Forward and inverse modeling of body and ocean load tides in a 3D Earth

Tidal deformations of the solid Earth, which are driven directly by gravitational interactions with the Moon and Sun (body tides) as well as indirectly by loading of the surface from Earth's fluid envelopes (load tides), are sensitive to the material properties of Earth's interior across a broad range of spatial and temporal scales.

The tidal responses provide key insights into mantle density and elastic structure. Recent studies have demonstrated that geodetic observations and tide models are now sufficiently precise to use measurements of tidally induced surface displacements as constraints in tomographic inversions. To this end, incorporating lateral heterogeneities into the mathematical model has become a necessary next step to possibly explain discrepancies between observed and predicted tidal responses.

We present a numerical approach to simultaneously account for 3D structure, topography, and internal discontinuities to constrain Earth's interior structure with tidal tomography using both body and ocean load tides. We show benchmarks for spherically symmetric Earth models and a sensitivity analysis using adjoint techniques to analyze the influence of 3D Earth structure on the displacement at the surface.

Our framework is based on the spectral-element method to simulate deformations under linear elasticity. The gravitational potential and mass-load forces, which generate the body and load tides, respectively, enter either as boundary conditions or as external sources. Using custom tailored mesh refinement and coarsening techniques, we can accurately discretize the coastlines of the Earth where the tidal loading response exhibits large amplitudes and high complexity. Furthermore, leveraging scientific libraries such as Salvus, PETSc and Eigen enables us (1) to handle 3D Earth models on fully unstructured meshes, (2) to include different physics and suitable interface conditions for mantle, core and the exterior domain above the Earth's surface, and (3) to develop a scalable, matrix-free linear solver with a custom preconditioner to efficiently solve the equations of motion and their adjoint counterpart.