3-D scattering of elastic waves by small-scale heterogeneities in the Earth’s mantle
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SUMMARY Small-scale heterogeneities in the Earth’s mantle, the origin of which is likely compositional anomalies, can provide critical clues on the evolution of mantle convection. Seismological investigation of such small-scale heterogeneities can be facilitated by forward modelling of elastic wave scattering at high frequencies, but doing so with conventional 3-D numerical methods has been computationally prohibitive. We develop an efficient approach for computing high-frequency synthetic wavefields originating from small-scale mantle heterogeneities. Our approach delivers the exact elastodynamic wavefield and does not restrict the geometry or physical properties of the local heterogeneity and the background medium. It combines the technique of wavefield injection and a numerical method called AxiSEM3D. Wavefield injection can decompose the total wavefield into an incident and a scattered part. Both these two parts naturally have low azimuthal complexity and can thus be solved efficiently using AxiSEM3D under two different coordinate systems. With modern high-performance computing (on an order of magnitude of 105 CPU-hr), we have achieved a 1 Hz dominant frequency for global-scale problems with strong deep Earth scattering. Compared with previous global injection approaches, ours allows for a 3-D background medium and yields the exact solution without ignoring any higher-order scattering by the background medium. Technically, we develop a traction-free scheme for realizing wavefield injection in a spectral element method, which brings in several flexibilities and simplifies the implementation by avoiding stress or traction computation on the injection boundary. For a spherical heterogeneity in the mid-lower mantle, we compare the 3-D full-wave solution with two approximate ones obtained, respectively, by the perturbation theory and in-plane (axisymmetric) modelling. As a comprehensive application, we study S-wave scattering by a 3-D ultra-low velocity zone, incorporating 3-D crustal structures on the receiver side as part of the background model.Hotspot (geology)
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Abstract Two new quantitative terms, the box replacement ratio and the pervasion ratio, are employed to investigate convective mantle mixing in this paper. The former is the ratio of the mantle boxes that have been replaced at least once by other mantle boxes to the total number of mantle boxes. The latter is the ratio of initial to final volumetric density of tracers which were initially confined in a small space. In this study we assume that mantle convection is steady, it is driven by plate motion or density anomalies in the mantle and the viscosities in the upper and lower mantle are different. In our numerical experiment the mantle is divided into 20736 boxes (5° × 5° × 300 km) and there are 2376 tracers placed on 5° × 5° grids at 100 km depth and at 100 km above CMB. The results show that the box replacement ratio of convective mantle mixing is over 80% for the whole mantle and is over 90% for upper mantle after 4 billion years. It means that most mantle boxes have been replaced. For two groups of 1681 tracers in a small space of 10° × 10° (at intervals of 0.25°) placed at the top and bottom of the mantle their pervasion ratios approach a constant and the initial tracers become widely distributed in the mantle after 3 billion years. These results indicate that the Earth's mantle, except for the lithosphere and “D” layer, has been mixed very well in the past 4 billion years. It is not likely that initial heterogeneity boxes greater than 5° × 5° × 300 km remain in the present mantle.
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Core–mantle boundary
Planetary differentiation
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I review the recent topics of the mantle convection, especially with regard to the scales of mantle flows. The studies of 3-D velocity structure of the earth's mantle, geoid, gravity and isotope geochemistry provide a new perspective of the flow in the mantle. Several workers show a clear correlation between the distribution of hotspots and the geoid anomalies obtained by subtracting the contribution of the subducted slabs. Assuming a spherically symmetric viscous earth, several researchers could constrain the form of mantle flow and viscosity structure in the earth by correlating the calculated geoid with the observed one. Seismological studies suggest the existence of aseismic slab beneath 650km discontinuity. If this is a case, the aseismic slab may be explained by several ways on the basis of convection theories, that is, whole mantle convection, layered convection with thermal coupling and the penetrative convection. 3-D velocity structure obtained by several workers show the correlation between the geoid and lower mantle heterogeneity at low degrees (l=2-3) and this correlation was explained by the flow models. Possible seismological indicators of mantle layering are proposed. Seismic anisotropy found by the studies of the long period surface wave correlates with some mantle flow model and may suggest the flow direction or stress field in the real earth. The topography of core-mantle boundary revealed by recent seismological and geodetic studies may constrain the viscosity and thermal properties of mantle near CMB. The heterogeneity in the CMB may be closely related to the dynamics near CMB, for example, entrainment of dense material by the convection and the double diffusive convection. Isotope geochemistry shows that there are many geochemical source regions which have various sizes and age distrbution. Convective mixing was investigated and two opposite views have been presented. In one view, the convection is strong enough to homogenize the geochemical heterogeneities within a geologically short time; in another, both small and large scale heterogeneities persist for 1-2 b. y. The studies mentioned above are combined into the flow models by several workers.
Core–mantle boundary
Slab
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Core–mantle boundary
Planetary differentiation
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Mantle convection patterns of the past are not well known, yet an understanding of changing mantle convection characteristics is fundamental to understanding the evolution of plate tectonics. There are very few ways to examine mantle characteristics of the past. Changes in spreading rate and volcanic activity with time have been used to draw conclusions about historic changes in mantle activity. Mantle temperature has been found to be related to crustal thickness. With this relationship, crustal thicknesses may now yield new conclusions about historic changes in mantle characteristics. We have inferred changes in mantle convection patterns throughout the last 180 m.y. by examining variations in assumed crustal thickness within the Pacific basin. Crustal thicknesses were calculated from residual depth anomalies by assuming that residual depth anomalies are the result of isostatic compensation of variations in crustal thickness. Crustal thickness is determined at the time of crustal formation and is dependent upon the temperature of the mantle source material. Intraplate hot spot volcanism effects on crustal thickness were not ignored. Examination of variations in crustal thickness of crust of different ages can reveal information about changing temperatures of the mantle at the ridge through time. We have learned that mantle temperatures at the ridge during the mid‐Cretaceous were more variable than those temperatures at the ridge after the mid‐Cretaceous. Furthermore, we have inferred from the data that mantle temperatures at hot spots were higher during the mid‐Cretaceous than those at hot spots existing after the mid‐Cretaceous. We suggest that mantle convection at the ridge was more rapid during the mid‐Cretaceous causing a higher variability of temperatures at the ridge. We also note that this period of increased mantle convection is concurrent with the increased mantle temperatures at hot spots within the Pacific basin.
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Crustal recycling
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Core–mantle boundary
Planetary differentiation
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Advancements in the study of mantle convection and the material movements in the deep Earth interior
Now geo-science realized that the mantle convection is not the imagination of few geodynamical studies. It is the main frame of the mantle thermodynamic system. The study of the mantle convection and plate tectonics has been transformed from the simple discussions of the driving mechanics either passive or active into the discussions of en united mantle thermodynamic system. The mantle convection system (including plumes) not only the main subjects in the study of the mantle evolution, but also in the study of the continent formation and evolution. At the same time, the geophysical (in particular seismic tomography) and geo-chemical observations turn into the main way to investigate the mantle convection system. However, these two groups of data set are inconsistent in the inferring the structure of mantle convection. Some new mantle thermodynamic models based on the geo- chemical data became the strong challenge to the study of the mantle convection.
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Mantle plume
Core–mantle boundary
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In this paper we attempt to find a solution of the following problem. It appears reasonable to expect that if thermal convection occurs in the Earth's mantle, it may also occur within the Moon and Mars. The dimensions of these latter two bodies are comparable to the thickness of the Earth's mantle. Presumably the amount of radioactive heat generated per unit mass is similar in all three bodies. Yet the surface morphology of the Earth, which many scientists believe arises ultimately from mantle convection, differs markedly from that of the Moon or Mars. The explanation advanced here for this difference is based on the effect produced on convection in the mantle by the presence of a low ‘viscosity’ or low creep strength layer. It is assumed that the low velocity layer of the mantle is such a low creep strength layer. A low viscosity layer changes the amount of ‘coupling’ between the outer crust and mantle convection. (The crust is ‘coupled’ if mantle convection produces stresses in the crust which are large enough to deform it plastically. The crust is ‘decoupled’ from the mantle if these stresses are insufficient to produce plastic deformation.) The theory assumes that the viscosity or creep strength is essentially zero in the low viscosity layer. The analysis is similar to that developed earlier for the calculation of stresses within the mantle. We find that the deeper within the mantle lies the low viscosity layer the greater is the coupling of the outer crust to the mantle convection currents. If the low creep strength layer lies close to the surface the outer crust is decoupled from the interior. According to the literature the depth of the low velocity layer is determined by the temperature and pressure profiles within the mantle. If the temperature profile were kept constant but the pressure reduced by changing g, the gravitational acceleration, the low velocity zone would be moved to a level closer to the surface. It is proposed that because of this interdependence between temperature, pressure and depth of the low velocity layer, the low velocity layers in Mars and the Moon (if such layers exist in these bodies) lie much closer to the surface than does the corresponding layer in the Earth. Hence the outer crusts of Mars and the Moon are more nearly decoupled from the interior than is the Earth's crust.
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Radiogenic nuclide
Planetary differentiation
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Mantle plume
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