This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

The global range of subduction zone thermal models

This chapter has four main aims. Provide a comprehensive picture of the composition of volcanic rocks from subduction-related magmatic arcs. Review evidence in favor of the existence of andesitic, as well as basaltic primary magmas in arcs. Present new data on the composition of arc lower crust, based mainly on our work on the Talkeetna arc section in southcentral Alaska. Summarize evidence from arc lower crustal sections that a substantial proportion of the dense, lower crustal pyroxenites and garnet granulites produced by crystal fractionation are missing.

One View of the Geochemistry of Subduction-Related Magmatic Arcs, with an Emphasis on Primitive Andesite and Lower Crust

A catalytic delamination-driven model for coupled genesis of Archaean crust and sub-continental lithospheric mantle

Seismic anisotropy is caused mainly by the lattice-preferred orientation of anisotropic minerals. Major breakthroughs have occurred in the study of lattice-preferred orientation in olivine during the past ∼10 years through large-strain, shear deformation experiments at high pressures. The role of water as well as stress, temperature, pressure, and partial melting has been addressed. The influence of water is large, and new results require major modifications to the geodynamic interpretation of seismic anisotropy in tectonically active regions such as subduction zones, asthenosphere, and plumes. The main effect of partial melting on deformation fabrics is through the redistribution of water, not through a change in deformation geometry. A combination of new experimental results with seismological observations provides new insights into the distribution of water associated with plume-asthenosphere interactions, formation of the oceanic lithosphere, and subduction. However, large uncertainties remain regarding the role of pressure and the deformation fabrics at low stress conditions.

/pdf/geodynamic-significance-of-seismic-anisotropy-of-the-upper-3ewwsj6pcw.pdf

Geodynamic Significance of Seismic Anisotropy of the Upper Mantle: New Insights from Laboratory Studies

We summarize petrological and seismic constraints on the temperature of arc lower crust and shallow mantle, and show that published thermal models are inconsistent with these constraints. We then present thermal models incorporating temperature-dependent viscosity, using widely accepted values for activation energy and asthenospheric viscosity. These produce thin thermal boundary layers in the wedge corner, and an overall thermal structure that is consistent with other temperature constraints. Some of these models predict partial melting of subducted sediment and/or basalt, even though we did not incorporate the effect of shear heating We obtain these results for subduction of 50 Myr old oceanic crust at 60 km/Myr, and even for subduction of 80 Myr old crust at 80 km/Myr, suggesting that melting of subducted crust may not be not restricted to slow subduction of young oceanic crust.

/pdf/thermal-structure-due-to-solid-state-flow-in-the-mantle-37vgdosfdt.pdf

Thermal Structure due to Solid-State Flow in the Mantle Wedge Beneath Arcs

[1] Residual mantle exposures in the accreted Talkeetna arc, Alaska, provide the first rock analog for the arc-parallel flow that is inferred from seismic anisotropy at several modern arcs. The peridotites exposed at the base of the Jurassic Talkeetna arc have a Moho-parallel foliation and indicate dislocation creep of olivine at temperatures of ∼1000° to >1100°C. Slip occurred chiefly on the (001)[100] slip system, which has only rarely been observed to be the dominant slip system in olivine. Stretching lineations and olivine [100] slip directions are subparallel to the long axis of the Talkeetna arc for over 200 km, indicating that mantle flow was parallel to the arc axis. The alignment of the olivine [100] axes yields a calculated S wave anisotropy with the fast polarization direction parallel to the arc. Thus (1) the fast polarization directions observed parallel to some modern arcs now have an exposed geological analog; (2) arc-parallel fast polarization directions can be caused by anisotropic peridotites and do not require the presence of fracture zones, fluid-filled pockets, or glide on the (010)[001] H2O-induced slip system; (3) seismic anisotropy beneath modern arcs may be due to slip on (001)[100] with a horizontal foliation rather than slip on (010)[100] with a vertical foliation; and (4) the observed dominance of the (001)[100] slip system may be due to high H2O concentrations, suggesting that strain in the oceanic upper mantle may be accommodated dominantly by (001)[100] olivine slip.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2002JB002233

Arc‐parallel flow within the mantle wedge: Evidence from the accreted Talkeetna arc, south central Alaska

[1] The Talkeetna arc is one of two intraoceanic arcs where much of the section from the upper mantle through the volcanic carapace is well exposed. We reconstruct the vertical section of the Talkeetna arc by determining the (re)crystallization pressures at various structural levels. The thermobarometry shows that the tonalites and quartz diorites intruded at ∼5–9 km into a volcanic section estimated from stratigraphy to be 7 km thick. The shallowest, Tazlina and Barnette, gabbros crystallized at ∼17–24 km; the Klanelneechena Klippe crystallized at ∼24–26 km; and the base of the arc crystallized at ∼35 km depth. The arc had a volcanic:plutonic ratio of ∼1:3–1:4. However, many or most of the felsic plutonic rocks may represent crystallized liquids rather than cumulates so that the liquid:cumulate ratio might be 1:2 or larger. The current 5- to 7-km structural thickness of the plutonic section of the arc is ∼15–30% of the original 23- to 28-km thickness. The bulk composition of the original Talkeetna arc section was ∼51–58 wt % SiO2.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2007JB005208

Reconstruction of the Talkeetna intraoceanic arc of Alaska through thermobarometry

The Solund-Hyllestad-Lavik area affords an excellent opportunity to understand the ultrahigh-pressure Scandian orogeny because it contains a near-complete record of ophiolite emplacement, high-pressure metamorphism and large-scale extension. In this area, the Upper Allochthon was intruded by the c. 434 Ma Sogneskollen granodiorite and thrust eastward over the Middle ⁄ Lower Allochthon, probably in the Wenlockian. The Middle ⁄ Lower Allochthon was subducted to c. 50 km depth and the structurally lower Western Gneiss Complex was subducted to eclogite facies conditions at c. 80 km depth by c. 410-400 Ma. Within 100. Exhumation to upper crustal levels was complete by c. 403 Ma. The Solund fault produced the last few km of tectonic exhumation, bringing the near- ultrahigh-pressure rocks to within c. 3 km vertical distance from the low-grade Solund Conglomerate.

/pdf/exhumation-of-high-pressure-rocks-beneath-the-solund-basin-4gn0d6s6jl.pdf

Luc Mehl

Papers

Thermal Structure due to Solid-State Flow in the Mantle Wedge Beneath Arcs

Arc‐parallel flow within the mantle wedge: Evidence from the accreted Talkeetna arc, south central Alaska

Reconstruction of the Talkeetna intraoceanic arc of Alaska through thermobarometry

Exhumation of high-pressure rocks beneath the Solund Basin, Western Gneiss Region of Norway