True polar wander driven by late-stage volcanism and the distribution of paleopolar deposits on Mars

The areal centroids of the youngest polar deposits on Mars are offset from those of adjacent paleopolar deposits by 5-10 degrees. We test the hypothesis that the offset is the result of true polar wander (TPW), the motion of the solid surface with respect to the spin axis, caused by a mass redistribution within or on the surface of Mars. In particular, we consider TPW driven by late-stage volcanism during the late Hesperian to Amazonian. There is observational and qualitative support for this hypothesis: in both North and South, observed offsets lie close to a great circle 90 degrees from Tharsis, as expected for polar wander after Tharsis formed. We calculate the magnitude and direction of TPW produced by mapped late-stage lavas for a range of lithospheric thicknesses, lava thicknesses, eruption histories, and prior polar wander events. If Tharsis formed close to the equator, the stabilizing effect of a fossil rotational bulge located close to the equator leads to predicted TPW of <2 degrees, too small to account for observed offsets. If, however, Tharsis formed far from the equator, late-stage TPW driven by low-latitude, late-stage volcanism would be 6-33 degrees, similar to that inferred from the location of paleopolar deposits. 4.4+/-1.3x10^19 kg of young erupted lava can account for the offset of the Dorsa Argentea Formation from the present-day south rotation pole. This mass is consistent with prior mapping-based estimates and would imply a mass release of CO2 by volcanic degassing similar to that in the atmosphere at the present time. The South Polar Layered Deposits are offset from the spin axis in the opposite sense to the other paleopolar deposits. This can be explained by an additional contribution from a plume beneath Elysium. We conclude with a list of observational tests of the TPW hypothesis.Comment: Accepted by Earth and Planetary Science Letters. 3 tables, 8 figure

A reappraisal of postglacial decay times from Richmond Gulf and James Bay, Canada

Decay times inferred from relative sea-level (RSL) histories of previously glaciated regions provide a potentially important constraint on mantle rheology. We present a new compilation of RSL data from Richmond Gulf and James Bay, Canada. This recompilation reveals errors in previous compilations that led to inaccurate estimates for the Richmond Gulf decay time in a series of recently published articles. We derive updated estimates for the decay time at Richmond Gulf and James Bay using a methodology that incorporates errors in both the age and the height of the sea-level markers. This exercise is guided by a series of synthetic RSL calculations that show that decay time estimates in the region can be significantly biased if the RSL time-series are not corrected for global eustatic sea-level trends, or if the estimates are based on composite RSL histories derived by combining data from both the Richmond Gulf and the James Bay regions. Our decay time analysis for Richmond Gulf applies the pioneering approach of Walcott (1980) to a large database and we derive a value of 4.0-6.6 kyr, where the range is defined by a misfit tolerance 10 per cent higher than the minimum. Our analysis for James Bay is based on the uplift curve derived by Hardy (1976), and we estimate a decay time of about 2.0-2.8 kyr. The difference between our estimates for Richmond Gulf and James Bay may be due to errors in the observational record from these regions, but could also be influenced by lateral variations in lithospheric structure associated with the assembly of Laurentia

Forward and inverse modelling of post-seismic deformation

We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.Natural Environment Research Council, British Antarctic Surve

Constraining proposed combinations of ice history and Earth rheology using VLBI determined baseline length rates in North America

We predict the present-day rates of change of the lengths of 19 North American baselines due to the glacial isostatic adjustment process. Contrary to previously published research, we find that the three dimensional motion of each of the sites defining a baseline, rather than only the radial motions of these sites, needs to be considered to obtain an accurate estimate of the rate of change of the baseline length. Predictions are generated using a suite of Earth models and late Pleistocene ice histories, these include specific combinations of the two which have been proposed in the literature as satisfying a variety of rebound related geophysical observations from the North American region. A number of these published models are shown to predict rates which differ significantly from the VLBI observations

Studies of regional and global tectonics and the rotation of the earth using very-long-baseline interferometry

Work is continuing on the study of atmospheric gradients. We include a preprint entitled 'The effect of turbulence on atmospheric gradient parameters determined from ground-based radiometric and space geodetic measurements'. Work has begun on a study of solid Earth tidal deformations using the VLBI data set. We have examined deformations at the semi-diurnal tidal period using the IRIS data set

Crustal loading near Great Salt Lake, Utah

Two sites of the BARGEN GPS network are located ∼30 km south of Great Salt Lake (GSL). Lake-level records since mid-1996 indicate seasonal water elevation variations of ∼0.3 m amplitude superimposed on a roughly “decadal” feature of amplitude ∼0.6 m. Using an elastic Green's function and a simplified load geometry for GSL, we calculate that these variations translate into radial crustal loading signals of ±0.5 mm (seasonal) and ±1 mm (decadal). The horizontal loading signals are a factor of ∼2 smaller. Despite the small size of the expected loading signals, we conclude that we can observe them using GPS time series for the coordinates of these two sites. The observed amplitudes of the variations agree with the predicted decadal variations to <0.5 mm. The observed annual variations, however, disagree; this difference may be caused by some combination of local precipitation-induced site motion, unmodeled loading from other nearby sources, errors in the GSL model, and atmospheric errors

The Mid-Pliocene sea-level conundrum: Glacial isostasy, eustasy and dynamic topography

Determining eustatic sea level during the Mid-Pliocene warm period (~ 3.3 to 2.9 Ma) has been a central but elusive goal in the study of past warm climates. Estimates of eustatic sea level based on geologic data span a broad range; variation that we now recognize is due in part to geographically varying post-depositional displacement caused by glacial isostatic adjustment and dynamic topography. In this study, we combine field observations and glacial isostatic adjustment modeling to estimate the dynamic topography signal in three areas that are important to paleo-sea level studies of the Mid-Pliocene warm period (South Africa, West Australia and southeastern United States). We show that dynamic topography played a significant role in the post-depositional displacement of Pliocene, and even younger Pleistocene, shorelines. In this regard, we provide a robust paleo-sea level elevation data set, corrected for glacial isostatic adjustment, that can be used to evaluate predictions from mantle flow models of dynamic topography

Anelasticity across seismic to tidal timescales: a self-consistent approach

In a pioneering study, Wahr & Bergen developed the widely adopted, pseudo-normal mode framework for predicting the impact of anelastic effects on the Earth's body tides. Lau $\textit{et al.}$ have recently derived an extended normal mode treatment of the problem (as well as a minor variant of the theory known as the direct solution method) that makes full use of theoretical developments in free oscillation seismology spanning the last quarter century and that avoids a series of assumptions and approximations adopted in the traditional theory for predicting anelastic effects. There are two noteworthy differences between these two theories: (1) the traditional theory only considers perturbations to the eigenmodes of an elastic Earth, whereas the new theory augments this set of modes to include the relaxation modes that arise in anelastic behaviour; and (2) the traditional theory approximates the complex perturbation to the tidal Love number as a scaled version of the complex perturbation to the elastic moduli, whereas the new theory computes the full complex perturbation to each eigenmode. In this study, we highlight the above differences using a series of synthetic calculations, and demonstrate that the traditional theory can introduce significant error in predictions of the complex perturbation to the Love numbers due to anelasticity and the related predictions of tidal lag angles. For the simplified Earth models we adopt, the computed lag angles differ by ∼20 per cent. The assumptions in the traditional theory have important implications for previous studies that use model predictions to correct observables for body tide signals or that analyse observations of body tide deformation to infer mantle anelastic structure. Finally, we also highlight the fundamental difference between apparent attenuation (i.e. attenuation inferred from observations or predicted using the above theories) and intrinsic attenuation (i.e. the material property investigated through experiments), where both are often expressed in terms of lag angles or $\textit{Q}$$^{-1}$. In particular, we demonstrate the potentially significant (factor of two or more) bias introduced in estimates of $\textit{Q}$$^{-1}$ and its frequency dependence in studies that have treated $\textit{Q}$$^{-1}$ determined from tidal phase lags or measured experimentally as being equal. The observed or theoretically predicted lag angle (or apparent $\textit{Q}$$^{-1}$) differs from the intrinsic, material property due to inertia, self-gravity and effects associated with the energy budget. By accounting for these differences we derive, for a special case, an expression that accurately maps apparent attenuation predicted using the extended normal mode formalism of Lau $\textit{et al.}$ into intrinsic attenuation. The theory allows for more generalized mappings which may be used to robustly connect observations and predictions of tidal lag angles to results from laboratory experiments of mantle materials.This work was supported by NSF EAR-1464024, NSF EAR-1215061, and Harvard University

On postglacial sea level—III. Incorporating sediment redistribution

We derive a generalized theory for gravitationally self-consistent, static sea level variations on earth models of arbitrary complexity that takes into account the redistribution of sediments. The theory is an extension of previous work that incorporated, into the governing equations, shoreline migration due to local sea level variations and changes in the geometry of grounded, marine-based ice. In addition, we use viscoelastic Love number theory to present a version of the new theory valid for spherically symmetric earth models. The Love number theory accounts for the gravitational, deformational and rotational effects of the sediment redistribution. As a first, illustrative application of the new theory, we compute the perturbation in sea level driven by an idealized pulse of sediment transport into the Gulf of Mexico. We demonstrate that incorporating a gravitationally self-consistent water load in this case significantly improves the accuracy of sea level predictions relative to previous simplified treatments of the sediment redistribution

Reciprocity and sensitivity kernels for sea level fingerprints

Reciprocity theorems are established for the elastic sea level fingerprint problem including rotational feedbacks. In their simplest form, these results show that the sea level change at a location x due to melting a unit point mass of ice at x' is equal to the sea level change at x' due to melting a unit point mass of ice at x. This identity holds irrespective of the shoreline geometry or of lateral variations in elastic Earth structure. Using the reciprocity theorems, sensitivity kernels for sea level and related observables with respect to the ice load can be readily derived. It is notable that calculation of the sensitivity kernels is possible using standard fingerprint codes, though for some types of observable a slight generalisation to the fingerprint problem must be considered. These results are of use within coastal hazard assessment and have a range of potential applications within studies of modern-day sea level change.Comment: Paper submitted to Geophysical Journal Internationa