Glacial Isostasy, Sea-Level and Mantle Rheology

704 Pages·1991·61.35 MB·English

by  W. Fjeldskaar, L. Cathles (auth.), R. Sabadini, K. Lambeck, E. Boschi (eds.)

Glacial Isostasy, Sea-Level and Mantle Rheology
NATO ASI Series
Advanced Science Institutes Series
A Series presenting the results of activities sponsored by the NA TO Science Committee,
which aims at the dissemination of advanced scientific and technological knowledge,
with a view to strengthening links between scientific communities.
The Series is published by an international board of publishers in conjunction with the
NATO Scientific Affairs Division
A Life Sciences Plenum Publishing Corporation
B Physics London and New York
C Mathematical Kluwer Academic Publishers
and Physical Sciences Dordrecht, Boston and London
D Behavioural and Social Sciences
E Applied Sciences
F Computer and Systems Sciences Springer-Verlag
G Ecological Sciences Berlin, Heidelberg, New York, London,
H Cell Biology Paris and Tokyo
I Global Environmental Change
Series C: Mathematical and Physical Sciences -Vol. 334
Glacial Isostasy,
Sea-Level and Mantie Rheology
edited by
R. Sabadini
Dipartimento di Fisica, Settore di Geofisica,
Universita degli Studi di Bologna,
Bologna, ltaly
K. Lambeck
The Australian National University,
Research School of Earth Sciences,
Canberra, Australia
and
E. Boschi
Istituto Nazionale di Geofisica,
Roma,ltaly
Springer Science+Business Media, B.V.
Proceedings of the NATO Advanced Research Workshop on
Glaciallsostasy, Sea-Level and Mantie Rheology
Erice, Italy
July 27-August 4,1990
Library of Congress Cataloging-in-Publication Data
NATD Advanced Research Workshop an Glacial Isostasy, Sea-level, and
Mantie Rheology <1990 Erice, Italy)
Glaclal isostasy, sea-level, and mantie rheology proceedings of
the NATD Advanced Research Workshop an Glacial Isostasy, Sea-level,
and Mantie Rheology, Erice, Italy, July 27-August 4, 1990 / edlted
by R. Sabadini, K. Lambeck, E. Boschi.
p. cm. -- (NATD ASI Ser les. Series C, Mathematlcal and
physical SClences ; val. 334)
"Published in cooperation with NATD Scientific Affalrs Divlsion."
ISBN 978·94-010-5492-8
1. Isostasy--Congresses. 2. Glacial epcch--Congresses. 3. Sea
level--Congresses. 4. Earth--Mantle--Congresses. 5. Geodynamics-
-Congresses. 6. Rheology--Congresses. 1. Sabadini, R.
II. Lambeck, Kurt, 1941- III. Boschi, E. IV. North Atlantic
Treat~ Drganization. SClentific Affairs Division. V. Title.
VI. Series· NATD ASI Ser Ies. Series C, Mathematical and physical
sciences ; no. 334.
QE511.N272 1990
55i.1'3--dC20 91-6984
CIP
ISBN 978-94-010-5492-8 ISBN 978-94-011-3374-6 (eBook)
DOI 10.1007/978-94-011-3374-6
Printed on acid-free paper
AII Rights Reserved
© 1991 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1991
Softcover reprint of the hardcover 1s t edition
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical, including photo
copying, recording or by any information storage and retrieval system, without written
permission from the copyright owner.
TABLE OF CONTENTS
Introduction ix
POST-GLACIAL REBOUND
W. Fjeldskaar and L. Cathles: "Rheology of mantle and lithosphere inferred 1
from post-glacial uplift in Fennoscandia"
P. Gasperini, R. Sabadini and D.A. Yuen: "Deep continental roots: the 21
effects of lateral variations of viscosity on post-glacial rebound"
K. Lambeck: "A model for Devensian and Flandrian glacial rebound and 33
sea-level change in Scotland"
J .X. Mitrovica and W.R. Peltier: "Radial resolution in the inference of 63
mantle viscosity from observations of glacial isostatic adjustment"
M. Nakada and K. Lambeck: "Late Pleistocene and Holocene sea-level 79
change; evidence for lateral mantle viscosity structure?"
W.R. Peltier: "The ICE-3G model of late Pleistocene deglaciation: construc- 95
tion, verification and applications"
G. Spada, R. Sabadini and D.A. Yuen: "The dynamical influences of a hard 121
transition zone on post-glacial uplifts and rotational signatures"
GLACIOLOGY AND CLIMATOLOGY
J.T. Andrews: "Relative Sea Levels, Northeastern margin of the Laurentide 143
ice sheet, on times cales of 103 and 102 A"
J.L. Fastook and T.J. Hughes: "Changing Ice loads on the Earth's surface 165
during the last glaciation cycle"
vi
G. Visconti: "Global warming expected from increase of greenhouse gases: a 203
forcing for sea level change"
SEA-LEVEL FLUCTUATIONS
R.J.N. Devoy: "The study of inferred patterns of Holocene sea-level change 213
from Atlantic and other European coastal margins as a means of testing
models of Earth crustal behaviour"
S.M. Nakiboglu and K. Lambeck: "Secular sea-level change" 237
P.A. Pirazzoli: "A survey of relative sea-level changes observed during the 259
Holocene"
A.S. Trupin and J .M. Wahr: "Constraints on long-period sea level variations 271
from global tide gauge data"
O. van de Plassche: "Coastal submergence of the Netherlands, NW Brittany 285
(France), Delmarva Peninsula (VA, USA), and Connecticut (USA) during
the last 5500 to 7500 sidereal years"
MANTLE RHEOLOGY
M. Caputo: " Threedimensional rheology" 301
L.A. Lliboutry: "Mantle viscosity: what are we exactly looking for?" 321
G. Ranalli: "The microphysical approach to mantle rheology" 343
MANTLE AND LITHOSPHERIC DYNAMICS
D.L. Anderson: "Chemical boundaries in the mantle" 379
M. Dragoni: "Crustal deformation due to aseismic slip on buried faults" 403
vii
A.M. Forte and W.R. Peltier: "Gross Earth data and mantle convection: 425
new inferences of mantle viscosity"
M. Gurnis: "Continental flooding and mantle-lithosphere dynamics" 445
B.H. Hager: "Mantle viscosity: a comparison of models from postglacial 493
rebound and from the geoid, plate driving forces, and advected heat flux"
A. Morelli and A.M. Dziewonski: "Joint determination oflateral heterogene- 515
ity and earthquake location"
R.J. O'Connell and B.H. Hager: "Toroidal-poloidal partitioning of litho- 535
spheric plate motions"
Y. Ricard and C. Froidevaux: "Seismic imaging, plate velocities and geoid: 553
the direct and inverse problem"
M.A. Richards: "Hotspots and the case for a high viscosity lower mantle" 571
R. Sabadini, G. Spada and Y. Ricard: "Perturbations in the Earth's rotation 589
induced by internal density anomalies: implications for sea-level fluctuations"
H. Schmeling: "Variable viscosity convection in a compressible upper mantle 607
and the thickness of continental lithosphere"
N.J. Vlaar and A.P. van den Berg: "Continental evolution and archaeo-sea- 637
levels"
D.A. Yuen, A.M. Leitch and U. Hansen: "Dynamical influences of pressure- 663
dependent thermal expansivity on mantle convection"
Discussion and recommendations 703
INTRODUCTION
by K. Lambeck, R. Sabadini and E. B08Chi
Viscosity is one of the important material properties of the Earth, controlling tectonic and
dynamic processes such as mantle convection, isostasy, and glacial rebound. Yet it
remains a poorly resolved parameter and basic questions such as whether the planet's
response to loading is linear or non-linear, or what are its depth and lateral variations
remain uncertain. Part of the answer to such questions lies in laboratory observations of
the rheology of terrestrial materials. But the extrapolation of such measurements from the
laboratory environment to the geological environment is a hazardous and vexing
undertaking, for neither the time scales nor the strain rates characterizing the geological
processes can be reproduced in the laboratory. General rules for this extrapolation are that
if deformation is observed in the laboratory at a particular temperature, deformation in
geological environments will occur at a much reduced temperature, and that if at laboratory
strain rates a particular deformation mechanism dominates over all others, the relative
importance of possible mechanisms may be quite different at the geologically encountered
strain rates. Hence experimental results are little more than guidelines as to how the Earth
may respond to forces on long time scales. Answers to the question as to what is the
appropriate responses of the Earth to forces acting upon it therefore rest largely upon the
analysis of these very processes, using a variety of geophysical, geochemical and
geological observations of the action and the reaction. This also is a high risk undertaking,
with the danger being that the deduced response is only as good as any assumptions made
about the forces that lead to that deformation.
The study of the viscosity of the Earth therefore requires a number of different
approaches that hopefully lead to convergence on the real viscosity structure of the planet as
well as lead to improved understanding of the forces acting on the Earth. Numerous
geophysical observations point to a non-elastic response when the Earth is subjected to
forces. They range (Figure 1) from the attenuation of seismic waves in the mantle, to the
lag in the response of the planet to tidal and rotational forces, to the rebound of the crust to
recent glacial unloading, to the general achievement of the state of isostatic compensation of
load anomalies within the lithosphere, to the occurrence of mantle convection, and to the
slow relaxation of stresses in the lithosphere. These phenomena cover a broad frequency
span from one Hertz to 10-14 Hertz and lower. The deformations are also occurring in
response to a wide range of stress magnitudes; from a few hundred MPa to less than one
MPa. The objective is therefore to find a stress relaxation function that describes the
response of the Earth over a wide range of frequencies and stress values. This response
may, in addition, be regionally variable within the Earth. Even with a number of different
geophysical observations available, few details about the nature of this response function
have so far emerged to permit us to say that we understand the viscosity of the Earth.
Hence, instead of searching for highly realistic viscosity models, current emphasis is on
establishing effective parameters that describe the response of the Earth, or part of the
Earth, when loads of a particular load cycle or of a particular magnitude are applied. These
effective viscosity parameters, however they may be defined, are analogous in many ways
to the Love numbers introduced to define the elastic response of the planet. At the high
frequency end of the spectrum illustrated in Figure I this parameter is often defined as the
Q or specific dissipation function. At the low frequency end of the spectrum this parameter
is often defined in terms of an effective Newtonian viscosity.
ix
x
Geophysical evidence points to a substantial frrst order stratification in viscosity: a high
viscosity lithosphere, an intermediate viscosity mantle, and a very low viscosity (outer)
core. Typical depth averaged values for these three layers would be 1025_1026 Pa s, 1021
Pa s and »100 Pa s. The viscosity of the lithosphere, with an effective relaxation time
constant (defined as viscosity/rigidity) of about 107 years, is an important parameter in
studies of tectonic processes that occur on time scales of a million years or longer. Such
processes include mountain building tectonics, sedimentary basin formation and continental
margin evolution. In such examples, the mantle can often be considered to respond as a
perfect fluid to any stresses transmitted to it through the lithosphere. Geophysical
problems that exist for estimating the viscosities of this layer include the lithospheric
deformations produced by sediment or volcanic loading. The big uncertainty here is the
need to know the loading histories of the sediments and the volcanics. For example, rarely
if ever, are the conditions implied by the widely used mathematical models for seamount
loading studies, met
An important line of evidence for the mantle viscosity comes from the Earth's gravity
field. Observations of this or of the geoid point to the existence of large scale density
anomalies distributed throughout the mantle and these can be interpreted in two
fundamentally different ways. Either the mantle is sufficiently rigid to be able to support
the density anomalies throughout geological time and they reflect conditions early in the
planet's life, or the anomalies are supported by mantle convection and they reflect the
dynamic nature of the Earth. Depending upon one's perceptions of planet Earth, the
gravity data can be used to reinforce either view. Few adherents to the first, static,
interpretation can now surely be found, but it remains of interest to examine the debate
between advocates of the two interpretations in the era before plate tectonics because this
emphasises once again the very fundamental ambiguity in the interpretation of this
important data set and that the outcome is strongly dependent on one's prejudices.
Fortunately there has been progress. In particular, the seismic evidence for global lateral
variations in P- and S- wave velocities has been important for mapping the three
dimensional structure of the Earth. It has now become possible to invert the gravity and
seismic velocity data subject to appropriate boundary conditions, to effectively estimate the
flow field that is required to support this three-dimensional structure, to predict the plate
motions that would result from this flow field, and then to adjust the mantle rheology
model so as to produce the best fit of predicted and observed plate velocity fields. Within
this calculation there is clearly scope for different assumptions and perceptions to be
introduced but to insist on this would be to distract from some wonderful work that has
been done in recent years towards solving this problem, some of which is reported in this
volume.
The viscous response of the Earth to forces on much shorter time scales is controlled
primarily by the mantle and here the lithosphere can often be treated as a simple elastic
layer. Thus, by examining the response of the planet to surface loads of distinctly different
loading cycles, it becomes possible to separate the viscosity of the lithosphere from that of
the mantle. The primary evidence for mantle deformation on time scales of 1()3 - 1()4 years
is the rebound of the crust following upon the glacial unloading, in latest Pleistocene time,
of the great ice sheets over northern Europe and North America. As the ice sheets decay,
the surface load is reduced, flow in the mantle is induced towards the region beneath the
formerly glaciated areas, and rebound of the crust results long after the original ice load has
vanished. Maximum thicknesses of the past ice sheets have reached three kilometers and
more so that stresses of the order of 100 MPa are transmitted to the mantle causing this
layer to flow with a characteristic time scale that is determined by its viscosity.
xi
Observations of the ongoing rebound therefore can constrain models of mantle viscosity
beneath the ice sheets if the history of glacial loading and unloading is adequately known.
More subtle changes also occur. As the ice sheets melt, the ocean volume is increased and
sea level can rise by 100 -150 m. The small stresses transmitted by this increased surface
load appear to be sufficient to produce flow in the mantle, away from beneath the oceans to
beneath the adjacent continents. This produces a small tilting and warping of continental
margins, observations of which permit, in principle at least, estimates to be made of the
mantle viscosity beneath. Here the question of lateral variations within the upper mantle
becomes important.
An important area of progress in the past two decades has been the recognition that the
glacial rebound problem is a global one; that a close interaction exists between the response
of the mantle and crust beneath and immediately adjacent to the former glaciated regions
and the sea level change along distant continental shorelines and ocean islands. By careful
combinations of observations of sea level change from these different localities, and by
using information from different time intervals during Late Pleistocene and Holocene time,
it becomes possible to separate out some of the parameters that influence the rebound
model, both Earth and ice sheet parameters, and to make progress in understanding the
solid Earth as well as the ice ages.
The glacial rebound problem is hardly new. T.F. Jamieson is generally credited with the
original suggestion, made in 1865, that the many elevated shorelines in northern Europe
were indicative of the Earth's adjustment to the removal of the Late Pleistocene ice sheets.
N.S. Shaler, reporting in 1874 on the apparent changing shorelines along the New England
coast of North America, made a similar suggestion. Attempts to quantitatively model this
rebound occurred only much later with solutions by N.A. Haskell, E. Niskanen,
B. Gutenberg, and F.A. Vening Meinesz in the 1940's. In the 1960's and early 1970's the
problem was reinvestigated by A.L. Bloom, R K. McConnell, R.J. O'Connell, and
R.I.Walcott. and in the mid and later half of the 1970's by L.M. Cathles, J.A. Clark,
W.R. Peltier, J. Chappell, and others. The glacial rebound problem continues to remain
one of the classical problems of geophysics and continues to draw the attention of
geophysicists and geologists. Each time the problem appears to have been resolved, new
conflicting observations have been found, contradictions in interpretation of theory have
been identified, or numerical methods have been improved.
Several factors account for this ongoing interest in the subject. One is that it is one of the
most appropriate experiments for estimating the mantle's non-elastic response on
intermediate geological time scales, and the determination of this response remains critical
to understanding the dynamics of the Earth. A second reason is that a great wealth of new
geomorphological evidence of sea level change in the recent geological past has become
available and which is important for constraining rebound models. A third reason is that
the problem has become relevant today in the context of the enhanced "greenhouse effect".
With the adage that in order to understand the present and future it is imperative that we
understand the past, the Late Pleistocene and Holocene data are becoming of renewed
interest for understanding possible future changes in sea level. Can the past behaviour of
sea level serve as a guide to how the present residual ice sheets may respond to increases in
temperature and to rising levels of the sea?
A fourth reason for the ongoing interest in the subject, and perhaps one as good as any of
the others, is the sheer challenge of a problem that has so many facets to it. An evaluation
of the problem requires examination of glaciological evidence, of ice sheet models, and of