On criteria for measures of compositional difference

Simple perceptions about the nature of compositions lead through logical necessity to certain forms of analysis of compositional data. In this paper the consequences of essential requirements of scale, perturbation and permutation invariance, together with that of subcompositional dominance, are applied to the problem of characterizing change and measures of difference between two compositions. It will be shown that one strongly advocated scalar measure of difference fails these tests of logical necessity, and that one particular form of scalar measure of difference (the sum of the squares of all possible logratio differences in the components of the two compositions), although not unique, emerges as the simplest and most tractable satisfying the criteria.     

Microwave response of green vegetation

The cavity perturbation technique has been used to measure the dielectric constant of vegetation, such as soyabean, grass, corn and green spruce at 9.5 GHz. The dielectric properties of these vegetations are highly dependent upon the moisture content. For freshly plucked specimen the dielectric constant was found to be maximum which decreased gradually as the specimen dried up. The role of these basic physical parameters in microwave scatterometer experiment has been discussed. Some parameters of remote sensing application have been estimated from these measurements and their practical role has been discussed     

Tomographic determination of the upper crustal structure in the Jiashi strong earthquake swarm region

IntroductionBetween January and April of 1997, 7 earthquakes with M(6.0 occurred successively in Jiashi, Xinjiang. The continual occurrence of strong earthquakes within such a small area and in such a short period of time is exceptional for intraplate earthquakes. The Jiashi earthquake swarm took place on the northeast side of the Pamirs, where the Tarim basin, South Tianshan and West Karakoram meet (HU, et al, 1989). This is also a place where a number of active faults develop, so it is…     

BLU Estimators and Compositional Data

One of the principal objections to the logratio approach for the statistical analysis of compositional data has been the absence of unbiasedness and minimum variance properties of some estimators: they seem not to be BLU estimator. Using a geometric approach, we introduce the concept of metric variance and of a compositional unbiased estimator, and we show that the closed geometric mean is a c-BLU estimator (compositional best linear unbiased estimator with respect to the geometry of the simplex) of the center of the distribution of a random composition. Thus, it satisfies analogous properties to the arithmetic mean as a BLU estimator of the expected value in real space. The geometric approach used gives real meaning to the concepts of measure of central tendency and measure of dispersion and opens up a new way of understanding the statistical analysis of compositional data.     

New Perspectives on Water Chemistry and Compositional Data Analysis

Water chemistry is commonly investigated to determine the suitability of water for various uses. With increased knowledge of aqueous chemistry, it has become possible to interpret the evolutionary processes that determine water composition and quality. This paper presents procedures for exploring and modeling the environment using compositional data from water analysis, utilizing statistical tools in an appropriate sample space. Our procedures build on a methodology based on log-ratios initiated by John Aitchison in the early 1980's. They are not only useful for interpreting the structure of the data, but also for characterizing and modeling the influence of geochemical processes acting on the environment. The geochemistry of water samples collected from wells on Vulcano Island (one of the Aeolian Islands of the Italian province of Sicily) will be used to illustrate the techniques, although an exhaustive overview would require many different examples. Vulcano island is a quiescent volcanic area where mobilization of chemical species by weathering of volcanic rocks and input of gaseous components from fumarolic activity has produced environmental changes expressed in the composition of phreatic waters at the surface and in the shallow subsurface. Changes in the chemical composition of waters in unconfined aquifers of the northwestern part of the island around the active crater appear to be useful in understanding the natural processes at work.     

Tomographic study of the deep tectonics in the Yecheng-Shiquanhe area of the Tibetan Plateau

The profile crossing the west Kunlun region cov-ers the area between the Tarim Basin and the Kara-korum Fault, which is the highest (~5000 m a.s.l.) andthe most narrow part (400—500 km from north tosouth) of the Tibetan Plateau, thus attracting great at-tention of the geological community because of itsunique tectonic features. The Geological Bureau of Xinjiang Uygur Auton-omous Region and Chinese Academy of Sciences(CAS) carried out mineral exploration and geologicalmapping in th…     

Sensitivities of seismic traveltimes and amplitudes in reflection tomography

Seismic traveltimes and amplitudes in reflection-seismic data show different dependences on the geometry of reflection interfaces, and on the variation of interval velocities. These dependences are revealed by eigenanalysis of the Hessian matrix, defined in terms of the Fréchet matrix and its adjoint associated with different norms chosen in the model space. The eigenvectors and eigenvalues of the Hessian clearly show that for reflection tomographic inversion, traveltime and amplitude data contain complementary information. Both for reflector-geometry and for interval-velocity variations, the traveltimes are sensitive to the model components with small wavenumbers, whereas the amplitudes are more sensitive to the components with high wavenumbers. The model resolution matrices, after the rejection of eigenvectors corresponding to small eigenvalues, give us some insight into how the addition of amplitude information could potentially contribute to the recovery of physical parameters.
In order to cooperatively invert seismic traveltimes and amplitudes simultaneously, we propose an empirical definition of the data covariance matrix which balances the relative sensitivities of different types of data. We investigate the cooperative use of both data types for, separately, interface-geometry and 2-D interval-velocity variations. In both cases we find that cooperative inversions can provide better solutions than those using traveltimes alone. The potential benefit of including amplitude-data constraints in seismic-reflection traveltime tomography is therefore that it may be possible to resolve the known ambiguity between the reflector-depth uncertainty and the interval-velocity uncertainty better.