacial climax. ternary icecap and sea level changes, deformation profiles given in the next section for To make an estimate on the basis of icecap radius (L) the data for modern icecaps for various cases of glacio- and hydroisostasy the parameter H,/I2 will serve. Paterson were calculated. (1972) lists observed values of H,!L2 (mcters) between 7 and 11 for large icecaps: MODEL RESULTS I: for L = 1000 km, H is then likely t.o lie GLACIOISOSTATIC between 2.6 and 3.3 km. E’ield estimates RECONSTRUCTIONS suggest that the maximum Fennoscandian Reconstructions of glacioisostatic re- ice thickness exceeded 3 km (Holtedahl, bound are considered first, to estimate the 1967). Average icecap thickness (5) is the effects of model approximations, and of the important parameter in t,he glacioixostatic uncertainty associated with the relaxation calculations, and this is est,imated to bc spectrum. Icecap variations over the last about 0.75 H by Paterson (1972). on thtt 40,000 yr are taken into account, as relaxabasis of ice flow dynamics. Thus, a like]) tion times exceeding lo4 yr for lower wave range is 2.0 km < & < 2.5 km, for Fennonumbers imply that Holocene deformation scandia. A central value of 2.2 km was will hold a significant “memory” of ice chosen. A final parameter required for the loads prior to the last glacial maximum. calculations is flexural rigidity, n, of the Fennoscandia is the first case considered, lithosphere (Eq. 5). For both Fennoscandia with icecap history modeled as follows: (a) and North America the value of 5 X 102* from 8500 yr BP to the present, zero ice ; newton-meters, determined for the Cana(b) from 18,000-20,000 to 8500 BP-the dian shield by Walcott (1970), is used. maximum ice position on the southeasterly Deformation predicted by the model is traverse is represented by the Brandenburg compared in Fig. 5b with profiles of postand Frankfurt moraines (Woldstedt, 1967). glacial shorelines, and in Fig. 5c with meaThe icecap is modeled as having retreated surement,s of modern uplift. Dormer’s from this at a constant rate to become zero (1968) shoreline reconstru&on is used, size at 8500 BP and the Allerijd Inrather than that of Sauramo (1958) which terstadial (11,000 BP) thus is not taken McConnell (1968) used to estimate r(u) into account. Ice thickness is assumed pro- but which Hyyppa (1966) has criticised. portional to radius, i.e., Bloom’s (1971) Shoreline ages given by Donner are based The transform

Eq. (4a) of G(x$) comes to

J.

CHAPPELL

Years BP x loo0

Angermantand

lj

Observed (Conner,

warping 1968)

Predicted

warping

-

......‘....

Leningrad

..~~,:,

800

1000Km

FIQ. 5. Reconstruction of Holocene deformation of Fennoscandia, on southeastern crock section, calculated using relaxation spectrum “b” of Fig. 2b and lithosphere rigidity of 5 X Iv’ N-m. (a) model history of icecap radius; (b) predicted warping compared with Dormer’s (1968) reconstruction of actual warping; estimated remaining uplift also shown; (c) modern uplift-comparison of prediction and observation.

on numerous 14C dates. Although some uncertainty is introduced by the W yr: sidereal years discrepancy, which amounts to underestimation of age by 14C by 800 yr at 7000 BP (Stuiver, 1970; Damon et oz., 1973), the error is small compared with that associated with uncertainty about r(u). Comparison is made with Litorina Sea and Ancylus Lake shorelines, i.e., back to 9000 yr BP. Presence of a Fennoscandian

icecap prior to this time introduces an elastic deformation effect not considered in the relaxation model. The match is good between predicted and observed Ancylus and Litorina shorelines. Predicted profiles shown in Fig. 5b are adjusted for early Holocene lower sea levels, at which the shorelines formed. Paleo-sea level corrections are based on the curve in Bloom (1971), and are detailed

IROTATIC

RESPONSES

in the caption of Fig. 5. Agreement also is good between IG%riBinen’s (1966) determinations of modern uplift and the model estimates (Fig. 5~). Before passing on to. repeat the exercise for the Laurentide’ sheet, the question of t’he amount of uplift remaining can be discussed. The profile of remaining depression, calculated by the model, is shown in Fig. 5b, and Niskanen’s (1939) estimate also is shown. My estimate is considerably less than Niskanen’s, being 115-130 m at the center against 210 m. A third est’imate, by Lliboutry (1971), is 170 m at the center. These earlier estimates, b:*sed on ext’rapolation of uplift rates and on height-uplift correlations, are more likely to be in error than is a method which takes into account the dependence of relaxation time on deformation wavelength, and which integrates the effects of progressive deglaciation. Further, my estimate agrees with Walcotmt’s (1973) interpretation that the regional gravity anomaly indicates about 130 m of rebound remaining. Turning now to the Laurentide case, the calculation is made on similar lines to the Femloscandian example. The Hankel transform is less appropriate because the sheet was not approximately radially symmetrical, but the method is assumed to be appropriate enough when applied to the southeast’ern quarter of the region. In other words it is assumed that long-range effects of the westerly elongation of the ice sheet, and of multiple centers, are of secondary importance for southeasterly deformation. A “straight line” model is assumed for icecap advance and retreat, similar to that shown in Fig. 5a, but now extending to a maximum southeastern radius of 1600 km, corrcspending to the distance from east Hudson Bay to the maximal margin at New York (after Prest, 1969). Additionally, the ice ret,reat terminates 6.5 ka, rather than 8.5 ka. Because the ice retreated across the North American continent, continuous profiles of raised shorelines similar to those of the Baltic are not available for this traverse, and a comparison is made with published

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estimates of deformation for a 6 ka isobase. The continental uplift data is taken from e Andrews (1971, 1973). The additional element of forebulge downwarp, not idcntifiable on the southeastern traverse of Fennoscandia, can be estimated from studies of dated nearshore deposits below SW level along the Atlantic coast. This data caomes from Massachusetts, Connecticut~. and Kcw Jersey (Bloom, 1967)) Delaware (Kraft, 1971), and Florida (Scholl, Craighead, and Stuirer, 1969). The data are plotted ill Fig. 6a and are compared with the calculated deformation. Jlal;imum ice thickness was assumed to be 3.6 km, after Patclrson (1972)) with mean thickness thus ~2.7 km. The predicted deformation sh0Jv-s good ngrc>cment with observations. As was done for the Fennoscandian Wample, a comparison is made of predict’cd rates of modern uplift, against obscrvcd rates (from tide gauge ohsrrvnt8ions; Fig. 6b). The tide gauge data used arc the most recent assessments by Hicks (1972, 1973 1) rather than the somewhat less arc~vatc earlier estimates summarised by Walcott (3972b). Standard errors given by Hicks (19731 are < 512% of the plotted value in al1 but, three cases. A trend lint drawn by Hicks (1972) through the dense array of data from Chesapeake Bay to AIaincb is Shown in Fig. 5b. The curve of predicted modern forehulge movement shorn-s a fair parallelism with the data, although dil-crgcncee indicate two interesting points. Firstly, the northern part of the forebulge curve predicts rates of submergence less than those observed, wit’h a mean difference of ~1 mm,‘yr. The difference atj the hinge point is 1.3 mm/>-r. Thus, the apparent nonisostatic component in the tide gatrge records of movement along the north Atlantic U.S. seaboard is about 1.0 to 1.3 mm/yr submergence. This is very close to the estimate based on contemporary gIac>ial shrinkage, by Thorarinsson (1940). The second interesting possibility suggested by Fig. 5h is that, the southeastern U.S. may he a sepRrnte neotect$onir province. as the

416

J.

CHAPPELL

$

c” 3.

I Theoretical versus observed deformations of 6000 years BP. isobase (C years used), on a traverse from E. Hudson Bay-Delaware-Florida

0

b Modern deformation lleiemm fa displacementdata. I ekm. 1967 2 Ml 1971 3 SCM. et. al. 1969 4 h&em in flint 1971

4&l I I

3

1 II

and tide gauge records. Predicted deformationJ

rate curve.

I

A = 1.3mmlyr. at hinge

0

1 lsea Ied rise, 2

mmlyr.3

‘5.x Geographic trend
l

1

-v

t

l

T/--J-Charleston,

l

_

w SC.

8.

FIG. 6. Reconstruction of Holocene deformation of eastern North America, on approximate N-S section. (a) predicted Venus observed warping of 6000-yr BP isobase; (b) predicted modern subsidence south of maximal ice margin, compared with tide guage data.

1 mm/yr difference between predicted and observed submergence does not appear. Finally, the remaining uplift can be estimated. Not shown on Fig. 5, this comes to 240 m at the center, with the curve of remaining deformation resembling a magnified mirror image of the calculated curve for 6ka BP deformation, crossing a hinge point 1650 km from the model center. This value of remaining uplift at the center exceeds the estimate of 150 m by Andrews (1968), but is highly consistent with the smoothed regional gravity anomaly of -35 mgals, which implies about 250 m of remaining uplift (Walcott, 1972b, 1973). These results give confidence in the rectilinear Earth model and its underlying approximations, which now is used to estimate

hydroisostatic margins.

deformation

near

ocean

MODEL RESULTS II: HYDROISOSTATIC DEFORMATIONS Most estimates of postglacial sea levels come from the coasts and continental shelves of larger landmasses. In this transitional zone between downward deflected ocean basins and upward-moving continents, the flexural gradients are steepest, and hence the course of apparent sea level change will vary substantially with locality. Hydroisostatic flexure in this zone, and its local effect on relative sea level change, has to be considered jointly with the broad deflections of ocean basins, as the

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b

140%~ BP Input shore I

7000 BP to present

11000 BP input shore

Hooo BP 14000 BP to ocean center

. IShelfouter mawh

100 Km-;

l4OOJl BP hinge 11000 BP

d

e

FIG. 7. Model of hydroisostatic deformation near ocean margin. (a) curve A-model sea level change relative to ocean floor, B-sea level change relative to center of Earth; (b) changing water-load distribution; (c) sea floor deflection, as percentage of total sea level rise; (d) enlarged diagram of inner 50 km of shelf deformation; (e) sea level changes for last 8000 yr, arising from interaction of shelf deflection, with sea level changes relative to center of Earth.

418

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latter affect the course of sea level rise relative to any reference point (Fig. 3). The method of estimating interaction of flexure and eustatism, outlined in Fig. 7, is as follows: Deformation calculated by Eq. (3) is referred to an initial undeformed surface (Fig. 7~). Sea level changes relative to the ocean floor (e.g.. curve A, Fig. 7a) are converted to time-varying surface loads on the ocean basin and shelf (Fig. 7b). The resulting course of deformation in the ocean zone is exemplified in Fig. 7c; the case of a 100 km shelf with lithosphere Aexural rigidity of 1O24 N-m is illustrated. Further discussion will be assisted by now defining two terms: (i) input shoreline is the instantaneous shore position used in the calculations. It is the position where the shore would be if no deformation occurred. (ii) Hinge point on any profile of deformation is the point at which it crosses the undeformed initial profile. It is clear that deformation causes the actual shoreline to differ from the input shoreline, causing in turn an error in the deformation estimate. Determination of the actual shoreline is shown in Fig. 7d. Deflection of the shelf surface relative to the center of the Earth is subtracted from sea level change relative to the center of the earth (curve B, Fig. 7a), and from this value for relative sea level change the associated shoreline change is plotted. In the example of Fig. 7, the discrepancy is small between input and actual shorelines. The course of sea level changes relative to the modern coast in the model can be estimated by the same means, as shown in Fig. 7e. Amalgamation is made in Fig. 7 of the rectilinear Earth model for deformation near ocean margins, with the broad-scale results of the spherical model. It was assumed that the hinge points were the same in both models. This assumption is incorrect for hydroisostatic deformation of the real Earth, because the points of zero deflection (relative to the center of the Earth) vary with landmass size (discussed earlier),

and landmass is infinite in the rectilinear model. However, by comparing predictions made by the methods of Fig. 7 with observations of Holocene sea level changes from different places, such differential movements between landmasses may be identified. MODEL RESULTS VERSUS OBSERVATIONS OF LATE QUATERNARY SEA LEVELS Published estimates for paleo-sea levels of the last 20,000 yr are discussed in two groups. Evidence for sea level around the last glacial maximum is considered first, to see whether different results from different parts of the world are reconcilable by hydroisostasy. At a more detailed level, selected sea level records for the last 7000 yr are then compared with model predictions similar to that of Fig. 7. Sea Level at Last Glacial Maximum

Evidence for low sea level of the last glacial maximum has been recorded in many continental shelves, being deposits identified with shallow marine and nearshore environments and dated around G-20,000 BP. Shelves where observations are relatively numerous include those of Atlantic U.S., Texas, and the South China Sea. Scatter in the data is wide, however, and Emery, Niino, and Sullivan (1971)) in summarizing most such results, show a range from -65 to -150 m for the low point. The uncertainty to a large measure is attributable to 14C dating problems. Most of the estimates are based on mollusc or coral remains, which are susceptible to contamination via recrystallization. To illustrate the point, Chappell and Polach (1972) report corals which have recrystallised in a subaerial environment and which are known to be older than 45,000 yr, but which show 14C ages down to 11,000 yr. Chappell et al. (1973) report ccrals known to be 40,000 yr and having less than 10% recrystallization from aragonite to calcite, which yield 14C ages down to 19,000 yr. In the

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absence of diagenetic data for the samples, northern Australia there are two interesting the simplest test for acceptability of the sets reports of submarine terraces around -160 of dates reported in these studies is the con- m for which ages around 17,000 BP have sistency of the age to sample depth trend, been claimed. Observations were made back to about 20 ka. Judged on this basis, from both surface and submersible vessels. the results of Milliman and Emery (1968) The first case occurs at the Great, Barrier from the southeastern U.S. shelf, and Reef (Veeh and Veevers, 1970)) where coral Emery, Niino, and Sullivan (1971) from off the edge of a terrace at -160 m is dated the South China Sea, are the least satisfacat 17,000 BP by L’30Th/.‘3*U, and this age tory. Furthermore, both of these studies re- is supported by a 14,000-yr “C date for port “C determinations for material which beachrock on a second smaller terrace at is difficult t,o interpret: Milliman and -150 m. The second report comes from the Emery’s samples include beachrock, which Arafura Sea (Jongsma, 197Oj, where algal has been reported as having 6000 yr differrock around -150 m has a “C> age of ence between age estimates for the whole 18,700 BP and was interpreted as being asrock and for its constituent shells (Phipps, sociated with withdrawal of sea 1~~1 to 1970). They also use oolite samples, which perhaps as low as -170 m. Datrs in the can show at least 2000 yr between core and same age range from terraces or dredge outer layers (Olson and Broecker, 1959). sampIes around -130 m dcpt,h clstwhere Emery et nl. (1971) use dredgings of shell in Australia (Sahul Shelf, Van Andral and composites, which show ages for different Vecvers, 1967; northern Kcw South Wales, components of a singIe dredging as widely Phipps, 1970) do not disconfirm this -160 varied as 300030,000 yr. It is very dif?icult to -170 In low, as dating uncertainty to identify acceptable dated samples in makes pinpointing of paleo-sea levels diffitables of such data. cult, for a period when rates of sea level Xorth American shelf data showing change ranged up to 10 m/per 1000 yr. Sc:t level lowering at the last glacial maximum greatest consistency of age-depth trend come from the Texas shelf (Curray, 1960) thus was 30-70 m more than for eastern North America, in rough terms. and the northeast U.S. shelf (Emery and Garrison, 1967) ; the former indicate sea Hydroisostatic movements of eastern U.S. relative to Australia include the global level at -90 m, 17,000 y.a, compared with at least -130 m at 15,000 BP in the second elastic and relaxation effects, at a lnoatl scale, and differential shelf fIexurcs. at a case. Milliman and Emery (1968) report more Iocal scale. Assuming shelf flexures to samples indicating that sea level relative to the southern part of the U.S. Atlantic shelf be similar for similar shelves in different places, any differential observed between was about 100-110 m below present, strandline depths in comparable situa1%19,000 y.a. Some measure of the differtions-say at the outer margins of similar ences between these U.S. shelves is attributshelves-is then attributable to the globalable to isostatic movements: for example, scale flexures. Walcott’s (1972aj map of the Massachusetts-Delaware shelf appears elastic warping (Fig. la) predicts that Austo be a subsiding proglacial forebulge tralia will have the glacial maximum (Emery and Uchupi, 1972). Samples repstrandline about 25% lower than the southresenting the glacial maximum are few in east U.S., and about 40% lower than the each area, hoTever, and lesser differences sheIf of New York. Before Emery and Garsuch as between Texas and Carolina-Florrison’s estimate of -130 m lowering relative ida shelves tend to be submerged in dating to this northern shelf is accepted. the uncertainties. age-depth data of these authors should be Shelf samples of 15,000-20,000 yr age are corrected for displacement accompanying very sparse from most of the world. From

420

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a

200

Maximal

CHAPPELL

ice margin I

h\

i rebymd

from from ice maximum (16Ka)

b

20

15

years BP, x 1000 10

CO

5

0

3. / /

2. I / depth,meters

$5

il*‘j

-5O-

-4 I

13 I.9 ;:10 / ‘2 /

-loo-

16’/

/ -’

15./ /‘14

deglaciation curve of Bloom (1971)

?

FIG. 8. Age-depth estimates of late Quaternary sea levels, from northeast U.S. shelf (from Emery and Garrison, 1967), corrected for glacioisostatic deformation: (a) curves of isobase rebound near maximal ice margin, calculated as for Figs. 5 and 6; (b) geographic positions of Emery and Garrison’s sample sites, and of maximal ice margin; (c) plot of sample ages versus depths, corrected for rebound displacements. The mean of Bloom’s (1971) curves of deglaciation is fitted to the plotted points. relaxation of the glacioisostatic forebulge. Figure 8a shows curves of isobase rebound

in the forebulge zone, calculated by the same model as Fig. 6. Emery and Garri-

son’s sample

localities

are shown

in Fig. 8b,

and their data corrected for forebulge rebound are plotted in an age-depth frame in Fig. SC. Superimposed on the corrected

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data is Bloom’s (1971) envelope of sea level rise, based on limiting cases for models of deglaciation. This envelope, given by Bloom is dimensionless form, is scaled to give a best fit over the corrected age-depth points, and projects to a glacial low value of about -115 m at 17,000 BP relative to the outer margin of the shelf off New York. Given the elastic warping differential of 40%) this is equivalent to -160 m off the broad Northern Australian shelves, which matches observation. Subtracting elastic effects from these figures puts the glacial maximum sea level around -135 m, relative to outer margins of broad continental shelves. Judged against this, Curray’s -90 m estimate from the Texas shelf, and Milliman and Emery’s lowest values for the Carolina shelf (about -110 m) , are seen as upper limits, with the possibility remaining of future discoveries of 17,000-yr strandlines at greater depths in these places. Eustatic lowering relative to the “mean floor” of the great ocean basins may be somewhat less than the 130-135 m derived from the northeast U.S. and Australian shelf-margin data, with elastic deformation effects subtracted. This is because calculations of hydroisostasy indicate a broad downwarp may occur near ocean margins (Fig. 9). The magnitude of this effect is difficult to estimate, as it should be determined by the spherical harmonic met’hod rather than the rectilinear model. The rectilinear model profile for oceanic lithosphere (Fig. 9c) suggests 15 m downwarp at the present day, relative to the ocean center: this can be taken as the upper limit of the effect. For a 100 km shelf over continental lithosphere the overdeepening effect is less than 5 m (Fig. 9a), however; the implication is that eustatic lowering relative to the great ocean basins was not very much different from 130 to 135 m at the last glacial maximum. This reckoning agrees well with Flint’s (1971) estimate of ice volume, which is equivalent to about 130 m of lowering. Not in complete agreement is a re-

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cent and thorough analysis by Paterson (1927) of Laurentide ice volumes, who suggests that Flint’s estimate may be too high. Paterson estimat#es that the Laurentide icecap at Late Wisconsin maximum was equivalent to 66 3- 10 m, and suggests that t,his was at least two-thirds of the total ice excess. The upper limits of Paterson’s estimate is around 115 m sea level lowering. Apparently not included, hoffever, is the extension of Fennoscandian ice across the Barents Sea, which appears to have existed around glacial maximum times (Schytte and othes, 1967). This was probably around 1.5 X lo6 square km in area, adding another 5-7 m of sea level lowering. Whether or not the 10-15 m discrepancy is significant, between Paterson’s upper estimate of ice volume and either Flint’s estimate or the estimate made here of 130-135 m lowcring, is left as an open question. The issue could be resolved by discovering and measuring submarine terraces formed 17,000 y.a. around oceanic islands. Sea level change relative to the ocean floor exceeds change relative to the modern coast. Hydroisostatic deflection increases away from the land (Figs. 7 and 9)! and thus any 17,000-yr strandlines which lie drowned within deep rias or fjords should occur at depths less than at outer shelf margins. The dept,h difference increases with shelf width, and decreases as flexurnl rigidity of the lithosphere increases. Figure 9 indicates about 8 m differential across a 100 km shelf over shield lithosphere, and more over oceanic lithosphere. Shelf gromctry affects warping: for broad “box-se?tion” shelves such as occur in parts of the Great Barrier Reef, Australia, the deflection is somewhat greater (Fig. 9c). Sea Levels Over the Last 7000 yr

Several comparisons have been made between Holocene sea level curves from coastal regions around the world, showing there to be substantial divergences (Shepard and Curray, 1972; MSrner. 1970). In glacial forebulge regions the divergences

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CHAPPELL

BP

Inputsealwel 12c00Bp 1&)

17000 BP

0,

1po

Km

a

//-shelf , / I

-/ / I I

Deflection as % of total sea levelchange

b

C

o

o-7000

BP

12000 BP 1oo

170w BP

FIG. 9. (a-c). Illustrating the effects of shelf geometry and lithosphere rigidity on the course of hydroisostatic deformation near ocean margins, arising from sea level changes shown at the top.

largely arise from rebound effects (Mkirner, op. cit. ; Walcott, 1972b; see also Fig. 6, above). Elsewhere, hydroisostasy and local tectonics must cause the differences. Model Holocene sea level curves resulting from any input curve of deglaciation can be estimated for any coastal situation, as shown in Fig. 7e. This method neglects global lower-degree relaxation movements, however, and tectonic factors affecting Holocene sea level records must therefore be identified independently. Upper Quaternary tectonism can be identified on many coasts from flights of raised shorelines; par-

titularly useful in this regard is the terrace which formed 120-130,000 y a. This widely recognized shoreline occurs between 2 and 7 m above sea level in places remote from plate boundaries, and is becoming widely used as an Upper Quaternary sea level datum (reviewed in Bloom et al., 1974; Chappell, 1974). Thus, in places where the 120,000-yr terrace occurs higher than about 7 m, tectonic uplift can be inferred. In order to introduce an interpretation of the differences between Holocene sea level records from certain coasts which are thought to be stable, the relaxation effect

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a

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pparent sea level curve at continental

A

boy

OF

shore

Simple hypothesis of sea level relative to ocean basms.

F

4

z

o

4 Christchurch, N.Z.: Suggate, 1968 5 SE. Australia: Thorn and Chappall, 1974

elastic effect prior to 7000 BP

YearsBP x 1004 icronesia

M :Mean E :.%a

ofAustralian

(Bloom, 1970)

and N.Z. results

level relative to ocean basins, predicted

from M

FIG. 10. Interpretation of Holocene sea levels in terms of hydroisostasy: (a) relationship between model sea level change relative to mean ocean floor, and change relative to continental coast, and change relative to island subsiding faster than mean ocean floor (cf. Fig. 3); (b) selected Holocene sea level curves, from places remote from Pleistocene icecaps and seemingly stable tectonically; (c) prediction of sea level change relative to ocean basins (curve E), assuming that curves 4 and 5 of (b) are counterparts of curve B in (a).

associated with a simple model of sea level change is outlined again, in Fig. 10a. Model sea level rises uniformly until 7000 BP and then stabilizes: under these conditions the 7000 BP and younger shorelines at oontinental coasts would be emergent (curve B), while any point subsiding more rapidly than the mean ocean floor would record transgression until the present (curve C).

Shown in Fig. lob are five Holocene sea level curves from areas remote from glacioisostatic effects: these come from Florida (Scholl, Craighead, and Stuiver, 1969)) Micronesia (Bloom, 1970)) Bermuda (Neumann, 1972)) Christchurch, New Zealand (Suggate, 1968), and southeast Australia (Thorn and Chappell, 1974). With the exception of Christchurch, the 120,000

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BP shoreline is known to be within a few meters of sea level in each regioq2 and tectonic movements are assumed to be negligible. The Christchurch region appears to be a relatively stable part of New Zealand, as it is tied to a shield volcano which probably has not been much affected tectonically since lower Pliocene times (Stipp, 1968). These Holocene curves fall into contrasting groups. The Australian and New Zealand results show sea level rising from -20 around 8400 BP, to stabilize around the present level about 6000 y. a. The midocean islands of Micronesia and Bermuda show sea level below present until very recent times. Interestingly, the Florida curve resembles the oceanic island curves, rather than the Australian pattern. The Bermuda curve prior to 7000 BP is also shown on a comparable footing with Australia and New Zealand, after correction is made for elastic differential movements, i.e., about 25-30% (see Fig. la). Interpretation is as follows. The mean is taken of the Australian and New Zealand curves (curve M, figure lOc), and this is assumed to be a counterpart of the continental coast curve B of Fig. lOa, but stemming from a deglaciation course different from curve A. The course of sea 1eveI relative to the mean ocean floor which generates M is hatchured curve E of Fig. lOc, preceded by a straight line rise of 12.5 m/1000 yr since 17,000 BP (calculated by the same route as Fig. lOa). This predicted curve is interestingly close to the Micronesian “oceanic dipstick” curve of Bloom (1970). A test of this reconciliation, via hydroisostasy, of the Micronesian and Australian-New Zealand results, would come from extension back in time of the M&one&an record, or similar determinations of sea ’ The 120,000 shoreline has been dated in Florida by Broecker and Thurber (I%%), in Micronesia by Thurber et al. (1965), in Bermuda by Land, MacKenzie, and Gould (1967). It was dated in Western Australia by Veeh (1966) in a region with a Holocene record similar to southeast Australia (Thorn and Chappell, 1974).

level curves from other oceanic islands. The Bermuda results, presented by Neumann(1972) in summary form, appear to be the; only such data available, and do not compare particularly well with curve E. The Bermuda curve (i) lies ~2.5 m below E at 6000 BP, but (ii) intersects it as 8000 BP, even when corrected for differential elastic effects. Assuming E to be correct, the first point indicates relatively more rapid subsidence than mean ocean floors, while the second point suggests slower subsidence. Whether the discrepancy reflects either an error in estimating the elastic effect, .or other movements, or an error in the Bermuda curve, is not resolved here. The resemblance of the Florida curve to oceanic results rather than continental Australia also deserves mention. It would seem that either the hinge line of hydroisostatic warping lies further inland in Florida than Australia because of lithosphere differences, or that the Australian continent is rising relative to North America, as a result of differential relaxation on a global scale. Alternatively, the possibility that Florida is a neotectonic province separated from the remainder of eastern U.S. cannot be discounted. The postglacial transgression identified from Massachusetts to DeIaware seems explainable in terms of glacioisostasy (Fig. 6) ; if so, then the Florida transgression is to be explained differently. Other HoIocene data, from regions remote from Pleistocene icecaps and from plate boundaries, are suggestive of hydroisostatic movements on both global and local scales. These are “spot” results rather than time depth curves. In the Pacific, Eniwetok Atoll contrasts with the Micronesian Islands studied by Bloom (1970); by showing up.to 1 m emergence of a coral reef aged between 2000-4000 yr (Tracey and Ladd, 1973). Although there are differences of interpretation of Pacific Island evidence (Curray, Shepard, and Veeh, 1970; Newell and Bloom, 1970)) these reports do suggest a 2 m differential between Eniwetok and the islands 800 km westward.

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RESPONSES

Whether this is attributable to lower-degree relaxation is not resolved here, but the possibility should be considered. At the more local scale of continental shelf deformation, data from the archipelagic Great Barrier Reef are interesting. The Holocene crests of the reefs of the outer shelf are not emergent and appear to have grown upward unt,il the present day. The cays and low wooded isles, which lie about one-third of the distance from the coast to the shelf outer margin, show slightly emergent dead Holocene reef (R. F. McLean, pers. comnun.). A hinge line of variable location is indicated by emergent Holocene shorelines near the landward margin of the Great Barrier Reef, either at the North Queensland coast (Bird, 1970), or offshore islands of t,he inner shelf (Hopley, 1973). Yet other parts of the Queensland coast have remained at sea level for the last 5000 yr (Cook and Polach, 1973). Undoubtedly this large shelf province, with its variations of geometry and possibly of upper Earth parameters, will yield very useful evidence for testing hydroisostatic predictions, from its archipelagoes of “dipsticks.” CONCLUDING

DISCUSSION

The question of whether the fluctuating sea levels of the Quaternary Era have induced deformation of the ocean basins and their margins, in a manner similar to the known deformations induced by Fennoscandian and Laurentide icecaps, is interesting from several viewpoints. A particular area, dealt with in the latter part of the paper, is to do with resolution of differences between eustatic histories from different parts of the world. Hydroisostatic processes, both global elastic is identified by Walcott, (1972aj, and relaxation on global and 1ocaI scales, appear substantially to explain such differences between records of the last 17,000 yr. In this paper, however, global relaxation movements expressible in lower-degree harmonics, have not been resolved. To predict these theoretically is fraught with uncertainty arising from im-

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precise knowledge of the Earth’s relaxation behavior. Probably more useful here than any other single category of observation will be identification of the depth of the 17,000 BP strandline at many sites around the world. Not only wiII this aid the undcrstanding of global relaxation, but also the estimation of hydroisostatic effect,s on (nontinental shelves. A useful cross-check of hydroisostatic models of shelf deformation calibrated against local eustatic data for the last 17,000 yr could come from rstimates of upper Earth rheology basctl on other geophysical methods, such as sc+mic results (see, e.g., Chappell, 1974a). Hydroisostatic global relaxation 011 the scale suggested by the opposite motions of continents and oceans shown in Fig. 3 is geophysically interesting, because mantle flows of a large magnitude are implied. The maximum mass transfer rate from beneath oceans to beneath continents comes to about 8 X 1Ol7 cm3/yr, around 7000 9.3. By comparison, mass transfer by subduction at plate boundaries is about 2.5 X 1017 cm3/yr (mean subduction rate -5 cm/yr, along -50,000 km; Le Pichon, 1968). Frictiona dissipation is smaller in the isostatic processes, however, as flow here is throughout the whole mantle as against dissipation in a thin layer bounding the subducting slabs. Viscous dissipation 4 = ‘I(&/@) ” for flow u in a parallel channel : viscous dissipation of isostatic flow throughout the upper mantle will thus be at least an order of magnitude smaller than dissipation in subduction zones. Energy dissipation of t’his magnitude is acceptable: total subduction energy is -3 x 10’” (from data in ergs/set Schubert and Turcot’te, 19711, and thus t8hc global isostatic process will involve less than 10’” ergs/see. This is compat.ible with the energy of nontidal acceleration, which is one-third that of tidal acceleration (Munk and MacDonald, 1960:204), which is sufficient to absorb the viscous dissiption of isostatic flow. Such large-scal(h mantle flows, caused by changing ice-water

426

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loads, are an interesting tectonic engine. Any difference between flows associated with the deglaciation hemicycle on one hand, and the advancing glaciation hemicycle, on the other, will have epeirogenic consequences. For example, if interglacials and interstadials are longer than glacial maxima, there would occur a slow upward pumping of landmasses throughout repeated glaciation. To conclude these remarks, it can be noted that the mean modern upward motion of continents relative to their coasts, predicted from Fig. 3 scaled to a total sea level change of 130 m, is about 2-3 mm/yr. This is in fair agreement with geodetic relevelling results from the U.S., reported by Meade (1971), which indicate uplift generally increasing away from the east coast, reaching -5 mm/yr around Iowa. Hydroisostasy has been shown here to be an important phenomenon, potentially accounting for nontectonic differences between Upper Quaternary sea level records from different places. Reconciliation of differences between published data (i) suggests that sea level lowering relative to the mean ocean floor was 130 m, 17,000 y.a.; (ii) confirms Walcott’s (1972a) estimation of elastic deformation; (iii) indicates that relaxation flexures near ocean margins are pronounced, and that landmasses are likely currently to be rising, perhaps at different rates. Full treatment of hydroisostasy on a viscoelastic Earth must go beyond this paper. Investigation is necessary of the global relaxation figure. Finally, pointed out to me by Walcott (pers. commun.), analysis should take account of the modification by elastic deformation of the forces which generate viscous relaxation: this has not been touched on here. ACKNOWLEDGMENTS I warmly thank Professor A. L. Bloom of Cornell University, and Dr. B. G. Thorn of Australian National University, for discussions and contributions to the development of this paper. I espe-

cially thank Dr. R. I. Walcott for his very constructive criticism of the first draft of the paper.

REFERENCES B. G. (1965). The Quaternary of Norway. In “The Quaternary 1” (K. Rankama, ed.), pp. 91-138. Interscience, N.Y. ANDERSEN, D. L. AND R. O’CONNELL (1967). Viscosity of the earth. Geophysical Journal of the Royal Astronomy Society 14, 287-295. ANDREWS, J. T. (1968). Postglacial rebound in Arctic Canada: similarity and prediction of uplift curves. Canadian Journal of Earth Science ANDERSEN,

5, 3947.

ANDREWS, J. T. (1971), In “Glacial and Quaternary Geology” (E. K. Flint, ed.), p. 363. Wiley, N.Y. ANDREWS, J. T. (1973). The Wisconsin Laurentide ice sheet: dispersal centers, problems of rates of retreat, and climatic implications. Arctic and Alpine Research 5, 185199. BIRD, E. C. F. (1971). The fringing reefs near Yule Point, North Queensland. Australian Geographical Studies 7, 107-115. BLOOM, A. L. (1967). Pleistocene shorelines: a new test of isostasy. Geological Society of America Bulletin 78, 1477-1494. BLOOM, A. L. (1970). Paludel stratigraphy of Truk, Ponape and Kusaie, Eastern Caroline islands. Geological Society of America Bulletin 81, 1895. BLOOM, A. L. (1971). Glacio-eustatic and isostatic controls of sea level since the last glaciation. In “Late Cenozoic Glacial Ages” (K. Turekian, ed.), pp. 355-379. Yale Univ. Press. BLOOM, A. L., W. S. BROECKER, J. CHAPPELL, R. S. MATTHEWS, AND K. J. ME~~LELLA (1974). Quaternary sea level fluctuations on a tectonic coast: new ThZ”/US’ dates from the Huon Peninsula, New Guinea. Quaternary Research 4, 185-205.

BROECKER, W. S., AND D. L. THURBER (1965). Uranium-series dating of corals and oolites from Bahamian and Florida Key limestones, Science 149, 5&60. CHAPPELL, J. (1974a). Upper mantle rheology in a tectonic region: evidence from New Guinea. J. Geophysic(c1 Research 79, 390-398. CHAPPELL, J. (197413). Geology of coral terraces on Huon Peninsula, New Guinea: a study of Quaternary tectonic movements and sea level changes. Geological Society of America Bulletin 85,

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CHAPPELL, J., AND H. A. POLACH (1972). Some effects of partial recrystallisation on “Cl dating late Pleistocene corals and molluscs. Quaternary Research 2, 244-252. CHAPPELL, J., W. S. BROECKER, H. A. POLACH, AND B. G. THOM (1973). Problem of dating Pleisto-

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cene sea levels from coral reef areas. Second International Coral Reef Symposium (Abstract), University of Queensland, Australia 87, (in press). COOK, P. J. AND H. A. POLACH (1973). A chenier sequence at Broad Sound, Queensland, and evidence against a Holocene high sea level. Marine Geology 14, 253-268. C)URRAT, J. (1960). Sediments and history of Holocene transgression, continental shelf, northwest Gulf of Mexico. Zn “Recent Sediments, Northwest Gulf of Mexico.” (F. P. Shepard et al., cds.), pp. 22-266. American Association of Petroleum Geologists, Tulsa, Oklahoma. CURRAY, J., F. P. SHEPARD, AND H. VEEH (1970). Late Quaternary sea level Studies in Micronesia : CARMARSEL Expedition. Geological Society o j America Bulletin 81, 1865-1880. CURK~Y, J. R. AND E. P. SHEPARD (1972). Abstracts. dnd National AMQUA Conference, 16, Miami, Florida. DALY, R. A. (1925). Pleistocene changes of sla level. American Journal of Science 6th Series 10, 281-313. DAMON, P. E., A. LONG, E. I. WALLICK, AND C. W. FER(:USON (1973). Dendrochronologic calibration of the c” time scale ZNQUA, 9th Congress, Christchurch,

NZ

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