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

Sea-level constraints on the amplitude and source distribution of Meltwater Pulse 1A.

During the last deglaciation, sea levels rose as ice sheets retreated. This climate transition was punctuated by periods of more intense melting; the largest and most rapid of these—Meltwater Pulse 1A—occurred about 14,500 years ago, with rates of sea-level rise reaching approximately 4 m per century1, 2, 3. Such rates of rise suggest ice-sheet instability, but the meltwater sources are poorly constrained, thus limiting our understanding of the causes and impacts of the event4, 5, 6, 7. In particular, geophysical modelling studies constrained by tropical sea-level records1, 8, 9 suggest an Antarctic contribution of more than seven metres, whereas most reconstructions10 from Antarctica indicate no substantial change in ice-sheet volume around the time of Meltwater Pulse 1A. Here we use a glacial isostatic adjustment model to reinterpret tropical sea-level reconstructions from Barbados2, the Sunda Shelf3 and Tahiti1. According to our results, global mean sea-level rise during Meltwater Pulse 1A was between 8.6 and 14.6 m (95% probability). As for the melt partitioning, we find an allowable contribution from Antarctica of either 4.1 to 10.0 m or 0 to 6.9 m (95% probability), using two recent estimates11, 12 of the contribution from the North American ice sheets. We conclude that with current geologic constraints, the method applied here is unable to support or refute the possibility of a significant Antarctic contribution to Meltwater Pulse 1A

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

The precession constant and its long-term variation

The dynamical flattening of the Earth, H, related to the precession constant, is a fundamental astro-geodetic parameter that appears in studies of the Earth's rotation and orbital evolution. We present numerical predictions and observations of the variation in H over time scales ranging from tens of millions of years to decades. The geophysical processes controlling this variation include solid-state convection in the rocky mantle of the Earth that drives plate tectonics, isostatic adjustments due to ice age loading, and ice-ocean mass transfer linked to modern global climate change. The time dependence of H is complex and non-linear, and thus, in contrast to previous suggestions, cannot be captured by a constant rate parameter

The effect of lateral variations in Earth structure on Last Interglacial sea level

It is generally agreed that the Last Interglacial (LIG; ∼130–115 ka) was a time when global average temperatures and global mean sea level were higher than they are today. However, the exact timing, magnitude and spatial pattern of ice melt is much debated. One difficulty in extracting past global mean sea level from local observations is that their elevations need to be corrected for glacial isostatic adjustment (GIA), which requires knowledge of Earth’s internal viscoelastic structure. While this structure is generally assumed to be radially symmetric, evidence from seismology, geodynamics and mineral physics indicates that large lateral variations in viscosity exist within the mantle. In this study, we construct a new model of Earth’s internal structure by converting shear wave speed into viscosity using parametrizations from mineral physics experiments and geodynamic constraints on Earth’s thermal structure. We use this 3-D Earth structure, which includes both variations in lithospheric thickness and lateral variations in viscosity, to calculate the first 3-D GIA prediction for LIG sea level. We find that the difference between predictions with and without lateral Earth structure can be metres to 10s of metres in the near field of former ice sheets, and up to a few metres in their far field. We demonstrate how forebulge dynamics and continental levering are affected by laterally varying Earth structure, with a particular focus on those sites with prominent LIG sea level records. Results from four 3-D GIA calculations show that accounting for lateral structure can act to increase local sea level by up to ∼1.5 m at the Seychelles and minimally decrease it in Western Australia. We acknowledge that this result is only based on a few simulations, but if robust, this shift brings estimates of global mean sea level from these two sites into closer agreement with each other. We further demonstrate that simulations with a suitable radial viscosity profile can be used to locally approximate the 3-D GIA result, but that these radial profiles cannot be found by simply averaging viscosity below the sea level indicator site

Global and local sea level during the Last Interglacial: A probabilistic assessment

The Last Interglacial (LIG) stage, with polar temperatures likely 3-5 C warmer than today, serves as a partial analogue for low-end future warming scenarios. Based upon a small set of local sea level indicators, the Intergovernmental Panel on Climate Change (IPCC) inferred that LIG global sea level (GSL) was about 4-6 m higher than today. However, because local sea levels differ from GSL, accurately reconstructing past GSL requires an integrated analysis of globally distributed data sets. Here we compile an extensive database of sea level indicators and apply a novel statistical approach that couples Gaussian process regression of sea level to Markov Chain Monte Carlo modeling of geochronological errors. Our analysis strongly supports the hypothesis that LIG GSL was higher than today, probably peaking at 6-9 m. Our results highlight the sea level hazard associated with even relatively low levels of sustained global warming.Comment: Preprint version of what has since been published in Natur

The PRISM4 (mid-Piacenzian) paleoenvironmental reconstruction

The mid-Piacenzian is known as a period of relative warmth when compared to the present day. A comprehensive understanding of conditions during the Piacenzian serves as both a conceptual model and a source for boundary conditions and means of verification of global climate model experiments. In this paper we present the PRISM4 reconstruction, a palaeoenvironmental reconstruction of the mid-Piacenzian (~3 Ma) containing data for palaeogeography, land and sea-ice, sea-surface temperature, vegetation, soils and lakes. Our retrodicted palaeogeography takes into account glacial isostatic adjustments and changes in dynamic topography. Soils and lakes, both significant as land surface features, are introduced to the PRISM reconstruction for the first time. Sea-surface temperature and vegetation reconstructions are unchanged but now have confidence assessments. The PRISM4 reconstruction is being used as boundary condition data for the Pliocene Model Intercomparison Project, Phase 2 (PlioMIP2) experiments

Mid-mantle deformation inferred from seismic anisotropy

With time, convective processes in the Earth's mantle will tend to align crystals, grains and inclusions. This mantle fabric is detectable seismologically, as it produces an anisotropy in material properties—in particular, a directional dependence in seismic-wave velocity. This alignment is enhanced at the boundaries of the mantle where there are rapid changes in the direction and magnitude of mantle flow, and therefore most observations of anisotropy are confined to the uppermost mantle or lithosphere and the lowermost-mantle analogue of the lithosphere, the D" region. Here we present evidence from shear-wave splitting measurements for mid-mantle anisotropy in the vicinity of the 660-km discontinuity, the boundary between the upper and lower mantle. Deep-focus earthquakes in the Tonga–Kermadec and New Hebrides subduction zones recorded at Australian seismograph stations record some of the largest values of shear-wave splitting hitherto reported. The results suggest that, at least locally, there may exist a mid-mantle boundary layer, which could indicate the impediment of flow between the upper and lower mantle in this region

Development of anisotropic structure in the Earth's lower mantle by solid-state convection

Seismological observations reveal highly anisotropic patches at the bottom of the Earth's lower mantle, whereas the bulk of the mantle has been observed to be largely isotropic(1-4). These patches have been interpreted to correspond to areas where subduction has taken place in the past or to areas where mantle plumes are upwelling, but the underlying cause for the anisotropy is unknown-both shape-preferred orientation of elastically heterogenous materials(5) and lattice-preferred orientation of a homogeneous material(6-8) have been proposed. Both of these mechanisms imply that large-strain deformation occurs within the anisotropic regions, but the geodynamic implications of the mechanisms differ. Shape-preferred orientation would imply the presence of large elastic (and hence chemical) heterogeneity whereas lattice-preferred orientation requires deformation at high stresses. Here we show, on the basis of numerical modelling incorporating mineral physics of elasticity and development of lattice-preferred orientation, that slab deformation in the deep lower mantle can account for the presence of strong anisotropy in the circum-Pacific region. In this model-where development of the mineral fabric (the alignment of mineral grains) is caused solely by solid-state deformation of chemically homogeneous mantle material-anisotropy is caused by large-strain deformation at high stresses, due to the collision of subducted slabs with the core-mantle boundary.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62804/1/416310a.pd