Global Models From Sparse Data: A Robust Estimate of Earth's Residual Topography Spectrum

A significant component of Earth's surface topography is maintained by stresses induced by underlying mantle flow. This “dynamic” topography cannot be directly observed, but it can be approximated—particularly at longer wavelengths—from measurements of residual topography, which are obtained by removing isostatic effects from the observed topography. However, as these measurements are made at discrete, unevenly distributed locations on Earth's surface, inferences about global properties can be challenging. In this paper, we present and apply a new approach to transforming pointwise measurements into a continuous global representation. The approach, based upon the statistical theory of Gaussian processes, is markedly more stable than existing approaches—especially for small data sets. We are therefore able to infer the spatial pattern, wavelength, and amplitude of residual topography using only the highest quality oceanic spot measurements within the database of Hoggard et al. (2017, https://doi.org/10.1002/2016JB013457). Our results indicate that the associated spherical harmonic power spectrum peaks at l = 2, with power likely in the range 0.46–0.76 km2. This decreases by over an order of magnitude to around 0.02 km2 at l = 30. Around 85% of the total power is concentrated in degrees 1–3. Our results therefore confirm previous findings: Earth's residual topography expression is principally driven by deep mantle flow, but shallow processes are also crucial in explaining the general form of the power spectrum. Finally, our approach allows us to determine the locations where collection of new data would most impact our knowledge of the spectrum. Plain Language Summary As the mantle flows, it induces deformation at Earth's surface, pushing it up at some locations and pulling it down elsewhere. This deformation can be quantified by measuring so‐called residual topography, at specific locations. However, we only have a small number of such measurements, and they are clustered in particular areas on Earth's surface: inferring a global representation of residual topography is therefore a challenge. In this paper, we develop a new method for deriving robust global maps from such data and apply this to a set of measurements of residual topography. An advantage of our method is that it remains effective for small data sets, enabling a more conservative approach to data selection. Our results complement recent studies on residual topography, highlighting how mantle d