Load-Tide Sensitivity to 3-D Earth Structure

Earth deformation caused by the tidal redistribution of ocean mass is governed by the material properties of Earth's interior. Surface displacements induced by ocean tidal loading can exceed several centimeters over periods of hours. The rich spectrum of elastic and gravitational responses of the solid Earth produced by the load tides are predominantly sensitive to crust and upper-mantle structure, and inverting load-tide observations for Earth structure can complement independent constraints inferred from seismic tomography and Earth's body tides. 

Global Navigation Satellite Systems (GNSS) record the load-tide displacements with sub-millimeter precision and at high temporal resolution on the order of minutes. Recent studies have demonstrated agreement between predicted and GNSS-observed oceanic load tides in several regions worldwide to a similar level of accuracy. However, residuals between load-tide observations and predictions, which have been limited to spherically symmetric models for Earth structure, exhibit spatially coherent patterns that cannot be fully explained by random measurement or tide-model error and therefore present key opportunities to refine our understanding of Earth's 3-D structure at depths important to mantle convection and plate tectonics. 

Here, we present a novel numerical approach based on a preconditioned conjugate-gradient solver and the spectral-element method to investigate the sensitivities of Earth's load tides to 3-D variations in elastic Earth structure, including ellipticity, topography, and lateral contrasts in elasticity, density and crustal thickness. We leverage and extend the Salvus high-performance library to include gravitational physics and to solve quasi-static problems. High-order shape transformations and adaptive mesh refinement allow us to capture the spatial heterogeneity of the ocean tides with kilometer resolution as well as the large scale of exterior domain, which is needed to model the gravitational potential at reasonable computational cost. We perform a series of benchmark tests to verify the 3-D numerical-modeling approach against established quasi-analytical methods for modeling load-induced Earth deformation (LoadDef software). We then compute the sensitivities of load-induced surface displacements to 3-D Earth structure in two ways: (1) direct comparison of predicted surface displacements computed using 1-D and 3-D Earth models, and (2) direct computation of derivatives of surface displacements with respect to density and elasticity structure using the adjoint method.

Additional high-impact applications of the surface-load modeling capabilities include: quantifying seasonal fluctuations in mountain snowpack, tracking the depletion of groundwater reservoirs during periods of drought, improving constraints on ocean-tide models and refining the load-tide corrections employed in GNSS signal processing.