Erik Roman Ivins

Predictions of Antarctic crustal motions driven by present-day ice sheet evolution and by isostatic memory of the Last Glacial Maximum

Detectable crustal motion and secular rate of change of solid-surface gravity may be produced by the Earths response to present-day and past ice mass changes in Antarctica. Scenarios of present-day ice mass balance, previously utilized to explore the global geodetic signatures of the Antarctic ice sheet, produce elastic crustal responses that are typically bounded by uplift rates ≤5 mm/yr, horizontal motion ≤1 mm/yr, and solid-surface gravity change rates ≤1 μGal/yr. In a restricted locality, one scenario produces uplift rates slightly in excess of 10 mm/yr and correspondingly enhanced horizontal and gravity rates. In contrast, the viscoelastic response to ice mass changes occurring since Last Glacial Maximum (LGM) exceeds 5 mm/yr (uplift) over substantial portions of West Antarctica for a wide range of plausible choices of timing and magnitude of deglaciation and mantle viscosity. Similarly, viscoelastic gravity rate predictions exceed 1 μGal/yr (decrease) over large regions, confirming suggestions that a Global Positioning System (GPS) and absolute gravity-based program of crustal monitoring in Antarctica could potentially detect postglacial rebound. A published revision to the CLIMAP model of the Antarctic ice sheet at LGM, herein called the D91 model, features a substantially altered West Antarctic ice sheet reconstruction. This revision predicts a spatial pattern of present-day crustal motion and surface gravity change that diverges strikingly from CLIMAP-based models. Peak D91 crustal rates, assuming deglaciation begins at 12 kyr and ends at 5 kyr, are around 16 mm/yr (uplift), 2 mm/yr (horizontal), and −2.5 μGal/yr (gravity). Tabulated crustal response predictions for selected Antarctic bedrock sites indicate critical localities in the interior of West Antarctica where expected responses are large and D91 predictions differ from CLIMAP-based models by a factor of 2 or more. Observations of the postglacial rebound signal in Antarctica might help constrain Antarctic mass balance and contribution to sea level rise over the past 20,000 years.

Global geodetic signatures of the Antarctic Ice Sheet

Four scenarios of present day Antarctic ice sheet mass change are developed from comprehensive reviews of the available glaciological and oceanographic evidence. The gridded scenarios predict widely varying contributions to secular sea level change ranging from −1.1 to 0.45 mm/yr, and predict polar motion and time-varying low-degree gravitational coefficients that differ significantly from earlier estimates. A reasonably linear relationship between the rate of sea level change from Antarctica A and the predicted Antarctic is found for the four scenarios. This linearity permits a series of forward models to be constructed that incorporate the effects of ice mass changes in Antarctica, Greenland, and distributed smaller glaciers, as well as postglacial rebound (assuming the ICE-3G deglaciation history), with the goal of obtaining optimum reconciliation between observed constraints on and sea level rise . Numerous viable combinations of lower mantle viscosity and hydrologie sources are found that satisfy “observed” in the range of 1 to 2–2.5 mm/yr and observed for degrees 2, 3, and 4. In contrast, rates of global sea level rise above 2.5 mm/yr are inconsistent with available observations. The successful composite models feature a pair of lower mantle viscosity solutions arising from the sensitivity of to glacial rebound. The paired values are well separated at  mm/yr, but move closer together as is. increased, and, in fact, merge around =2-2.5 mm/yr, revealing an intimate relation between and preferred lower mantle viscosity. This general pattern is quite robust and persists for different solutions, for variations in source assumptions, and for different styles of lower mantle viscosity stratification. Tighter constraints for l > 2 may allow some viscosity stratification schemes and source assumptions to be excluded in the future. For a given total observed , the sea level rise from Antarctica A is tightly constrained and ranges from 0 to + 1 mm/yr (corresponding to an ablating ice sheet) as estimates of are raised from 1 to 2.5 mm/yr. However, when the degree 3 zonal harmonic constraint is removed, the solutions show little sensitivity to Antarctic mass balance, emphasizing the need for a well determined odd-degree secular zonal harmonic for determining polar ice mass balance.

Deep mantle viscous structure with prior estimate and satellite constraint

Radial viscosity profiles are constructed for the mantle using plausible temperature profiles and high-temperature creep models in olivine. While it is possible to specifically design mantle thermal profiles that produce relatively constant viscosity, temperatures deduced from parametric and/or full numerical simulation of convection predict steep increases of viscosity with depth. The most ubiquitous trend is an increase in viscosity from about 800 to 900 km depth to the top of the D″ layer. Predicted increase of viscosity in this portion of the lower mantle ranges from a factor of 102 to 104. Precise estimates are impossible due uncertainty in determining activation volume V* and activation energy E*. Zeroth-order extrapolation of a creep law to lower mantle conditions requires the assumption that diffusion of a single ionic species controls dislocation mobility. The extrapolation is useful in spite of its great uncertainty. Our rationale consists of two essential elements: (1) Creep laws with depth-dependent prefactor A(r) and depth-dependent activation volume V*(r), energy E*(r), and enthalpy S*(r) can be parameterized using estimates of diffusion constants based on elasticity. (2) Secular changes in Earths gravity field, particularly the zonal coefficients Jl are now detected in the orbits of artificial satellites such as LAGEOS and Starlette. These secular changes are believed to be dominated by postglacial rebound, although there is some contribution from present-day glacial melting. These gravity field measurements, when combined with constraints on glacial melting, provide a sensitive set of constraints on lower mantle viscous response to the Last glacial epoch and, hence, provide a test of a priori estimates. A radially stratified and incompressible Earth model is used to test sensitivity of data to viscosity increases with depth and convective boundary layer structure. Prior estimates and observed nontidal J2(−C20) are consistent with a layered lower mantle viscosity. Details of this layering are examined by comparing predicted and observed J3, J4. Speculation that a high-viscosity layer exists above D″ is considered. With a 650-km-thick deep high-viscosity layer (η ≈ 6.0 × 1023 Pa s) the remaining lower mantle is in one of two ranges: 1.5 to 3.5 × 1020 or 3.5 to about 10. × 1022 Pa s. Observational bounds on secular gravity coefficients C30, C40, C50, and C70 using LAGEOS, Starlette, or Etalon satellite data could eliminate the ambiguity between these two viscosity ranges.

Transient creep of a composite lower crust: 1. Constitutive theory

A composite model is proposed to describe the time-dependent response of the Earths lower crust. The motivation for such a model is twofold: First, new observations of widespread postseismic deformation indicate that the deep continental crust responds viscoelastically, having both long- and short-term decay times. Second, by any number of observationally based rationales, the lower crust is compositionally and structurally heterogeneous over many length scales. For heterogeneities that have much smaller characteristic lengths than the minimum deformation wavelength of interest, the aggregate rheology can be described by composite media theory. For wavelengths of the order of the thickness of the lower crust (≈25–40 km) and larger, composite theory may be applied to heterogeneities that are smaller than about several hundred meters, or equivalent to the vertical extent of a thick lower crustal mylonitic shear zone. The composite media theory developed here is constructed using both Eshelby-Mori-Tanaka theory for aligned generalized spheroidal inclusions and a generalized self-consistent method. The inclusions and matrix are considered to be Maxwellian viscoelastic: a rheology that is consistent with past homogeneous models of postseismic stress relaxation. The composite theory presented here introduces a transient response to a suddenly imposed stress field which does not appear in homogeneous Maxwell models. Analytic expressions for the amplitude and duration of the transient and for the effective long- and short-term viscosities of the composite are given which describe the sensitivity to inclusion concentration (Φ), to shape, and to ratio of inclusion-to-matrix viscosity (R).

Correction to “Transient creep of a composite lower crust: 2. A polymineralic basis for rapidly evolving postseismic deformation modes” by Erik R. Ivins

Ivins used three relations for estimating the effective viscosity of quartzites and crustal rocks having strong quartz affinity.