A linear viscoelasticity for decadal to centennial time scale mantle deformation

The extended Burgers material (EBM) model provides a linear viscoelastic theory for interpreting a variety of rock deformation phenomena in geophysics, playing an increasingly important role in parameterizing laboratory data, providing seismic wave velocity and attenuation interpretations, and in analyses of solid planetary tidal dispersion and quality factor Q. At the heart of the EBM approach is the assumption of a distribution of relaxation spectra tied to rock grain boundary and interior granular mobility. Furthermore, the model incorporates an asymptotic long-term limiting behavior that is Maxwellian. Here we use the extensively developed linear theory of viscoelasticity to isolate those parameters of EBM that apply to both post-seismic relaxation processes involving flow of olivine rich upper mantle material and to studies of tides, where periods of forcing range from 12 h to 18.6 years. The isolated EBM parameters should also apply to theoretical and geodetic studies of glacial isostatic adjustment, especially when the initiation of continuous cryospheric surface unloading dates to the 20th or 21st century. Using analytical Laplace transformed solutions of Boussinesq's half-space load problem, we show that the effects of EBM transient rheology may have substantial influence on geodetic interpretations of unloading induced crustal motions even on time scales that are sub-decadal.

The melt content of the low velocity layer atop the mantle transition zone: Theory and method of calculation

The melt content is significant characteristic for the low velocity layer, so it is very necessary to set up the quantitative relationship between the low velocity anomaly and the melt fraction. We describe the computational methods for melt volume fractions and discussed the parameter selections for the theoretical computations.

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We discuss the seismic wave velocity characteristics and the equilibrium geometry model in the partial melting system.

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Equations for computing the elastic properties atop the LVL are presented.

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Parameter selection of the equilibrium geometry model is shown.

Seismic evidence of effects of water on melt transport in the Lau back-arc mantle

Processes of melt generation and transport beneath back-arc spreading centres are controlled by two endmember mechanisms: decompression melting similar to that at mid-ocean ridges and flux melting resembling that beneath arcs. The Lau Basin, with an abundance of spreading ridges at different distances from the subduction zone, provides an opportunity to distinguish the effects of these two different melting processes on magma production and crust formation. Here we present constraints on the three-dimensional distribution of partial melt inferred from seismic velocities obtained from Rayleigh wave tomography using land and ocean-bottom seismographs. Low seismic velocities beneath the Central Lau Spreading Centre and the northern Eastern Lau Spreading Centre extend deeper and westwards into the back-arc, suggesting that these spreading centres are fed by melting along upwelling zones from the west, and helping to explain geochemical differences with the Valu Fa Ridge to the south, which has no distinct deep low-seismic-velocity anomalies. A region of low S-wave velocity, interpreted as resulting from high melt content, is imaged in the mantle wedge beneath the Central Lau Spreading Centre and the northeastern Lau Basin, even where no active spreading centre currently exists. This low-seismic-velocity anomaly becomes weaker with distance southward along the Eastern Lau Spreading Centre and the Valu Fa Ridge, in contrast to the inferred increase in magmatic productivity. We propose that the anomaly variations result from changes in the efficiency of melt extraction, with the decrease in melt to the south correlating with increased fractional melting and higher water content in the magma. Water released from the slab may greatly reduce the melt viscosity or increase grain size, or both, thereby facilitating melt transport.

Anelasticity and grain boundary sliding

We describe a theoretical and numerical analysis of an existing model of anelasticity owing to grain boundary sliding. Two linearly elastic layers having finite thickness and identical material constants are separated by a given fixed spatially periodic interface across which the normal component of velocity is continuous, whereas the tangential component has a discontinuity determined by the shear stress σ * ns and the boundary sliding viscosity η *. We derive asymptotic forms giving the complex rigidity for the extremes of low-frequency forcing and of high-frequency forcing. Using those forms, we create master variables allowing results for different interface shapes, and arbitrary forcing frequency, to be collapsed (very nearly) into a single curve. We then analyse numerically, with finite interface slope, three proposed factors that may weaken and broaden the theoretical prediction of a single Debye peak in the loss spectrum. They are, namely, stress concentrations at interface corners, spatial variation in grain size and spatial variation in boundary sliding viscosity η *. Our results show that all these factors can, indeed, contribute to a moderate weakening of the loss peak. By contrast, the loss peak markedly broadens only when the boundary sliding viscosity η * differs by an order of magnitude across adjacent interface. The shape of the loss spectrum (self-similar to a single Debye peak) is insensitive to the other two factors.

Geophysical evidence from the MELT area for compositional controls on oceanic plates

Magnetotelluric and seismic data, collected during the MELT experiment at the southern East Pacific Rise, constrain the distribution of melt beneath this mid-ocean-ridge spreading centre and also the evolution of the oceanic lithosphere during its early cooling history. Here we focus on structures imaged at distances approximately 100 to 350 km east of the ridge crest, corresponding to seafloor ages of approximately 1.3 to 4.5 million years (Myr), where the seismic and electrical conductivity structure is nearly constant and independent of age. Beginning at a depth of about 60 km, we image a large increase in electrical conductivity and a change from isotropic to transversely anisotropic electrical structure, with higher conductivity in the direction of fast propagation for seismic waves. Conductive cooling models predict structure that increases in depth with age, extending to about 30 km at 4.5 Myr ago. We infer, however, that the structure of young oceanic plates is instead controlled by a decrease in water content above a depth of 60 km induced by the melting process beneath the spreading centre.