The possibility of a transient rheological response to ice age loading, first discussed in the literature of the 1980s, has received renewed attention. Transient behaviour across centennial to millennial timescales has been invoked to reconcile apparently contradictory inferences of steady-state (Maxwell) viscosity based on two distinct data sets from Greenland: Holocene sea-level curves and Global Navigation Satellite System (GNSS) derived modern crustal uplift data. To revisit this issue, we first compute depth-dependent Fréchet kernels using 1-D Maxwell viscoelastic Earth models and demonstrate that the mantle resolving power of the two Greenland data sets is highly distinct, reflecting the differing spatial scale of the associated surface loading: the sea-level records are sensitive to viscosity structure across the entire upper mantle while uplift rates associated with post-1000 CE fluctuations of the Greenland Ice Sheet have a dominant sensitivity to shallow asthenosphere viscosity. Guided by these results, we present forward models which demonstrate that a moderate low viscosity zone beneath the lithosphere in Maxwell Earth models provides a simple route to simultaneously reconciling both data sets by significantly increasing predictions of present-day uplift rates in Greenland whilst having negligible impact on predictions of Holocene relative sea-level curves from the region. Our analysis does not rule out the possibility of transient deformation, but it suggests that it is not required to simultaneously explain these two data sets. A definitive demonstration of transient behaviour requires that one account for the resolving power of the data sets in modelling the glacial isostatic adjustment process.
A key initial step in geophysical imaging is to devise an effective means of mapping the sensitivity of an observation to the model parameters, that is to compute its Fréchet derivatives or sensitivity kernel. In the absence of any simplifying assumptions and when faced with a large number of free parameters, the adjoint method can be an effective and efficient approach to calculating Fréchet derivatives and requires just two numerical simulations. In the Glacial Isostatic Adjustment problem, these consist of a forward simulation driven by changes in ice mass and an adjoint simulation driven by fictitious loads that are applied at the observation sites. The theoretical basis for this approach has seen considerable development over the last decade. Here, we present the final elements needed to image 3-D mantle viscosity using a dataset of palaeo sea-level observations. Developments include the calculation of viscosity Fréchet derivatives (i.e. sensitivity kernels) for relative sea-level observations, a modification to the numerical implementation of the forward and adjoint problem that permits application to 3-D viscosity structure, and a recalibration of initial sea level that ensures the forward simulation honours present-day topography. In the process of addressing these items, we build intuition concerning how absolute sea-level and relative sea-level observations sense Earth’s viscosity structure and the physical processes involved. We discuss examples for potential observations located in the near field (Andenes, Norway), far field (Seychelles), and edge of the forebulge of the Laurentide ice sheet (Barbados). Examination of these kernels: (1) reveals why 1-D estimates of mantle viscosity from far-field relative sea-level observations can be biased; (2) hints at why an appropriate differential relative sea-level observation can provide a better constraint on local mantle viscosity and (3) demonstrates that sea-level observations have non-negligible 3-D sensitivity to deep mantle viscosity structure, which is counter to the intuition gained from 1-D radial viscosity Fréchet derivatives. Finally, we explore the influence of lateral variations in viscosity on relative sea-level observations in the Amundsen Sea Embayment and at Barbados. These predictions are based on a new global 3-D viscosity inference derived from the shear-wave speeds of GLAD-M25 and an inverse calibration scheme that ensures compatibility with certain fundamental geophysical observations. Use of the 3-D viscosity inference leads to: (1) generally greater complexity within the kernel; (2) an increase in sensitivity and presence of shorter length-scale features within lower viscosity regions; (3) a zeroing out of the sensitivity kernel within high-viscosity regions where elastic deformation dominates and (4) shifting of sensitivity at a given depth towards distal regions of weaker viscosity. The tools and intuition built here provide the necessary framework to explore inversions for 3-D mantle viscosity based on palaeo sea-level data.
more » « less- Award ID(s):
- 2142592
- NSF-PAR ID:
- 10482618
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Geophysical Journal International
- Volume:
- 236
- Issue:
- 2
- ISSN:
- 0956-540X
- Format(s):
- Medium: X Size: p. 1139-1171
- Size(s):
- ["p. 1139-1171"]
- Sponsoring Org:
- National Science Foundation
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SUMMARY Earth structure beneath the Antarctic exerts an important control on the evolution of the ice sheet. A range of geological and geophysical data sets indicate that this structure is complex, with the western sector characterized by a lithosphere of thickness ∼50–100 km and viscosities within the upper mantle that vary by 2–3 orders of magnitude. Recent analyses of uplift rates estimated using Global Navigation Satellite System (GNSS) observations have inferred 1-D viscosity profiles below West Antarctica discretized into a small set of layers within the upper mantle using forward modelling of glacial isostatic adjustment (GIA). It remains unclear, however, what these 1-D viscosity models represent in an area with complex 3-D mantle structure, and over what geographic length-scale they are applicable. Here, we explore this issue by repeating the same modelling procedure but applied to synthetic uplift rates computed using a realistic model of 3-D viscoelastic Earth structure inferred from seismic tomographic imaging of the region, a finite volume treatment of GIA that captures this complexity, and a loading history of Antarctic ice mass changes inferred over the period 1992–2017. We find differences of up to an order of magnitude between the best-fitting 1-D inferences and regionally averaged depth profiles through the 3-D viscosity field used to generate the synthetics. Additional calculations suggest that this level of disagreement is not systematically improved if one increases the number of observation sites adopted in the analysis. Moreover, the 1-D models inferred from such a procedure are non-unique, that is a broad range of viscosity profiles fit the synthetic uplift rates equally well as a consequence, in part, of correlations between the viscosity values within each layer. While the uplift rate at each GNSS site is sensitive to a unique subspace of the complex, 3-D viscosity field, additional analyses based on rates from subsets of proximal sites showed no consistent improvement in the level of bias in the 1-D inference. We also conclude that the broad, regional-scale uplift field generated with the 3-D model is poorly represented by a prediction based on the best-fitting 1-D Earth model. Future work analysing GNSS data should be extended to include horizontal rates and move towards inversions for 3-D structure that reflect the intrinsic 3-D resolving power of the data.
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We have formulated the Fréchet kernel computation using the adjoint-state method based on a fractional viscoacoustic wave equation. We first numerically prove that the 1/2- and the 3/2-order fractional Laplacian operators are self-adjoint. Using this property, we find that the adjoint wave propagator preserves the dispersion and compensates the amplitude, whereas the time-reversed adjoint wave propagator behaves identically to the forward propagator with the same dispersion and dissipation characters. Without introducing rheological mechanisms, this formulation adopts an explicit [Formula: see text] parameterization, which avoids the implicit [Formula: see text] in the conventional viscoacoustic/viscoelastic full-waveform inversion ([Formula: see text]-FWI). In addition, because of the decoupling of operators in the wave equation, the viscoacoustic Fréchet kernel is separated into three distinct contributions with clear physical meanings: lossless propagation, dispersion, and dissipation. We find that the lossless propagation kernel dominates the velocity kernel, whereas the dissipation kernel dominates the attenuation kernel over the dispersion kernel. After validating the Fréchet kernels using the finite-difference method, we conduct a numerical example to demonstrate the capability of the kernels to characterize the velocity and attenuation anomalies. The kernels of different misfit measurements are presented to investigate their different sensitivities. Our results suggest that, rather than the traveltime, the amplitude and the waveform kernels are more suitable to capture attenuation anomalies. These kernels lay the foundation for the multiparameter inversion with the fractional formulation, and the decoupled nature of them promotes our understanding of the significance of different physical processes in [Formula: see text]-FWI.more » « less
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Abstract Contemporary crustal uplift and relative sea level (RSL) 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 RSL 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 behavior 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.
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Abstract. Accurate glacial isostatic adjustment (GIA) modelling in the cryosphere is required for interpreting satellite, geophysical and geological recordsand for assessing the feedbacks of Earth deformation and sea-level change on marine ice-sheet grounding lines. GIA modelling in areas of active ice lossin West Antarctica is particularly challenging because the ice is underlain by laterally varying mantle viscosities that are up to several orders ofmagnitude lower than the global average, leading to a faster and more localised response of the solid Earth to ongoing and future ice-sheet retreatand necessitating GIA models that incorporate 3-D viscoelastic Earth structure. Improvements to GIA models allow for computation of the viscoelasticresponse of the Earth to surface ice loading at sub-kilometre resolution, and ice-sheet models and observational products now provide the inputs toGIA models at comparably unprecedented detail. However, the resolution required to accurately capture GIA in models remains poorly understood, andhigh-resolution calculations come at heavy computational expense. We adopt a 3-D GIA model with a range of Earth structure models based on recentseismic tomography and geodetic data to perform a comprehensive analysis of the influence of grid resolution on predictions of GIA in the AmundsenSea Embayment (ASE) in West Antarctica. Through idealised sensitivity testing down to sub-kilometre resolution with spatially isolated ice loadingchanges, we find that a grid resolution of ∼ 13 of the radius of the load or higher is required to accurately capture the elasticresponse of the Earth. However, when we consider more realistic, spatially coherent ice loss scenarios based on modern observational records andfuture ice-sheet model projections and adopt a viscoelastic Earth, we find that predicted deformation and sea-level change along the grounding lineconverge to within 5 % with grid resolutions of 7.5 km or higher, and to within 2 % for grid resolutions of 3.75 km andhigher, even when the input ice model is on a 1 km grid. Furthermore, we show that low mantle viscosities beneath the ASE lead to viscousdeformation that contributes to the instrumental record on decadal timescales and equals or dominates over elastic effects by the end of the 21stcentury. Our findings suggest that for the range of resolutions of 1.9–15 km that we considered, the error due to adopting a coarser gridin this region is negligible compared to the effect of neglecting viscous effects and the uncertainty in the adopted mantle viscosity structure.more » « less
