Summary Trace-element data for mid-ocean ridge basalts (MORBs) and ocean island basalts (OIB) are used to formulate chemical systematics for oceanic basalts. The data suggest that the order of trace-element incompatibility in oceanic basalts is Cs ≈ Rb ≈ (≈ Tl) ≈ Ba(≈ W) > Th > U ≈ Nb = Ta ≈ K > La > Ce ≈ Pb > Pr (≈ Mo) ≈ Sr > P ≈ Nd (> F) > Zr = Hf ≈ Sm > Eu ≈ Sn (≈ Sb) ≈ Ti > Dy ≈ (Li) > Ho = Y > Yb. This rule works in general and suggests that the overall fractionation processes operating during magma generation and evolution are relatively simple, involving no significant change in the environment of formation for MORBs and OIBs. In detail, minor differences in element ratios correlate with the isotopic characteristics of different types of OIB components (HIMU, EM, MORB). These systematics are interpreted in terms of partial-melting conditions, variations in residual mineralogy, involvement of subducted sediment, recycling of oceanic lithosphere and processes within the low velocity zone. Niobium data indicate that the mantle sources of MORB and OIB are not exact complementary reservoirs to the continental crust. Subduction of oceanic crust or separation of refractory eclogite material from the former oceanic crust into the lower mantle appears to be required. The negative europium anomalies observed in some EM-type OIBs and the systematics of their key element ratios suggest the addition of a small amount (⩽1% or less) of subducted sediment to their mantle sources. However, a general lack of a crustal signature in OIBs indicates that sediment recycling has not been an important process in the convecting mantle, at least not in more recent times (⩽2 Ga). Upward migration of silica-undersaturated melts from the low velocity zone can generate an enriched reservoir in the continental and oceanic lithospheric mantle. We propose that the HIMU type (eg St Helena) OIB component can be generated in this way. This enriched mantle can be re-introduced into the convective mantle by thermal erosion of the continental lithosphere and by the recycling of the enriched oceanic lithosphere back into the mantle.

Chemical and isotopic systematics of oceanic basalt : implications for mantle composition and processes

Chemical and isotopic systematics of oceanic basalts. Implications for Mantle Composition and Processes

The composition of the Earth

Preliminary reference earth model

This chapter reviews the present-day composition of the continental crust, the methods employed to derive these estimates, and the implications of the continental crust composition for the formation of the continents, Earth differentiation, and its geochemical inventories. We review the composition of the upper, middle, and lower continental crust. We then examine the bulk crust composition and the implications of this composition for crust generation and modification processes. Finally, we compare the Earth's crust with those of the other terrestrial planets in our solar system and speculate about what unique processes on Earth have given rise to this unusual crustal distribution.

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Composition of the Continental Crust

Empirical relations involving seismic moment M_o, magnitude M_S, energy E_S and fault dimension L (or area S) are discussed on the basis of an extensive set of earthquake data (M_S ≧ 6) and simple crack and dynamic dislocation models. The relation between log S and log M_o is remarkably linear (slope ∼ 2/3) indicating a constant stress drop Δσ; Δσ = 30, 100 and 60 bars are obtained for inter-plate, intra-plate and “average” earthquakes, respectively. Except for very large earthquakes, the relation M_S ∼ (2/3) log M_o ∼ 2 log L is established by the data. This is consistent with the dynamic dislocation model for point dislocation rise times and rupture times of most earthquakes. For very large earthquakes M_S ∼ (1/3) log M_o ∼ log L ∼ (1/3) log E_S. For very small earthquakes M_S ∼ log M_o ∼ 3 log L ∼ log E_S. Scaling rules are assumed and justified. This model predicts log E_S ∼ 1.5 M_S ∼ 3 log L which is consistent with the Gutenberg-Richter relation. Since the static energy is proportional to σL^3, where σ is the average stress, this relation suggests a constant apparent stress ησ where η is the efficiency. The earthquake data suggest ησ ~ 1/2 Δσ. These relations lead to log S ∼ M_S consistent with the empirical relation. This relation together with a simple geometrical argument explains the magnitude-frequency relation log N ∼ − M_S.

/pdf/theoretical-basis-of-some-empirical-relations-in-seismology-1e9arnhgn6.pdf

Theoretical basis of some empirical relations in seismology

Theory of Earth

The maturing of the Earth sciences has led to a fragmentation into subdisciplines which speak imperfectly to one another. Some of these subdisciplines are field geology, petrology, mineralogy, geochemistry, geodesy and seismology, and these in turn are split into even finer units. The science has also expanded to include the planets and even the cosmos. The practitioners in each of these fields tend to view the Earth in a completely different way. Discoveries in one field diffuse only slowly into the consciousness of a specialist in another. In spite of the fact that there is only one Earth, there are probably more Theories of the Earth than there are of astronomy, particle physics or cell biology where there are uncountable samples of each object. Even where there is cross-talk among disciplines, it is usually as noisy as static. Too often, one discipline's unproven assumptions or dogmas are treated as firm boundary conditions for a theoretician in a slightly overlapping area. The data of each subdiscipline are usually consistent with a range of hypotheses. The possibilities can be narrowed considerably as more and more diverse data are brought to bear on a particular problem. The questions of origin, composition and evolution of the Earth require input from astronomy, cosmochemistry, meteoritics, planetology, geology, petrology, mineralogy, crystallography, materials science and seismology, at a minimum. To a student of the Earth, these are artificial divisions, however necessary they are to make progress on a given front.

In Theory of the Earth I attempt to assemble the bits and pieces from a variety of disciplines which are relevant to an understanding of the Earth. Rocks and magmas are our most direct source of information about the interior, but they are biased toward the properties of the crust and shallow mantle. Seismology is our best source of information about the deep interior; however, the interpretation of seismic data for purposes other than purely structural requires input from solid-state physics and experimental petrology. Although this is not a book about seismology, it uses seismology in a variety of ways.

The "Theory of the Earth" developed here differs in many respects from conventional views. Petrologists' models for the Earth's interior usually focus on the composition of mantle samples contained in basalts and kimberlites. The simplest hypothesis based on these samples is that the observed basalts and peridotites bear a complementary relation to one another, that peridotites are the source of basalts or the residue after their removal, and that the whole mantle is identical in composition to the inferred chemistry of the upper mantle and the basalt source region. The mantle is therefore homogeneous in composition, and thus all parts of the mantle eventually rise to the surface to provide basalts. Subducted slabs experience no barrier in falling through the mantle to the core-mantle boundary.

Theory of the Earth

The concept of a relaxation spectrum is used to compute the absorption and dispersion of a linear anelastic solid. The Boltzmann after-effect equation is solved for a solid having a linear relationship between stress and strain and their first time derivatives, the ‘standard linear solid’, and having a distribution of relaxation times. The distribution function is chosen to give a nearly constant Q over the seismic frequency range. Both discrete and continuous relaxation spectra are considered. The resulting linear solid has a broad absorption band which can be interpreted in terms of a superposition of absorption peaks of individual relaxation mechanisms. 

The accompanying phase and group velocity dispersion imply that one cannot directly compare body wave, surface wave, and free oscillation data or laboratory and seismic data without correcting for absorption. The necessary formalism for making these corrections is given. In the constant Q regions the correction is the same as that implied in the theories of Futterman, Lomnitz, Strick and Kolsky.

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Don L. Anderson

Papers

Preliminary reference earth model

Theoretical basis of some empirical relations in seismology

Theory of Earth

Theory of the Earth

Velocity dispersion due to anelasticity; implications for seismology and mantle composition