We apply the Backus-Gilbert approach to normal mode center frequency data, to constrain jumps in P, S, bulk-sound speed and density at the “660” discontinuity in the earth’s mantle (∼650–670 km depth). Different 1-D models are considered to compute sensitivity kernels. When using model PREM (Dziewonski & Anderson, 1981, Physics of the Earth and Planetary Interiors, 25, 297–356. doi:10.1016/0031-9201(81)90046-7) as reference, with a “660” at 670 km depth, the best-fitting jumps in density, P- and S-wave speeds range from (5.1–8.2)%, (5.3–8.0)%, (5.0–7.0)%, respectively, so the PREM values lie outside the ranges of acceptable density and P wave speed jumps. When shifting the depth of “660” to 660 km, the density and S wave speed jumps increase, while the P-wave speed jump decreases. Normal mode data do not support a global transition at 650 km depth. The density jumps are closer to those of pyrolite than PREM, while our bulk-sound wave speed jumps suggest a larger garnet proportion at “660.”.

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.

Tides and Earth-Moon system evolution are coupled over geological time. Tidal energy dissipation on Earth slows Earth's rotation rate, increases obliquity, lunar orbit semi-major axis and eccentricity, and decreases lunar inclination. Tidal and core-mantle boundary dissipation within the Moon decrease inclination, eccentricity and semi-major axis. Here we integrate the Earth-Moon system backwards for 4.5 Ga with orbital dynamics and explicit ocean tide models that are "high-level" (i.e., not idealized). To account for uncertain plate tectonic histories, we employ Monte Carlo simulations, with tidal energy dissipation rates (normalized relative to astronomical forcing parameters) randomly selected from ocean tide simulations with modern ocean basin geometry and with 55, 116, and 252 Ma reconstructed basin paleogeometries. The normalized dissipation rates depend upon basin geometry and Earth's rotation rate. Faster Earth rotation generally yields lower normalized dissipation rates. The Monte Carlo results provide a spread of possible early values for the Earth-Moon system parameters. Of consequence for ocean circulation and climate, absolute (un-normalized) ocean tidal energy dissipation rates on the early Earth may have exceeded today's rate due to a closer Moon. Prior to ∼3Ga , evolution of inclination and eccentricity is dominated by tidal and core-mantle boundary dissipation within the Moon, which yield high lunar orbit inclinations in the early Earth-Moon system. A drawback for our results is that the semi-major axis does not collapse to near-zero values at 4.5 Ga, as indicated by most lunar formation models. Additional processes, missing from our current efforts, are discussed as topics for future investigation.