Thermally dominated deep mantle LLSVPs: A review

The two large low shear-wave velocity provinces (LLSVPs) that dominate lower-mantle structure may hold key information on Earth’s thermal and chemical evolution. It is generally accepted that these provinces are hotter than background mantle and are likely the main source of mantle plumes. Increasingly, it is also proposed that they hold a dense (primitive and/or recycled) compositional com- ponent. The principle evidence that LLSVPs may represent thermo-chemical ‘piles’ comes from seismic constraints, including: (i) their long-wavelength nature; (ii) sharp gradients in shear-wave velocity at their margins; (iii) non-Gaussian distributions of deep mantle shear-wave velocity anomalies; (iv) anti-correlated shear-wave and bulk-sound velocity anomalies (and elevated ratios between shear- and compressional-wave velocity anomalies); (v) anti-correlated shear-wave and density anomalies; and (vi) 1-D/radial profiles of seismic velocity that deviate from those expected for an isochemical, well-mixed mantle. In addition, it has been proposed that hotspots and the reconstructed eruption sites of large ig- neous provinces correlate in location with LLSVP margins. In this paper, we review recent results which indicate that the majority of these constraints do not require thermo-chemical piles: they are equally well (or poorly) explained by thermal heterogeneity alone. Our analyses and conclusions are largely based on comparisons between imaged seismic structure and synthetic seismic structures from a set of thermal and thermo-chemical mantle convection models, which are constrained by ∼ 300 Myr of plate motion histories. Modelled physical structure (temperature, pressure and composition) is converted into seismic velocities via a thermodynamic approach that accounts for elastic, anelastic and phase con- tributions and, subsequently, a tomographic resolution filter is applied to account for the damping and geographic bias inherent to seismic imaging. Our results indicate that, in terms of large-scale seismic structure and dynamics, these two provinces are predominantly thermal features and, accordingly, that chemical heterogeneity is largely a passive component of lowermost mantle dynamics

Sensitivity kernels for body tides on laterally heterogeneous planets based on adjoint methods

SUMMARY We apply the adjoint method to efficiently calculate the linearized sensitivity of body tide observations to perturbations in density, elastic/anelastic moduli and boundary topography. This theory is implemented practically within the context of normal mode coupling calculations, with an advantage of this approach being that much of the necessary technical machinery is present in existing coupling codes. A range of example sensitivity kernels are calculated relative to both spherically symmetric and laterally heterogeneous background models. These results reaffirm the conclusions of earlier studies that the M2 body tide is strongly sensitive to spherical harmonic degree-2 density variations at the base of the mantle. Moreover, it is found that the sensitivity kernels are only weakly dependent on the background model, and hence linearized methods are likely to be effective within inversions of body tide observations.NSF grant EAR-192386

Anelasticity across seismic to tidal timescales: a self-consistent approach

In a pioneering study, Wahr & Bergen developed the widely adopted, pseudo-normal mode framework for predicting the impact of anelastic effects on the Earth's body tides. Lau $\textit{et al.}$ have recently derived an extended normal mode treatment of the problem (as well as a minor variant of the theory known as the direct solution method) that makes full use of theoretical developments in free oscillation seismology spanning the last quarter century and that avoids a series of assumptions and approximations adopted in the traditional theory for predicting anelastic effects. There are two noteworthy differences between these two theories: (1) the traditional theory only considers perturbations to the eigenmodes of an elastic Earth, whereas the new theory augments this set of modes to include the relaxation modes that arise in anelastic behaviour; and (2) the traditional theory approximates the complex perturbation to the tidal Love number as a scaled version of the complex perturbation to the elastic moduli, whereas the new theory computes the full complex perturbation to each eigenmode. In this study, we highlight the above differences using a series of synthetic calculations, and demonstrate that the traditional theory can introduce significant error in predictions of the complex perturbation to the Love numbers due to anelasticity and the related predictions of tidal lag angles. For the simplified Earth models we adopt, the computed lag angles differ by ∼20 per cent. The assumptions in the traditional theory have important implications for previous studies that use model predictions to correct observables for body tide signals or that analyse observations of body tide deformation to infer mantle anelastic structure. Finally, we also highlight the fundamental difference between apparent attenuation (i.e. attenuation inferred from observations or predicted using the above theories) and intrinsic attenuation (i.e. the material property investigated through experiments), where both are often expressed in terms of lag angles or $\textit{Q}$$^{-1}$. In particular, we demonstrate the potentially significant (factor of two or more) bias introduced in estimates of $\textit{Q}$$^{-1}$ and its frequency dependence in studies that have treated $\textit{Q}$$^{-1}$ determined from tidal phase lags or measured experimentally as being equal. The observed or theoretically predicted lag angle (or apparent $\textit{Q}$$^{-1}$) differs from the intrinsic, material property due to inertia, self-gravity and effects associated with the energy budget. By accounting for these differences we derive, for a special case, an expression that accurately maps apparent attenuation predicted using the extended normal mode formalism of Lau $\textit{et al.}$ into intrinsic attenuation. The theory allows for more generalized mappings which may be used to robustly connect observations and predictions of tidal lag angles to results from laboratory experiments of mantle materials.This work was supported by NSF EAR-1464024, NSF EAR-1215061, and Harvard University

“Measures of Dissipation in Viscoelastic Media” Extended: Toward Continuous Characterization Across Very Broad Geophysical Time Scales

We develop a conceptual/quantitative framework whereby measurements of Earth's viscoelasticity may be assessed across the broad range of geophysical processes, spanning seismic wave propagation, postseismic relaxation, glacial isostatic adjustment, and mantle convection. Doing so requires overcoming three challenges: (A) separating spatial variations from intrinsic frequency dependence in mechanical properties; (B) reconciling different conceptual and constitutive viscoelastic models used to interpret observations at different frequencies; and (C) improving understanding of linear and nonlinear transient deformation mechanisms and their extrapolation from laboratory to earth conditions. We focus on (B), first demonstrating how different mechanical models lead to incompatible viscosity estimates from observations. We propose the determination of the “complex viscosity”—a frequency-dependent parameter complementary to other measures of dissipation (including frequency-dependent moduli and attenuation)—from such observations to reveal a single underlying broadband mechanical model. The complex viscosity illuminates transient creep in the vicinity of the Maxwell time, where most ambiguity lies

An analysis of core-mantle boundary Stoneley mode sensitivity and sources of uncertainty

Stoneley modes are a special subset of normal modes whose energy is confined along the core–mantle boundary (CMB). As such, they offer a unique glimpse into Earth structure at the base of the mantle. They are often observed through coupling with mantle modes due to rotation, ellipticity and lateral heterogeneity, though they can be detected without such coupling. In this study, we explore the relative sensitivities of seismic spectra of two low-frequency Stoneley modes to several factors, taking as reference the fully coupled computation up to 3 mHz in model S20RTS. The factors considered are (i) theoretical, by exploring the extent to which various coupling approximations can accurately reproduce reference spectra and (ii) model-based, by exploring how various Earth parameters such as CMB topography, attenuation and S- and P-wave structures, and the seismic source solution may influence the spectra. We find that mode-pair coupling is insufficiently accurate, but coupling modes within a range of ±0.1 mHz produces acceptable spectra, compared to full coupling. This has important implications for splitting function measurements, which are computed under the assumption of isolated modes or at best, mode-pair or group coupling. We find that uncertainties in the P-wave velocity mantle model dominate compared to other model parameters. In addition, we also test several hypothetical models of mantle density structure against real data. These tests indicate that, with the low-frequency Stoneley mode spectral data considered here, it is difficult to make any firm statement on whether the large-low-shear-velocity-provinces are denser or lighter than their surroundings. We conclude that better constraints on long wavelength elastic mantle structure, particularly P-wave velocity, need to be obtained, before making further statements on deep mantle density heterogeneity. In particular, a dense anomaly confined to a thin layer at the base of the mantle (less than ∼100–200 km) may not be resolvable using the two Stoneley modes tested here, while the ability of higher frequency Stoneley modes to resolve it requires further investigations

Adjoint sensitivity kernels for free oscillation spectra

Summary We apply the adjoint method to efficiently calculate sensitivity kernels for long-period seismic spectra with respect to structural and source parameters. Our approach is built around the solution of the frequency-domain equations of motion using the Direct Solution Method (DSM). The DSM is currently applied within large-scale mode coupling calculations and is also likely to be useful within finite-element type methods for modelling seismic spectra that are being actively developed. Using mode coupling theory as a framework for solving both the forward and adjoint equations, we present numerical examples that focus on the spectrum close to four eigenfrequencies (the low-frequency mode, 0S2, and higher frequency modes, namely 2S2, 0S7, and 0S10 for comparison). For each chosen observable, we plot sensitivity kernels with respect to 3D perturbations in density and seismic wave-speeds. We also use the adjoint method to calculate derivatives of observables with respect to the matrices occurring within mode coupling calculations. This latter approach points towards a generalisation of the two-stage splitting function method for structural inversions that does not rely on inaccurate self-coupling or group-coupling approximations. Finally, we verify through direct calculation that our sensitivity kernels correctly predict the linear dependence of the chosen observables on model perturbations. In doing this, we highlight the importance of non-linearity within inversions of long-period spectra.</jats:p

Constraints on mantle viscosity and Laurentide ice sheet evolution from pluvial paleolake shorelines in the western United States

The deformation pattern of the paleoshorelines of extinct Lake Bonneville were among the first features to indicate that Earth's interior responds viscoelastically to changes in surface loads (Gilbert, 1885). Here we revisit and extend this classic study of isostatic rebound with updated lake chronologies for Lake Bonneville and Lake Lahontan as well as revised elevation datasets of shoreline features. The first order domal pattern in the shoreline elevations can be explained by rebound associated with the removal of the lake load. We employ an iterative scheme to calculate the viscoelastic lake rebound, which accounts for the deformation of the solid Earth and gravity field, to calculate a lake load that is consistent with the load-deformed paleotopography. We find that the domal deformation requires a regional Earth structure that exhibits a thin elastic thickness of the lithosphere (15–25 km) and low sublithospheric Maxwell viscosity (∼1019 Pa s). After correcting for rebound due to the lake load, shoreline feature elevations reveal a statistically significant northward dipping trend. We attribute this trend to continent-scale deformation caused by the ice peripheral bulge of the Laurentide ice sheet, and take advantage of the position of these lakes on the distal flank of the peripheral bulge to provide new insights on mantle viscosity and Laurentide ice sheet reconstructions. We perform ice loading calculations to quantify the deformation of the solid Earth, gravity field, and rotation axis that is caused by the growth and demise of the Laurentide ice sheet. We test three different ice reconstructions paired with a suite of viscosity profiles and confirm that the revealed trend can be explained by deformation associated with the Laurentide ice sheet when low viscosities below the asthenosphere are adopted. We obtain best fits to shoreline data using ice models that do not have the majority of ice in the eastern sectors of the Laurentide ice sheet, with the caveat that this result can be affected by lateral variations in viscosity. We show that pluvial lakes in the western United States can place valuable constraints on the Laurentide ice sheet, the shape of its peripheral bulge, and the underlying mantle viscosity

Ice age effects on the satellite-derived J˙<inf>2</inf> datum: Mapping the sensitivity to 3D variations in mantle viscosity

Studies of glacial isostatic adjustment (GIA) based on spherically symmetric viscoelastic Earth models have argued that the rate of change of the degree 2 zonal harmonic of the Earth’s geopotential, or J˙2, provides an important constraint on mean viscosity in the deep mantle (Mitrovica and Peltier, 1993; Nakada et al., 2015; Lau et al., 2016). To refine this constraint, we compute Fr´echet kernels using an adjoint methodology that reveal the sensitivity of the datum to 3D variations in mantle viscosity. We demonstrate that the mantle sensitivity of the datum is largely limited to the region below the ancient Laurentide ice sheet that covered Canada and significant portions of the northeastern United States at Last Glacial Maximum (LGM). In the bottom half of the lower mantle, this region of maximum sensitivity lies outside the location of Large Low Shear Velocity Provinces (LLSVPs) imaged from seismic tomographic studies. Thus, if the low shear velocity of these provinces originates from thermal effects, previous inferences of viscosity based upon the J˙ 2 datum are likely higher than the actual mean viscosity of the lower mantle