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Abstract. We present results from a combined multichannel seismic reflection (MCS) and wideangle onshore/offshore seismic experiment conducted in 1996 across the southeast Greenland continental margin. A new seismic tomographic method is developed to jointly invert refraction and reflection travel times for a two-dimensional velocity structure. We employ a hybrid raytracing scheme based on the graph method and the local ray-bending refinement to efficiently obtain an accurate forward solution, and we employ smoothing and optional damping constraints to regularize an iterative inversion. We invert 2318 Pg and 2078 PmP travel times to construct a compressional velocity model for the 350-km-long transect, and a long-wavelength structure with strong lateral heterogeneity is recovered, including (1) -30-km-thick, undeformed continental crust with a velocity of 6.0 to 7.0 km/s near the landward end, (2) 30-to 15-km-thick igneous crust within a 150-km-wide continent-ocean transition zone, and (3) 15-to 9-km-thick oceanic crust toward the seaward end. The thickness of the igneous upper crust characterized by a highvelocity gradient also varies from 6 km within the transition zone to -3 km seaward. The bottom half of the lower crust generally has a velocity higher than 7.0 km/s, reaching a maximum of 7.2 to 7.5 km/s at the Moho. A nonlinear Monte Carlo uncertainty analysis is performed to estimate the a posteriori model variance, showing that most velocity and depth nodes are well determined with one standard deviation of 0.05-0.10 km/s and 0.25-1.5 km, respectively. Despite significant variation in crustal thickness, the mean velocity of the igneous crust, which serves as a proxy for the bulk crustal composition, is surprisingly constant (-7.0 km/s) along the transect. On the basis of a mantle melting model incorporating the effect of active mantle upwelling, this velocitythickness relationship is used to constrain the mantle melting process during the breakup of Greenland and Europe. Our result is consistent with a nearly constant mantle potential temperature of 1270-1340øC throughout the rifting but with a rapid transition in the style of mantle upwelling, from vigorous active upwelling during the initial rifting phase to passive upwelling in the later phase.

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[1] We present a new statistical method to construct a model for the chemical composition of Earth's primitive mantle along with its variance. Earth's primitive mantle is located on the melting trend exhibited by the global compilation of mantle peridotites, using cosmochemical constraints on the relative abundances of refractory lithophile elements (RLE). This so-called pyrolite approach involves the least amount of assumptions, thereby being probably most satisfactory compared to other approaches. Its previous implementations, however, suffer from questionable statistical treatment of noisy geochemical data, leaving the uncertainty of model composition poorly quantified. In order to properly take into account how scatters in peridotite data affect this geochemical inference, we combine the following statistical techniques: (1) modeling a nonlinear melting trend in the multidimensional compositional space through the principal component analysis, (2) determining the primitive mantle composition on the melting trend by simultaneously imposing all of cosmochemical constraints with least squares, and (3) mapping scatters in original data into the variance of the final model through the bootstrap resampling technique. Whereas our model is similar to previous models in terms of Mg, Si, and Fe abundances, the RLE contents are at $2.16 ± 0.37 times the CI chondrite concentration, which is lower than most of previous estimates. The new model is depleted by >20% in a number of incompatible elements including heat-producing elements, U, Th, and K, and this depleted nature is further amplified (up to 60%) in terms of predicted composition for the present-day mantle.

The Urey ratio describes the contribution of internal heat production to planetary‐scale energy balance, and knowing this thermal budget for Earth is essential to understand its long‐term evolution. Internal heat production is provided by the decay of radiogenic elements, whose budget is constrained by geochemical models of Earth. Understanding the thermal budget thus requires contributions from both geophysics and geochemistry. The purpose of this review is to elucidate various geochemical and geophysical arguments and to delineate the most likely thermal budget of Earth. While the bulk Earth Urey ratio is probably ∼0.35, the convective Urey ratio is estimated to be ∼0.2. That is, only ∼20% of convective heat flux seems to originate from radiogenic elements at present, so the rest should be supported by secular cooling. A likely scenario for Earth's thermal history indicates that the peculiarity of today's significant imbalance between heat production and heat loss may result from the initiation of plate tectonics in the early Earth.

The inception of plate tectonics on Earth and its subsequent evolution are discussed on the basis of theoretical considerations and observational constraints. The likelihood of plate tectonics in the past depends on what mechanism is responsible for the relatively constant surface heat flux that is indicated by the likely thermal history of Earth. The continuous operation of plate tectonics throughout Earth's history is possible if, for example, the strength of convective stress in the mantle is affected by the gradual subduction of surface water. Various geological indicators for the emergence of plate tectonics are evaluated from a geodynamical perspective, and they invariably involve certain implicit assumptions about mantle dynamics, which are either demonstrably wrong or yet to be explored. The history of plate tectonics is suggested to be intrinsically connected to the secular evolution of the atmosphere, through sea-level changes caused by ocean-mantle interaction.

Possible geodynamic regimes that may have prevailed in the Archean are investigated by back-tracking the thermal history of Earth from the present-day conditions. If the temporal evolution of plate-tectonic convection is modulated by strong depleted lithosphere created at mid-ocean ridges, more sluggish plate tectonics is predicted when the mantle was hotter, contrary to commonly believed, more rapid tectonics in the past. This notion of sluggish plate tectonics can simultaneously satisfy geochemical constraints on the abundance of heat-producing elements and petrological constraints on the degree of secular cooling, in the framework of simple whole-mantle convection. The geological record of supercontinents back to ~2.7 Ga is shown to be broadly consistent with the accelerating plate motion as predicted by the new model. Furthermore, the very fact of repeated continental aggregation indicates that thicker depleted lithosphere in the past needs to move more slowly to become negatively buoyant by thermal contraction and also needs to be strong enough to support resulting thermal boundary layer. The concept of many small plates covering Archean ocean basins is thus physically implausible. As a consequence of reduced heat flux in the past, mantle plumes are expected to have been weaker in the Archean. The chemical evolution of Earth's mantle may have been encumbered by sluggish plate tectonics and weak mantle plumes, maintaining its compositional heterogeneity at various spatial scales to the present day. Internal heat production probably played an important role in controlling plate dynamics in the early Archean, for which a different mode of mantle convection is suggested.

[1] We present a new quantitative framework to understand the process of mantle melting based on the velocity structure of igneous crust. Our approach focuses on the lower crustal section, which is expected to be least affected by porosity and seawater alteration, especially for thick igneous crust. Our methodology is thus best for constraining the origin of large igneous provinces. First, a quantitative relation between bulk crustal velocity and mantle melting parameters is established on the basis of data from mantle melting experiments. Second, we show how lower crustal velocity can be used to place bounds on the expected range of bulk crustal velocity, despite ambiguity in crustal emplacement processes. By modeling fractional crystallization processes at a range of crustal pressures, these bounds are derived as a function of the proportion of lower versus upper crust. Finally, a simple mantle melting model is constructed to illustrate the effects of potential temperature, active upwelling, and a preexisting lithospheric lid on predicted crustal thickness and velocity. As an example, this new interpretation is applied to a seismic transect across the southeast Greenland margin to constrain mantle dynamics during the opening of the North Atlantic. Some complicating factors in seismological inference on mantle melting process, such as the possibilities of subcrustal igneous fractionation and mantle source heterogeneity, are also discussed with this example.