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The Antarctic bedrock is evolving as the solid Earth responds to the past and ongoing evolution of the ice sheet. A recently improved ice loading history suggests that the Antarctic Ice Sheet (AIS) has generally been losing its mass since the Last Glacial Maximum. In a sustained warming climate, the AIS is predicted to retreat at a greater pace, primarily via melting beneath the ice shelves.We employ the glacial isostatic adjustment (GIA) capability of the Ice Sheet System Model (ISSM) to combine these past and future ice loadings and provide the new solid Earth computations for the AIS.We find that past loading is relatively less important than future loading for the evolution of the future bed topography. Our computations predict that the West Antarctic Ice Sheet (WAIS) may uplift by a few meters and a few tens of meters at years AD 2100 and 2500, respectively, and that the East Antarctic Ice Sheet is likely to remain unchanged or subside minimally except around the Amery Ice Shelf. The Amundsen Sea Sector in particular is predicted to rise at the greatest rate; one hundred years of ice evolution in this region, for example, predicts that the coastline of Pine Island Bay will approach roughly 45mmyr−1 in viscoelastic vertical motion. Of particular importance, we systematically demonstrate that the effect of a pervasive and large GIA uplift in the WAIS is generally associated with the flattening of reverse bed slope, reduction of local sea depth, and thus the extension of grounding line (GL) towards the continental shelf. Using the 3-D higher-order ice flow capability of ISSM, such a migration of GL is shown to inhibit the ice flow. This negative feedback between the ice sheet and the solid Earth may promote stability in marine portions of the ice sheet in the future.

Both the Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellites are returning rich data for the study of the solid earth, the oceans, and the climate. Current software analysis tools do not provide researchers with the ease and flexibility required to make full use of this data. We evaluate the capabilities and shortcomings of existing software tools including Mathematica, the GOCE User Toolbox, the ICGEM's (International Center for Global Earth Models) web server, and Tesseroids. Using existing tools as necessary, we design and implement software with the capability to produce gridded data and publication quality renderings from raw gravity data. The straight forward software interface marks an improvement over previously existing tools and makes new space gravity data more useful to researchers. Using the software we calculate Bouguer anomalies of the gravity tensor's vertical component in the Gulf of Mexico, Antarctica, and the 2010 Maule earthquake region. These maps identify promising areas of future research.

Sea level rise in the Gulf of Mexico has occurred at a rate of 1.8-2.2 mm/yr during the 20th century, or nearly the same as observed globally due to combined steric and water mass changes. Tide gauges in coastal Louisiana, however, record a substantially larger rate of rise and while a number of causal mechanisms may be responsible, their specific contribution is poorly understood. Using a realistic viscoelastic Earth model, detailed geologic parameters for south Louisiana and new GPS data, we demonstrate that Holocene sedimentary loading in the Gulf and Mississippi River delta is capable of contributing to 1-8 mm/yr of subsidence over areas of 30-0.75 x 10(exp 3) km(exp 2).

Precise GPS measurements of elastic relative site displacements due to surface mass loading offer important constraints on global surface mass transport. We investigate effects of site distribution and aliasing by higher- degree (n ≥ 2) loading terms on inversion of GPS data for n = 1 load coefficients and geocenter motion. Covariance and simulation analyses are conducted to assess the sensitivity of the inversion to aliasing and mismodeling errors and possible uncertainties in the n = 1 load coefficient determination. We found that the use of center-of-figure approximation in the inverse formulation could cause 10– 15% errors in the inverted load coefficients. n = 1 load estimates may be contaminated significantly by unknown higher-degree terms, depending on the load scenario and the GPS site distribution. The uncertainty in n = 1 zonal load estimate is at the level of 80–95% for two load scenarios.

Great strides have been made during the past 30 years in refining models of the last global glaciation. The refinements draw upon a vastly expanded relative sea level and sedimentary core record. Furthermore, we now possess a sharpened understanding of the mechanisms that drive climate changes associated with deglaciation. Some 15 years ago, using only 5.5 years of ranging data, analyses of the drift in LAGEOS I node acceleration was used to infer that postglacial rebound was responsible for a secular change in the Earth's ellipsoidal shape (Yoder et al., .1983]. Today there exists a wealth of geodynamics satellite orbit data that constrain the secular time-dependence of the Earth's shape and low order gravity field, which includes mass redistribution from present-day glacier and great ice sheet imbalance and from postglacial rebound. We have shown that an unambiguous determination of the secular variation in the Earth's pear shaped harmonic (l = 3, m = 0) might provide information that bears on the present-day mass balance of Antarctica. This issue is revisited in light of new constraints on glacial loading during the late-Pleistocene and Holocene. An especially critical issue for the interpretation of secular odd degree zonal harmonics, l = 3 to 7, is the timing and magnitude of the deglaciation of Antarctica from Last Glacial Maximum. We explore ways in which the recovery of secular variation in both zonal and non-zonal harmonics for l = 2 through 7 can improve constraints on both rebound and present-day ice sheet balance.

Detectable crustal motion and secular rate of change of solid-surface gravity may be produced by the Earth's response to present day and/or past ice mass changes in Antarctica.

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 xi ranging from -1.1 to 0.45 mm/yr, and predict polar motion m and time-varying low-degree gravitational coefficients J(sub l) that differ significantly from earlier estimates. A reasonably linear relationship between the rate of sea level change from Antarctica xi(sub A) and the predicted Antarctic J(sub l) 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 J(sub l) and sea level rise xi. Numerous viable combinations of lower mantle viscosity and hydrologic sources are found that safely "observed" in the range of 1 to 2-2.5 mm/yr and observed J(sub l) for degrees 2, 3, and 4. In contrast, rates of global sea level rise above 2.5 mm/yr are inconsistent with available J(sub l) observations. The successful composite models feature a pair of lower mantle viscosity solutions arising from the sensitivity of J(sub l) to glacial rebound. The paired values are well separated at xi = 1 mm/yr, but move closer together as xi is increased, and, in fact, merge around xi = 2 - 2.5 mm/yr, revealing an intimate relation between xi and preferred lower mantle viscosity. This general pattern is quite robust and persists for different J(sub l) solutions, for variations in source assumptions, and for different styles of lower mantle viscosity stratification. Tighter J(sub l) constraints for l greater than 2 may allow some viscosity stratification schemes and source assumptions to be excluded in the future. For a given total observed xi the sea level rise from Antarctica xi(sub A) is tightly constrained and ranges from 0 to + 1 mr/yr (corresponding to an ablating ice sheet) as estimates of xi 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.

Postseismic horizontal strain and displacement following the June 28, 1992, Landers, California, earthquake (M(sub W) 7.3) is broad scale and cannot be explained solely by delayed afterslip located at the rupturing fault trace. Both the observed strain at Pifion Flat Observatory (PFO) and observed Global Positioning System receiver velocities evolve rapidly after the Landers-Big Bear earthquake sequence. The observed exponential decay of these motions, with timescales of 4-34 days, may reflect a soft creep rheology in the lower crust and brittle-ductile transition zone or even within the seismogenic crust itself. Here a simple model of a two-dimensional screw dislocation in a layered Maxwell viscoelastic Earth is employed in conjunction with a composite rheology to demonstrate that the short timescale transient response modes (approx. = 4-34 days) are consistent with the behavior of a biviscous lower crust. The lowest viscosity of this system is derivable from laboratory experimental data on the long-term creep of natural quarztites, and the highest viscosity is consistent with isostasy-related lower crustal flow in a continental extensional tectonic environment. The model predicts significant stress relaxation at the base of the seismogenic crust. Near the base of the seismogenic zone, and about 4 km away from the mainshock, the rate of predicted relaxation is of the order of 0.01 MPa/ d during the first 20 days of postseismic flow. Oblate spheroidal inclusions at 5% concentration levels that are both aligned and fairly flat in shape and that have a viscosity of 3-4 x 10(exp 15) Pa s are consistent with both the amplitude and decay time of horizontal crustal strain observed at PFO after the Landers mainshock. It is speculated that the structures exposed in cross sections and in seismic reflection profiles of the lower crust that have mylonitic associations are, in part, the cause of such rapid postseismic evolution in southeastern California. Unmylonitized quartz-rich rock at sufficiently elevated temperatures could also contribute to the rapid decay modes.

The peak vertical velocities predicted by three realistic, but contrasting, present-day scenarios of Antarctic ice sheet mass balance are found to be of the order of several mm/a. One scenario predicts local uplift rates in excess of 5 mm/a. These rates are small compared to the peak Antarctic vertical velocities of the ICE-3G glacial rebound model, which are in excess of 20 mm/a. If the Holocene Antarctic deglaciation history portrayed in ICE-3G is realistic, and if regional upper mantle viscosity is not an order of magnitude below 10(exp 21) pa s, then a vast geographical region in West Antarctica is uplifting at a rate that could be detected by a future Global Positioning System (GPS) campaign. While present-day scenarios predict small vertical crustal velocities, their overall continent-ocean mass exchange is large enough to account for a substantial portion of the observed secular polar motion ((Omega)m(bar)) and time-varying zonal gravity field J(sub 1).

Mantle-wide heterogeneity is largely controlled by deeply penetrating thermal convective currents. These thermal currents are likely to produce significant lateral variation in rheology, and this can profoundly influence overall material behaviour. How thermally related lateral viscosity variations impact models of glacio-isostatic and tidal deformation is largely unknown. An important step towards model improvement is to quantify, or bound, the actual viscosity variations that characterize the mantle. Simple scaling of viscosity to shear-wave velocity fluctuations yields map-views of long- wavelength viscosity variation. These give a general quantitative description and aid in estimating the depth dependence of rheological heterogeneity throughout the mantle. The upper mantle is probably characterized by two to four orders of magnitude variation (peak-to-peak). Discrepant time-scales for rebounding Holocene shorelines of Hudson Bay and southern Iceland are consistent with this characterization. Results are given in terms of a local average viscosity ratio, (Delta)eta(bar)(sub i), of volumetric concentration, phi(sub i). For the upper mantle deeper than 340 km the following reasonable limits are estimated for (delta)eta(bar) approx. equal 10(exp -2): 0.01 less than or equal to phi less than or equal to 0.15. A spectrum of ratios (Delta)eta(bar)(sub i) less than 0.1 at concentration level eta(sub i) approx. equal 10(exp -6) - 10(exp -1) in the lower mantle implies a spectrum of shorter time-scale deformational response modes for second-degree spherical harmonic deformations of the Earth. Although highly uncertain, this spectrum of spatial variation allows a purely Maxwellian viscoelastic rheology simultaneously to explain all solid tidal dispersion phenomena and long-term rebound-related mantle viscosity. Composite theory of multiphase viscoelastic media is used to demonstrate this effect.

Seismic attenuation at low frequency has previously been modeled using two approaches: (1) Examination of all possible microstructural dislocation mechanisms that involve irreversible thermodynamics [Minster and Anderson 1981, P. Trans. R.S. Lond, A, 299]; (2) Parameterized superposition of one-dimensional analogue springs and dashpots, usually consisting of a three-parameter standard linear solid arrangement [Liu et al. 1976, G.J.R.A.S., 47]. The first approach is appealing in that a strong connection is made between micromechanical dissipation and short-term creep that can be studied in the laboratory. The second approach has the advantage of providing a robust 'fit' to actual seismic observations, but has little intrinsic physical content...