Statistical parameterization of inverse problems

Image restoration, computerized tomography, and other similar problems are considered as a unified class of stochastic inverse problems. The conventional approach to these problems that proceeds from some integral or functional equations suffers from three main shortcomings: (i) subjectivity, (ii) inability to account for the inner (radiational) noise, and (iii) inability to include the fundamental concept of the natural limit of solution accuracy. A general approach is developed, the Statistical Parameterization of Inverse Problems (SPIPR), that takes into account both the inner and external random noise and gives an explicit form of the above-mentioned natural limit. Applications of the SPIPR to various problems show that the maximum likelihood method as the concrete way to obtain an object estimate has practically limiting efficiency.Two new fields of applications of the SPIPR are outlined along with the image restoration problem: the elimination of blurring due to atmosphere turbulence and reconstruction of an object structure in the computerized tomography. The expressions for the main distribution function in all these problems are found. The corresponding real examples and model cases are considered as well.     

Resonant behaviour of MHD waves on magnetic flux tubes

Resonant absorption of MHD waves on a nonuniform flux tube is investigated as a driven problem for a 1D cylindrical equilibrium. The variation of the fractional absorption is studied as a function of the frequency and its relation to the eigenvalue problem of the MHD radiating eigenmodes of the nonuniform flux tube is established. The optimal frequencies producing maximal fractional absorption are determined and the condition for total absorption is obtained. This condition defines an impedance matching and is fulfilled for an equilibrium that is fine tuned with respect to the incoming wave. The variation of the spatial wave solutions with respect to the frequency is explained as due to the variation of the real and imaginary parts of the dispersion relation of the MHD radiating eigenmodes with respect to the real driving frequency.     

Current convection in solar active regions

Current carrying magnetic fields which penetrate sunspots can be unstable to current convective modes caused by the large gradient of electrical conductivity. The linear growth rates and wavelengths of the unstable modes are found. The unstable modes produce fine-scale vortices perpendicular to the magnetic field, which overshoot well into the solar corona. The modes provide a turbulent vorticity source at the photospheric footpoints of the field. This can cause braiding and reconnection of the coronal magnetic field. The modes twist the coronal magnetic field into loops with a typical radius of 200 km, consistent with recent X-ray observations.     

Purana basins of peninsular India: a review

Seven supracratonic, Proterozoic basins, occupying more than a fifth of the Precambrian exposures in the Indian Peninsula, comprise the Purana basins. A comprehensive review of the current status of knowledge of these voluminous orthoquartzite-carbonate-shale suites in the context of their contemporary lithostratigraphy, depositional environments and structural disposition is presented. Stromatolite biostratigraphy and available geochronological data are compared, to discern their age limits.
These basins contain perhaps one of the most elaborate records of Middle to Late Proterozoic (Riphean-Vendian) sedimentation preserved in an unmetamorphosed and only slightly deformed state. Further sedimentological and structural studies could lead to a better understanding of the Proterozoic craton-margin processes. Their close association with the Middle Proterozoic Mobile Belt of peninsular India is that of two contrasting tectonic regimes, contemporaneously adjoining each other. The existing lithostratigraphic classifications of many of these sequences may not stand the test of process - response considerations as demonstrated by the recent revisions in the stratigraphy of the Cuddapah and Bhima basins. The prolific stromatolitic, micro-organic and trace-fossil communities preserved in them require much more detailed, but cautious study, and may yield information on the Riphean-Vendian biota. However, these studies must be undertaken in association with elaborate geochronological determinations which are sparse at present.
Inadequacy of the existing knowledge of these basins is highlighted, with the view of inviting the attention of the geological community to these unique basins from peninsular India.     

Late Oligocene-Miocene syn-/-late-orogenic successions in Western and Central Mediterranean Chains from the Betic Cordillera to the Southern Apennines*

The identification of syn- and late-orogenic flysch deposits, extending from the Betic Cordillera to the Southern Apennines, assists in the reconstruction of the tectonic-sedimentary evolution of the perimediterranean chains. A microplate was located between the European and African Plates during the Late Jurassic–Early Cretaceous, bordered northwards by the Piemontese Ocean and southwards by another (North Africa ‘Flysch’ Basin or Maghrebian) Ocean. The Piemontese Ocean and the northern margin of the microplate were structured from the Late Cretaceous to the Eocene to create an Eo-alpine Chain. The southern margin of the microplate was deformed in the Aquitanian, when the internal areas of the Maghrebian Ocean were characterized by syn-orogenic flysch deposits. This episode culminated with metamorphism (25–22 Ma) and nappe emplacement, which destroyed the former palaeogeography and created an orogenic belt (AlKaPeCa). Afterwards, a lower Burdigalian late-orogenic cycle started in the deformed area, which as a result of the opening of the Algero-Provençal Basin, caused the fragmentation of the AlKaPeCa, its thrusting on the ‘Flysch’ Basin and the collision with the North Africa and South Iberia Margins. These latter were folded and thrusted, the ‘Flysch’ Units pushed over the External Domain and also back-thrusted. Langhian late-orogenic deposits suture the new tectonic features. Finally, the whole orogen was thrust onto the foredeep during the Middle–Late Miocene.     

Transient response of a circular cavity in a poroelastic medium

This paper considers the transient response of a pressurized long cylindrical cavity in an infinite poroelastic medium. To obtain transient solutions, Biot's equations for poroelastodynamics are specialized for this problem. A set of exact general solutions for radial displacement, stresses, pore pressure and discharge are derived in the Laplace transform space by using analytical techniques. Solutions are presented for three different types of prescribed transient radial pressures acting on the surface of a permeable as well as an impermeable cavity surface. Time domain solutions are obtained by inverting Laplace domain solutions using a reliable numerical scheme. A detailed parametric study is presented to illustrate the influence of poroelastic material parameters and hydraulic boundary conditions on the response of the medium. Comparisons are also presented with the corresponding ideal elastic solutions to portray the poroelastic effects. It is noted that the maximum radial displacement and hoop stress at the cavity surface are substantially higher than the classical static solutions and differ considerably from the transient elastic solutions. Time histories and radial variations of displacement, hoop stress, pore pressure and fluid discharge corresponding to a cavity in two representative poroelastic materials are also presented.     

Study of radiative energy losses in the moving envelopes of T Tau stars

Crimean Astrophysical Observatory. Translated from Astrofizika, Vol. 32, No. 1, pp. 69–83, January–February, 1990.     

A new method of palaeofield magnitude correction for thermally altered samples and its application to Lower Carboniferous lavas

Summary. Some lavas of Early Carboniferous age from Scotland and Derbyshire have been analysed for palaeofield magnitude by the application of a new correction to data obtained by the Shaw method. Its application has yielded field magnitude values from data which had previously been rejected. A modern pottery specimen and recent lavas from Sicily and Westman Island have also been analysed.
An average virtual dipole moment (VDM, Smith) of 2.5 ± 0.4 × 10²² A m² was determined for the Early Carboniferous. This is only 30 per cent of the present-day VDM.     

Auroral zone effects on hydrogen geocorona structure and variability

The instantaneous structure of planetary exospheres is determined by the time history of energy dissipation, chemical, and transport processes operative during a prior time interval set by intrinsic atmospheric time scales. The complex combination of diurnal and magnetospheric activity modulations imposed on the Earth's upper atmosphere no doubt produce an equally complex response, especially in hydrogen, which escapes continuously at exospheric temperatures. Vidal-Madjar and Thomas (1978) have discussed some of the persistent large scale structure which is evident in satellite ultraviolet observations of hydrogen, noting in particular a depletion at high latitudes which is further discussed by Thomas and Vidal-Madjar (1978). The latter authors discussed various causes of the H density depletion, including local neutral temperature enhancements and enhanced escape rates due to polar wind H⁺ plasma flow or high latitude ion heating followed by charge exchange. We have reexamined the enhancement of neutral escape by plasma effects including the recently observed phenomenon of low altitude transverse ion acceleration. We find that, while significant fluxes of neutral H should be produced by this phenomenon in the auroral zone, this process is probably insufficient to account for the observed polar depletion. Instead, the recent exospheric temperature measurements from the Dynamics Explorer-2 spacecraft suggest that neutral heating in and near the high latitude cusp may be the major contributor to depleted atomic hydrogen densities at high latitudes.