Oceanic Residual Topography Agrees With Mantle Flow Predictions at Long Wavelengths

Abstract

Dynamic topography, the surface deflection induced by sublithosheric mantle flow, is an important prediction made by geodynamic models, but there is an apparent disparity between geodynamic model predictions and estimates of residual topography (total topography minus lithospheric and crustal contributions). We generate synthetic global topography fields with different power spectral slopes and spatial patterns to investigate how well the long-wavelength (spherical degrees 1 to 3) components can be recovered from a discrete set of samples where residual topography has been recently estimated. An analysis of synthetic topography, along with observed geoid and gravity anomalies, demonstrates the reliability of signal recovery. Appropriate damping factors, which depend on the maximum degree in the spherical harmonic expansion that is used to fit the samples, must be applied to recover the long-wavelength topography correctly; large damping factors smooth the model excessively and suppress residual topography amplitude and power spectra unrealistically. Recovered long-wavelength residual topographies based on recent oceanic point-wise estimates with different spherical expansion degrees agree with each other and with the predicted dynamic topography from mantle flow models. The peak amplitude of the long-wavelength residual topography from oceanic observations is about 1 km, suggesting an important influence of large-scale deep mantle flow.

On the Scales of Dynamic Topography in Whole‐Mantle Convection Models

“…The discrepancy between numerical models of dynamic topography and observation-derived present-day dynamic topography remains debated (e.g., Hoggard et al, 2017Hoggard et al, , 2016Molnar et al, 2015;Steinberger et al, 2017;Watkins & Conrad, 2018;Yang & Gurnis, 2016;Yang et al, 2017). However, Yang and Gurnis (2016) and Yang et al (2017) advocate for low spherical degree of dynamic topography with amplitudes larger than ±1 km, based on a different analysis of residual topography data and consistently with previous numerical models based on seismic tomography or slab assimilation. More recently, Steinberger et al (2017) used a crustal model to estimate present-day continental residual topography and also found a limited degree-2 residual topography amplitude.…”

“…These processes produce dynamic topography over a range of spatial scales that cannot yet be taken into account in 3-D global models because of computational limitations. The discrepancy between numerical models of dynamic topography and observation-derived present-day dynamic topography remains debated (e.g., Hoggard et al, 2017Hoggard et al, , 2016Molnar et al, 2015;Steinberger et al, 2017;Watkins & Conrad, 2018;Yang & Gurnis, 2016;Yang et al, 2017). The dynamic topography spectra that we obtained (Figure 7) are comparable to those derived by recent inversions of present-day mantle structures (Yang & Gurnis, 2016) to simultaneously fit the long-wavelength geoid, free-air gravity anomalies, gravity gradients, and residual topography point data (Hoggard et al, 2016), and of a high-resolution upper mantle tomography model (Steinberger et al, 2017).…”

Earth’s multi-scale topographic response to global mantle flow

“…This is also true of a recent model by Yang & Gurnis (2016) [32], although they proposed that at least part of the long-wavelength discrepancy arises due to the sparse nature of the observational constraints [41]. Their study also demonstrates that the conclusions of [9] are sensitive to regularisation choices [44] and suggests that the maximum degree to which a spherical harmonic representation can be inferred from the point-wise residual topography measurements is l = 5 [32]. We note that these claims have since been refuted [41] and emphasise that the analyses of [9,41] and [32,44] are not directly comparable: power [8]; (b) inferred residual topography from observational constraints [9]; (c)/(d) simulated topography from our instantaneous-flow models, neglecting (c) and incorporating (d) shallow mantle and lithospheric structure, respectively; (e) spectral decomposition of published predictive models [29,30,31,42,8] and observation-based residual topography estimates [9,41].…”

“…Their study also demonstrates that the conclusions of [9] are sensitive to regularisation choices [44] and suggests that the maximum degree to which a spherical harmonic representation can be inferred from the point-wise residual topography measurements is l = 5 [32]. We note that these claims have since been refuted [41] and emphasise that the analyses of [9,41] and [32,44] are not directly comparable: power [8]; (b) inferred residual topography from observational constraints [9]; (c)/(d) simulated topography from our instantaneous-flow models, neglecting (c) and incorporating (d) shallow mantle and lithospheric structure, respectively; (e) spectral decomposition of published predictive models [29,30,31,42,8] and observation-based residual topography estimates [9,41]. Note that predictive models cover Earth's surface at high-resolution and have not been regularised, but residual topography estimates have, using an automatic regularisation parameter selection algorithm [43]; (f) unregularised spectral decomposition of our simulations -spectra computed from the predictive models are not directly comparable with the observational constraints, since they omit effects introduced by irregular sampling and processing choices [44].…”

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

“…A recent database of residual topography within the world's oceans, compiled by Hoggard et al (2016Hoggard et al ( , 2017, provides one of the most comprehensive data sets currently available. This has underpinned a series of studies into the spectral character of residual topography and its relationship to underlying mantle dynamics (e.g., Hoggard et al, 2016Hoggard et al, , 2017Steinberger, 2016;Steinberger et al, 2019;Yang & Gurnis, 2016;Yang et al, 2017;Watkins & Conrad, 2018). However, the conclusions from these studies have often appeared contradictory.…”