Tensor structure and the least squares

It is shown that for linear parametric adjustment models all the least-squares equations can be obtained from a commutative diagram, where the observation and parameter spaces are regarded as covariant. Their contravariant counterparts are defined through the metric property of the covariance matrix of the observations.     

European floods during the winter 1783/1784: scenarios of an extreme event during the ‘Little Ice Age’

The Lakagígar eruption in Iceland during 1783 was followed by the severe winter of 1783/1784, which was characterised by low temperatures, frozen soils, ice-bound watercourses and high rates of snow accumulation across much of Europe. Sudden warming coupled with rainfall led to rapid snowmelt, resulting in a series of flooding phases across much of Europe. The first phase of flooding occurred in late December 1783–early January 1784 in England, France, the Low Countries and historical Hungary. The second phase at the turn of February–March 1784 was of greater extent, generated by the melting of an unusually large accumulation of snow and river ice, affecting catchments across France and Central Europe (where it is still considered as one of the most disastrous known floods), throughout the Danube catchment and in southeast Central Europe. The third and final phase of flooding occurred mainly in historical Hungary during late March and early April 1784. The different impacts and consequences of the above floods on both local and regional scales were reflected in the economic and societal responses, material damage and human losses. The winter of 1783/1784 can be considered as typical, if severe, for the Little Ice Age period across much of Europe.     

Evolution of geochemistry and depositional settings of Early Palaeozoic siliciclastics of the Barrandian (Teplá-Barrandian Unit,Bohemian Massif,Czech Republic)

Cambrian and Ordovician-Middle Devonian sequences of two successive Early Palaeozoic basins of the Barrandian unconformably overlie Cadomian basement in the Bohemian Massif NW interior (Teplá-Barrandian unit) which is the easternmost peri-Gondwanan remnant within the Variscides. Correlation of stratigraphy and geochemistry of the Early Palaeozoic siliciclastic rocks elucidated sediment provenances. Sandstones of the Middle Cambrian Píbram-Jince Basin were derived from a Cadomian Neoproterozoic island arc. The source area of the Ordovician shallow-marine siliciclastics of the successor Prague Basin is a dissected Cadomian orogen. Late Cambrian acid volcanics of the Barrandian and Cambrian (meta)granitoids emplaced in the W part of the Teplá-Barrandian Cadomian basement are also discernible in these sediments. Old sedimentary component increased during the Ordovician. Early Llandovery siliciclastic rocks show characteristics of an abruptly weakened supply of terrigenous material and an elevated proportion of synsedimentary basic volcanics as a result of Silurian transgression. Emsian siliciclastics (intercalated in the Late Silurian to Early Devonian limestone suite) presumably comprise an addition of coeval basic/ultrabasic volcaniclastics. Middle Devonian flysch-like siliciclastics indicate reappearance of Cadomian source near the Barrandian during early Variscan convergences of Armorican microplates that preceeded accretion of the Teplá-Barrandian unit within the Bohemian Massif terrane mosaic.Dr. Patoka deceased in July 2004.     

Automatic tracing of the foot of the continental slope

The UNCLOS III (Article 76, Section 4(b)) defines the foot of the continental slope as the point of maximum change in the gradient at its base. It is impossible to locate so defined afoot and thus to trace the foot‐line objectively by eye. In this study we show a method designed automatically to detect and trace the foot‐line of the continental slope from an irregular array of bathymetrical data. Our algorithm first transforms the bathymetric surface to a maximum curvature surface. On this new surface, the foot‐line corresponds to one of the ridges; instead of tracing the foot‐line on the bathymetric surface, we now can trace the ridges on the maximum curvature surface. The tracing of the ridges can be done automatically and objectively and the foot‐line is identified as being one of these ridges. We devote particular attention to the case when the ridge‐line is not defined, i.e., to the case when the point of maximum gradient change becomes a region of maximum gradient change.     

Travel time curves for complex inhomogeneous slightly anisotropic media

Summary The linearization approach is used to compute the travel times in inhomogeneous slightly anisotropic media. The basic formulae are outlined and their accuracy demonstrated in comparison with the exact solution based on the zero-order ray theory and the Backus formula (1965). The linearization is extended also to complex media with curved interfaces. The computer program for calculating travel times in 2D, inhomogeneous, slightly anisotropic, complex media is briefly described. The numerical results obtained for a realistic situation and various types of waves are presented to enable the effects of anisotropy and the effects of inhomogeneity on the resulting travel times to be compared.

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Scattering by nonspherical particles and optical properties of Martian dust

Ultraviolet spectral reflectance data obtained from the Mariner 9 during the 1971 Mars dust storm were analyzed at two wavelengths to deduce the complex index of refraction of Martian dust. Martian dust particles were considered to be irregularly shaped and randomly oriented nonspherical particles. The analysis shows that the Mariner 9 data are consistent with the scattering by irregular particles with an index of refraction m = 1.59 ? 0.0015i at λ = 0.305 μm and m = 1.55 ? 0.004i at λ = 0.268 μm. Both the real and the imaginary parts of refractive index found are considerably smaller than previously reported results using a spherical shape model for Martian dust particles.     

A chromospheric response to pulse beam heating

Starting from the new flare models of Karlický (1990) and Karlický and Hénoux (1991), we present here the first time-dependent numerical simulations of hydrogen plasma excitation and ionization on time scales of less than one second. These time scales are consistent with the spiky behaviour of the kinetic temperature produced by non-thermal collisional processes. Such temperature spikes represent a chromospheric response to a series of short-duration electron beam pulses which are supposed to heat the flare atmosphere. Self-consistent numerical solution of a simplified, time-dependent, non-LTE problem for a three-level hydrogen atom model with continuum allows us to predict theoretically a qualitative behaviour of the H line intensity variations on very short time intervals. Our H temporal profiles, evaluated at the line center and for = 1 Å, can be qualitatively compared with some recent flare observations obtained with high temporal resolution.     

Approximate spectral analysis by least-squares fit

An approximate method of spectral analysis called successive spectral analysis based upon the mean-quadratic approximation of an empirical function by generalised trigonometric polynomial with both unknown frequencies and coefficients is developed. A few quotations describing some properties of the method as well as one of the possible methods for numerical solution are given.     

Some Aspects of Meteoric Head Echo Velocity Determination

Velocity determination of 131 head echoes recorded during Perseid meteor shower observations by the Canadian 2 MW radar, has been performed under the assumption of either their constant velocity or of its linear change with time. Even though the constant velocities concentrated at 60 km s-1 generally accepted for the Perseids, a substantial number of echoes had velocities either lower than 60 km s-1 or greater than this value. The inclusion of variable velocity into considerations led to surprising result that a great portion of the head echoes accelerated (3 possibly decelerating echoes in comparison with 33 accelerating cases on the level of relative standard deviations of output parameters not exceeding 10%). It seems that the allocation of the ionization responsible for the head echo is not entirely identical with the instantaneous meteoroid position. As a consequence, the velocity derived from the measured head echo coordinates can differ from the velocity of parent body. We are not able to explain this finding at present. This revised version was published online in July 2006 with corrections to the Cover Date.