Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

Aspherical correction for free vibration of elastically anisotropic solid by means of theXYZ algorithm

By applying the perturbation theory to theXYZ algorithm (a kind of variational method), the difference f in free vibration frequencies between sphere and ellipsoid was approximated as , where i and _i (i = x,y andz) (i=x, y andz) are aspherical coefficients and asphericities of the ellipsoid, respectively. We developed an analytic method to compute the aspherical coefficients719-4 by using theXYZ algorithm. A numerical example was given for an ellipsoidal olivine, and an attempt was made to estimate the asphericities of the specimen by a least-squares method, based on the relationship between frequency shift and asphericity.     

Reflection of waves from the boundary of a random elastic semi-infinite medium

In this paper the smooth perturbation technique is employed to investigate the problem of reflection of waves incident on the plane boundary of a semi-infinite elastic medium with randomly varying inhomogeneities. Amplitude ratios have been obtained for various types of incident and reflected waves. It has been shown that an incidentSH orSV type of wave gives rise to reflectedSH, P andSV waves, the main components beingSH andP, SV in the respective cases. The reflected amplitudes have been calculated depending upon the randomness of the medium to the square of the small quantity , where measures the deviation of the medium from homogeneity. An incidentP-type wave produces mainly aP component and also a weakSH component to the order of ². The reflected amplitudes obtainable for elastic media are also altered by terms of the same order. The direction of the reflected wave is influenced by randomness in some cases.     

Extreme value analysis of diamond-size distributions

Extreme value analysis provides a semiparametric method for analyzing the extreme long tails of skew distributions which may be observed when handling mining data. The estimation of important tail characteristics, such as the extreme value index, allows for a discrimination between competing distribution models. It measures the thickness of such long tailed distributions, if only a limited sample is available. This paper stresses the practical implementation of extreme value theory, which is used to discriminate a lognormal from a mixed lognormal distribution in a case study of size distributions for alluvial diamonds.     

Earthquake rupture complexity due to dynamic nucleation and interaction of subsidiary faults

We numerically study the dynamic interaction of propagating cracks. It is assumed that propagating cracks can nucleate and drive subsidiary cracks because of shear strain enhancement near the propagating crack tips. The critical strain fracture criterion is assumed in the analysis. Intense interaction is expected to occur among the cracks. All the cracks are assumed to be parallel and antiplane strain deformation is assumed in the computation.In the interaction of two non-coplanar cracks, a strain shadow is formed in the neighborhood of each crack because of the strain release by the introduction of the crack. The growth of each crack is accelerated when the propagating tips of each crack are outside of the strain shadow of the other crack. In general, the crack tips enter the strain shadow, and the crack tips decelerate. The calculation shows that only one of the two cracks can continue to grow, and the other's growth is decelerated and arrested. If we can assume that the suite of cracks interact in a pairwise manner only, then this may suggest that only a limited number of cracks can continue to grow during the final stage of the rupture process. Hence the crack interaction causes complexity in dynamic earthquake faulting. The concepts of barrier and asperity have been employed by many researchers for the interpretation of complex seismic wave data. However, the physical realities of such concepts are obscure. Our calculations show that dynamic crack interactions can produce barriers and asperities in some cases; the crack tip deceleration or arrest due to the interactions among non-coplanar cracks can be interpreted as being due to a barrier. The dynamic coalescence among the coplanar cracks can be regarded as an asperity.Umeda found a localized area that strongly radiates high-frequency seismic waves in the epicentral areas of some large shallow earthquakes. He defined this as an earthquake bright spot. Our analysis implies that only a limited number of cracks continue to grow when many interactive cracks nucleate, and that all other cracks stop extending soon after nucleation. Hence, if the nucleation and termination of several cracks occur in a localized area, it will be observed seismologically as an earthquake bright spot. This is because it is theoretically known that the sudden termination of crack growth and dynamic crack coalescence efficiently emits high-frequency elastic waves.     

THEORY AND PRACTICE FOR COMPILING THE ATLAS OF NATURAL DISASTERS IN CHINA

CompilinganatlasofnaturaldisastersinChinaisabasistoresearchintoregionaldisasterssystems,torevealthetemPOralandspatialpatternofnaturaldisasters,aswellastoestablishcountermeasuresopinstnamraldisasters.TaldngtheuAtlasOfNaturalDisastersinChina"**asanexample,thisarticleinquiresintotheoreticalandpracticalproblemsaboutcompilinganatlasofregionalnaturaldisasters.ThebasictheoryofcompilinganatlasOfregionaldisastershasbeenfOundedonthecombinati0nofthesciencesofdisasters,cart0graphyandregiotalmhy.Theref…     

The elastic properties of single-crystal fayalite as determined by dynamical measurement techniques

We present new elasticity measurements on single-crystal fayalite and combine our results with other data from resonance, pulse superposition interferometry, and Brillouin scattering to provide a set of recommended values for the adiabatic elastic moduliC _ij and their temperature variations. We use a resonance method (RPR) with specimens that were previously investigated by pulse superposition experiments. The nineC _ij of fayalite are determined from three new sets of measurements. One set of our newC _ij data is over the range 300–500 K. We believe that the relatively large discrep ncies found in someC _ij are due in large part to specimen inhomogeneities (chemical and microstructural) coupled with differences in the way various techniques sample, rather than only systematic errors associated with experimental procedures or in the preparations of the specimens.Our recommendeaC _ij's (GPa) and (C _ij/T) _p (GPa/K) are: The resulting values for the isotropic bulk and shear moduli,K _s and , and their temperature derivatives are:K _s=134(4) GPa; =50.7(0.3) GPa; (K _s/T) _p =–0.024(0.005) GPa/K; and (/T) _p =–0.013(0.001) GPa/K. An important conclusion is thatK _s increases as the Fe/(Fe+Mg) ratio in olivine is increased.     

On the physical model of earthquake precursor fields and the mechanism of precursors＇timespace distribution──origin and evidences of the strong body earthquake──generating model

Ｏｎｔｈｅｐｈｙｓｉｃａｌｍｏｄｅｌｏｆｅａｒｔｈｑｕａｋｅｐｒｅｃｕｒｓｏｒｆｉｅｌｄｓａｎｄｔｈｅｍｅｃｈａｎｉｓｍｏｆｐｒｅｃｕｒｓｏｒｓ＇ｔｉｍｅｓｐａｃｅｄｉｓｔｒｉｂｕｔｉｏｎ──ｏｒｉｇｉｎａｎｄｅｖｉｄｅｎｃｅｓｏｆ　ｔｈｅｓｔｒｏｎ...     

Hamiltonian perturbation theory on a manifold

This paper deals with Hamiltonian perturbation theory for systems which, like Euler-Poinsot (the rigid body with a fixed point and no torques), are degenerate and do not possess a global system of action-angle coordinates. It turns out that the usual methods of perturbation theory, which are essentially local being based on the construction of normal forms within the domain of a local coordinate system, are not immediately usable to study perturbations of these systems, since degeneracy makes impossible to control that the system does not fall into a singularity of the coordinates. To overcome this difficulty, we develop a global formulation of Hamiltonian perturbation theory, in which the normal forms are globally defined on the phase space manifold. The key for this study lies in the geometry of the fibration by the invariant tori of an integrable degenerate Hamiltonian system, which is described by some generalizations of the Liouville-Arnol'd theorem and is reviewed in the paper. As an application, we provide a global formulation of Nekhoroshev's theorem on the stability for exponentially long times.     

新地球观

One of the most important achivements on science in 20th century is the new recognition on the Earth:the Earth,out of the other planets, exhibits very peculiar features because it has an extremely complex and active periphery part (surfacial layers). This periphery part is an open system sustained by inputting solar energe , which is captured , transfered and stored by life. Through the system , cyclings of matters and energe flow are driven and regulated by life activities. This system is self-equilibrated,self-controlled and far away from astrophysical and thermodynamic equilibria mainly because of life and life activities.
Development of human calture influences increasingly on流Earth's periphery system , at last , the natural biosphere that has existed for 3 billion years on the Earth's surface will inavoidably be replaced by so called "noosphere",which is man一reconstructed,man-controlled and unstable system. Thus the fate of the Earth,to a great extent,will be determined by the direction of human calture evolution.