Inference of the timescale-dependent apparent viscosity structure in the upper mantle beneath Greenland

Contemporary crustal uplift and relative sea level change in Greenland is caused by the response of the solid Earth to ongoing and historical ice mass change. Glacial isostatic adjustment (GIA) models, which seek to match patterns of land surface displacement and relative sea level change, typically employ a linear Maxwell viscoelastic model for the Earth’s mantle. In Greenland, however, upper mantle viscosities inferred from ice load changes and other geophysical phenomena occurring over a range of timescales vary by up to two orders of magnitude. Here, we use full-spectrum rheological models to examine the influence of transient deformation within the Greenland upper mantle, which may account for these differing viscosity estimates. We use observations of shear wave velocity combined with constitutive rheological models to self-consistently calculate mechanical properties including the apparent upper mantle viscosity and lithosphere thickness across a broad spectrum of frequencies. We find that the contribution of transient behaviour is most significant over loading timescales of 102–103 years, which corresponds to the timeframe of ice mass loss over recent centuries. Predicted apparent lithosphere thicknesses are also in good agreement with inferences made across seismic, GIA, and flexural timescales. Our results indicate that full-spectrum constitutive models that more fully capture broadband mantle relaxation provide a means of reconciling seemingly contradictory estimates of Greenland’s upper mantle viscosity and lithosphere thickness made from observations spanning a range of timescales

Modelling converted seismic waveforms in isotropic and anisotropic 1-D gradients: discontinuous versus continuous gradient representations

Over the past decade, there have been numerous receiver function studies directed at imaging the lithosphere-asthenosphere boundary (LAB). Although it is generally accepted that receiver function phases observed in these studies are derived from physical mode conversions at depth within the lithosphere-asthenosphere transition, it is still debatable as to whether these phases are directly indicative of the LAB. This is because interpretation of receiver function LAB signals relies on understanding the elastic characteristics of the Earth’s outer thermal boundary layer. The main issues for receiver function imaging are the sharpness of the elastic material property transition and, more importantly, what specifically are the material gradients. To test the various transition models, a forward modelling approach is required that allows accurate waveform synthetics for a range of discontinuous and continuous gradients in anisotropic, elastic media. We present a derivation of the reflection and transmission response for continuous one-dimensional (1-D) gradients in generally anisotropic elastic media. We evaluate the influence of 1-D isotropic and anisotropic elastic gradients on the seismic waveform by comparing numerical results of models for discontinuous and continuous transitions. The results indicate that discontinuous representations using layers each with uniform parameters and with thicknesses on the order of approximately 1/3 to 1/8 of the dominant seismic wavelength can be used to accurately model P-to-S and S-to-P mode conversions due to continuous transitions of both isotropic and anisotropic elastic properties. From a practical point of view, when comparing synthetic modelling with observation, this constraint can be relaxed further. The presence of signal noise and/or the result of receiver function stacking techniques will likely obscure these subtle waveform effects. Hence this study suggests that accurate synthetic waveforms for LAB transitions can be modelled with discontinuous gradient representations using a reasonable number of discrete transition layers with layer thicknesses no greater than 1/2 to 1/3 the dominant seismic wavelength