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Journal ArticleDOI

The impulse response of a Maxwell Earth

01 Nov 1974-Reviews of Geophysics (John Wiley & Sons, Ltd)-Vol. 12, Iss: 4, pp 649-669
TL;DR: In this paper, an extended form of the correspondence principle is employed to determine directly the quasi-static deformation of viscoelastic earth models by mass loads applied to the surface.
Abstract: An extended form of the correspondence principle is employed to determine directly the quasi-static deformation of viscoelastic earth models by mass loads applied to the surface. The stress-strain relation employed is that appropriate to a Maxwell medium. Most emphasis is placed on the discussion of spherically stratified self-gravitating earth models, although some consideration is given to the uniform elastic half space and to the uniform viscous sphere, since they determine certain limiting behaviors that are useful for interpretation and proper normalization of the general problem. Laplace transform domain solutions are obtained in the form of ‘s spectra’ of a set of viscoelastic Love numbers. These Love numbers are defined in analogy with the equivalent elastic problem. An efficient technique is described for the inversion of these s spectra, and this technique is employed to produce sets of time dependent Love numbers for a series of illustrative earth models. These sets of time dependent Love numbers are combined to produce Green functions for the surface mass load boundary value problem. Through these impulse response functions, which are obtained for radial displacement, gravity anomaly, and tilt, a brief discussion is given of the approach to isostatic equilibrium. The response of the earth to an arbitrary quasi-static surface loading may be determined by evaluating a space-time convolution integral over the loaded region using these response functions.
Citations
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Journal ArticleDOI
TL;DR: The impact of the changing surface ice load upon both Earth's shape and gravitational field, as well as upon sea-level history, have come to be measurable using a variety of geological and geophysical techniques.
Abstract: ▪ Abstract The 100 kyr quasiperiodic variation of continental ice cover, which has been a persistent feature of climate system evolution throughout the most recent 900 kyr of Earth history, has occurred as a consequence of changes in the seasonal insolation regime forced by the influence of gravitational n-body effects in the Solar System on the geometry of Earth's orbit around the Sun. The impacts of the changing surface ice load upon both Earth's shape and gravitational field, as well as upon sea-level history, have come to be measurable using a variety of geological and geophysical techniques. These observations are invertible to obtain useful information on both the internal viscoelastic structure of the solid Earth and on the detailed spatiotemporal characteristics of glaciation history. This review focuses upon the most recent advances that have been achieved in each of these areas, advances that have proven to be central to the construction of the refined model of the global process of glacial isos...

2,333 citations

Journal ArticleDOI
27 Apr 2001-Science
TL;DR: For example, in this paper, the authors show that the earth-response function is depth dependent as well as spatially variable, and that the migration of coastlines can be predicted during glacial cycles, including the anthropologically important period from about 60,000 to 20,000 years ago.
Abstract: Sea level change during the Quaternary is primarily a consequence of the cyclic growth and decay of ice sheets, resulting in a complex spatial and temporal pattern. Observations of this variability provide constraints on the timing, rates, and magnitudes of the changes in ice mass during a glacial cycle, as well as more limited information on the distribution of ice between the major ice sheets at any time. Observations of glacially induced sea level changes also provide information on the response of the mantle to surface loading on time scales of 10 3 to 10 5 years. Regional analyses indicate that the earth-response function is depth dependent as well as spatially variable. Comprehensive models of sea level change enable the migration of coastlines to be predicted during glacial cycles, including the anthropologically important period from about 60,000 to 20,000 years ago.

1,600 citations

Journal ArticleDOI
TL;DR: From ∼1,000 observations of sea level, allowing for isostatic and tectonic contributions, this work quantified the rise and fall in global ocean and ice volumes for the past 35,000 years and provides new constraints on the fluctuation of ice volume in this interval.
Abstract: The major cause of sea-level change during ice ages is the exchange of water between ice and ocean and the planet's dynamic response to the changing surface load. Inversion of ∼1,000 observations for the past 35,000 y from localities far from former ice margins has provided new constraints on the fluctuation of ice volume in this interval. Key results are: (i) a rapid final fall in global sea level of ∼40 m in <2,000 y at the onset of the glacial maximum ∼30,000 y before present (30 ka BP); (ii) a slow fall to -134 m from 29 to 21 ka BP with a maximum grounded ice volume of ∼52 × 10(6) km(3) greater than today; (iii) after an initial short duration rapid rise and a short interval of near-constant sea level, the main phase of deglaciation occurred from ∼16.5 ka BP to ∼8.2 ka BP at an average rate of rise of 12 m⋅ka(-1) punctuated by periods of greater, particularly at 14.5-14.0 ka BP at ≥40 mm⋅y(-1) (MWP-1A), and lesser, from 12.5 to 11.5 ka BP (Younger Dryas), rates; (iv) no evidence for a global MWP-1B event at ∼11.3 ka BP; and (v) a progressive decrease in the rate of rise from 8.2 ka to ∼2.5 ka BP, after which ocean volumes remained nearly constant until the renewed sea-level rise at 100-150 y ago, with no evidence of oscillations exceeding ∼15-20 cm in time intervals ≥200 y from 6 to 0.15 ka BP.

1,558 citations

Journal ArticleDOI
08 Jul 1994-Science
TL;DR: The results show that LGM ice volume was approximately 35 percent lower than suggested by the CLIMAP reconstruction and the maximum heights of the main Laurentian and Fennoscandian ice complexes are inferred to have been commensurately lower with respect to sea level.
Abstract: A gravitationally self-consistent theory of postglacial relative sea level change is used to infer the variation of surface ice and water cover since the Last Glacial Maximum (LGM). The results show that LGM ice volume was approximately 35 percent lower than suggested by the CLIMAP reconstruction and the maximum heights of the main Laurentian and Fennoscandian ice complexes are inferred to have been commensurately lower with respect to sea level. Use of these Ice Age boundary conditions in atmospheric general circulation models will yield climates that differ significantly from those previously inferred on the basis of the CLIMAP data set.

1,176 citations

References
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Journal ArticleDOI
TL;DR: In this article, it is suggested that mosaic boundaries and boundaries between grains of nearly the same orientation may not serve as sources or sinks of the diffusion currents, in which case the creep rate will depend only on the configuration of grain boundaries having a sizable orientation differen...
Abstract: According to a suggestion of Nabarro, any crystal can change its shape by self‐diffusion in such way as to yield to an applied shearing stress, and this can cause the macroscopic behavior of a polycrystalline solid to be like that of a viscous fluid. It is possible that this phenomenon is the predominant cause of creep at very high temperatures and very low stresses, though not under more usual conditions. The theory underlying it is developed quantitatively, and calculations of rate of creep, or equivalently of effective viscosity, are given for aggregates of quasi‐spherical grains and for wires composed of cylindrical grains. Allowance is made for the effect of tangential stress relaxation at the grain boundaries. It is suggested that mosaic boundaries and boundaries between grains of nearly the same orientation may be unable to serve as sources or sinks of the diffusion currents, in which case the creep rate will depend only on the configuration of grain boundaries having a sizable orientation differen...

2,214 citations

Book
01 Jan 1956

1,961 citations

Journal ArticleDOI
TL;DR: In this article, the static deformation of an elastic half-space by surface pressure is reviewed and a brief mention is made of methods for solving the problem when the medium is plane-strategized, but the major emphasis is on the solution for spherical, radially stratified, gravitating earth models.
Abstract: The static deformation of an elastic half-space by surface pressure is reviewed. A brief mention is made of methods for solving the problem when the medium is plane stratified, but the major emphasis is on the solution for spherical, radially stratified, gravitating earth models. Love-number calculations are outlined, and from the Love numbers, Green's functions are formed for the surface mass-load boundary-value problem. Tables of mass-load Green's functions, computed for realistic earth models, are given, so that the displacements, tilts, accelerations, and strains at the earth's surface caused by any static load can be found by evaluating a convolution integral over the loaded region.

1,588 citations

Book
01 Jan 1969

1,398 citations

Journal ArticleDOI
TL;DR: In this article, the authors show how to determine whether a given finite set of gross Earth data can be used to specify an Earth structure uniquely except for fine-scale detail, and the shortest length scale which the given data can resolve at any particular depth.
Abstract: A gross Earth datum is a single measurable number describing some property of the whole Earth, such as mass, moment of interia, or the frequency of oscillation of some identified elastic-gravitational normal mode. We show how to determine whether a given finite set of gross Earth data can be used to specify an Earth structure uniquely except for fine-scale detail; and how to determine the shortest length scale which the given data can resolve at any particular depth. We apply the general theory to the linear problem of finding the depth-variation of a frequency-independent local Q from the observed quality factors Q of a finite number of normal modes. We also apply the theory to the non-linear problem of finding density vs depth from the total mass, moment, and normal-mode frequencies, in case the compressional and shear velocities are known.

1,371 citations