A comparison between two internal structure models of the Earth

1991 ◽  
Vol 54 (2) ◽  
pp. 129-143 ◽  
Author(s):  
C. Z. Zhang
2004 ◽  
Vol 12 (1) ◽  
pp. 111-119
Author(s):  
SIEGFRIED J. BAUER

Planet Earth is unique in our solar system as an abode of life. In contrast to its planetary neighbours, the presence of liquid water, a benign atmospheric environment, a solid surface and an internal structure providing a protective magnetic field make it a suitable habitat for man. While natural forces have shaped the Earth over millennia, man through his technological prowess may become a threat to this oasis of life in the solar system.


2004 ◽  
Vol 219 ◽  
pp. 395-399
Author(s):  
G. Cayrel de Strobel

Astrometric, kinematic, spectroscopic and internal stellar structure data of 59 out of 102, extra-solar planet stars (thereafter ESPs), as yet discovered, are herewith discussed. The remaining 43 have been discarded, because they are not yet subjected to detailed spectroscopic analyses. The assembling of true physical parameters of ESPs has been made with the help of the Hipparcos and the [Fe/H] Catalogues. The retained 59 ESPs, could be divided into three sub-samples: midly metal poor, metal normal and metal enriched ESPs. Three observational (logTeff, Mbol) diagrams for each of the metallicity groups have been constructed and interpreted with the help of theoretical HR diagrams, computed for metal-poor, metal-normal, and metal-rich internal structure models. The age of 47 evolved ESPs of the sample has been estimated from the relevant isochrones. Even if the age difference between some of the ESPs is great, (from 1 to >12 Gyr) stars as young as the Hyades (670 Myr) have not been found. ESPs are biased towards metallicities higher than solar. In this sample the number of ESPs with metallicity [Fe/H]>0 is 2.4 times the number of ESPs with [Fe/H] < 0, whereas the proportion is roughly inverted in a sample of non ESPs.


The aim of this review is to bring together and relate recent progress in three subjects - the internal structure of the Earth, the behaviour of materials at very high pressures and the dynamical properties of the planets. Knowledge of the internal structure of the Earth has been advanced in recent years, particularly by observations of free oscillations of the whole Earth excited by the very largest earthquakes; as a consequence, it is clear that K. E. Bullen’s hypothesis that bulk modulus is a smooth function of pressure irrespective of composition is close to the truth for the Earth. Understanding of the behaviour of materials at very high pressure has increased as a result both of experiments on the propagation of shock waves and of theoretical investigations along a number of lines and it can now be seen that Bullen’s hypothesis is not true irrespective of chemical composition and crystal structure but that it happens to apply to the Earth because of particular circumstances. Studies of the orbits of artificial satellites and space probes have led to better knowledge of the dynamics of the Moon, Mars and Venus, and there have also been recent improvements in the traditional studies of Uranus and Neptune. Our knowledge of the dynamics of the planets is on the whole rather restricted, and Bullen’s hypothesis only applies directly to the Moon (for which the application is trivial) and possibly to Mars; the dynamical properties do none the less set fairly restrictive limits to the models that can be constructed for other planets. It would be possible for all planets to have cores of similar composition to the Earth ’s, surrounded by mantles of different sorts, silicates for the terrestrial planets and mostly hydrogen for Jupiter, Saturn, Uranus and Neptune.


Nature ◽  
1990 ◽  
Vol 344 (6262) ◽  
pp. 106-106 ◽  
Author(s):  
Bernard Wood ◽  
George Helffrich
Keyword(s):  

2016 ◽  
Author(s):  
Mohammad Hosseini ◽  
Mohammad Ali Riahi

Abstract. In the earth sciences, there is only one single true reality for a property of any dimension whereas many realization models of the reality might exist. In other words, a set of interpreted multiplicities of an unknown property can be found but only one unique fact exists and the task is to return from the multiplicities to the uniqueness of the reality. Such an objective is mathematically provided by sparse approximation methods. The term "approximation" indicate the sufficiency of an interpretation that is close enough to the true mode, i.e. reality. In geosciences, the multiplicities are provided by multiple-point statistical methods. Realistic modeling of the earth interior demands for more sophisticated geostatistical methods based on true available images, i.e. the training images. Among available MPS methods, the DisPat algorithm is a distance-based MPS method which generate appealing realizations for stationary and nonstationary training images by classifying the patterns based on distance functions using kernel methods. Advances in nonstationary image modeling is an advantage of the DisPat method. Realizations generated by the MPS methods form the training set for the sparse approximation. Sparse approximation is consisted of two steps, i.e. sparse coding and dictionary update, which are alternately used to optimize the trained dictionary. Model selection algorithms like LARS are used for sparse coding. LARS optimizes the regression model sequentially by choosing a proper number of variables and adding the best variable to the active set in each iteration. Out of numerous training dictionary methods given in the literature, the ILS-DLA is a variant of the MOD algorithm where the latter is inspired by the GLA and the whole trained dictionary is sequentially updated by alternating between sparse coding and dictionary training steps. The ILS-DLA is different from the MOD for addressing the internal structure of the dictionary by considering overlapping or non-overlapping blocks and modifying the MOD algorithm according to the internal structure of the trained dictionary. The ILS-DLA is faster than the MOD in the sense that it inverts for smaller blocks constructing the trained dictionary rather than inverting for the entire block. The subject of this paper is an integration study between sparse approximations from image processing and compressed sensing, multiple-point statistics from the field of geostatisitcs, and the geophysical methods and reservoir engineering from the branch of petroleum science. This paper specifically emphasizes the utilization of image processing in solving reservoir complexities and enhancing reservoir models.


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