How selection and weighting of astrometric observations influence the impact probability. The case of asteroid (99942) Apophis

The aim of this paper is to show that in the case of a low probability of asteroid collision with the Earth, the appropriate selection and weighting of the data are crucial for the impact investigation and for analysing the impact possibilities using extensive numerical simulations. By means of the Monte Carlo special method, a large number of 'clone' orbits have been generated. A full range of orbital elements in the six-dimensional parameter space, that is, in the entire confidence region allowed by the observational material, has been examined. On the basis of 1000 astrometric observations of (99942) Apophis, the best solutions for the geocentric encounter distance of  6.065 ± 0.081 R_⊕  (without perturbations by asteroids) or  6.064 ± 0.095 R_⊕  (including perturbations by the four largest asteroids) were derived for the close encounter with the Earth on 2029 April 13. The present uncertainties allow for special configurations ('keyholes') during this encounter that may lead to very close encounters in future approaches of Apophis. Two groups of keyholes are connected with the close encounter with the Earth in 2036 (within the minimal distance of  5.7736−5.7763 R_⊕  on 2029 April 13) and 2037 (within the minimal distance of  6.3359–6.3488 R_⊕  ). The nominal orbits for our most accurate models run almost exactly in the middle of these two impact keyhole groups. A very small keyhole for the impact in 2076 has been found between these groups at the minimal distance of 5.97347   R_⊕  . This keyhole is close to the nominal orbit. The present observations are not sufficiently accurate to eliminate definitely the possibility of impact with the Earth in 2036 and for many years after.     

An algorithm for the optimum distribution of a regional seismic network—I

Summary An algorithm for the optimum distribution of any number of regional seismic stations is formulated. The information needed from a given region is the relative distribution of seismic intensity and the travel times of seismic waves used in earthquake location procedure. To define the optimum distribution of a regional network, some generalization of D-planning (minimization of the ellipsoid volume of earthquake location errors) was applied. The D-optimum criterion is generalized for a case where equations describing the process are nonlinear and when the most probable values of the sought parameters (origin time and earthquake focus coordinates) are not known.As an example of the algorithm application, the optimum distribution of seismic stations in the central district of the Lublin Coal Basin in Poland is given.     

GOCE satellite orbit in the aspect of selected gravitational perturbations

In this work, the GOCE satellite orbit is described in the aspect of perturbations in the Keplerian osculating elements. The perturbations come from the Earth and ocean tides, the gravitation of the Moon, the gravitation of the Sun, the gravitation of planets and Pluto, and the relativity effects. These perturbations are computed for the 30-day interval with a sampling of 2 min. To obtain the simulated orbit, the Cowell numerical integration method of 8th order is used. The first part of the work contains the root mean square (RMS) values of aforementioned perturbations due to the specified forces. The perturbations were compared taking into account their RMS characteristics.     

Point-to-curve ray tracing in complicated geological models1

Boundary-value problems (BVPs) for seismic rays generally have multiple solutions. In practical applications the number of solutions can be large. The algorithm presented below solves a one-parameter family of BVPs and makes it easy to obtain all the solutions of a BVP.     

Anisotropic viscoelastic models with singular memory

The physical background of singular memory models and in particular the Cole–Cole model is discussed. Three models of anisotropic linear viscoelasticity with frequency-dependent stiffness coefficients are considered. The models are constructed in such a way that anisotropic properties are separated from anelastic effects. Two of these models represent finite-speed wave propagation with singularities at the wavefronts (the exponential relaxation model) and without singularities at the wavefronts (the Cole–Cole model), while a third model called the fractional model is related to the constant Q with unbounded propagation speed. The Cole–Cole and fractional models belong to the class of singular memory models studied earlier because of their applications in polymer rheology, poroelasticity, poroacoustics, seismic wave propagation and other applications. Well-posedness of initial boundary value problems with mixed Dirichlet–Neumann boundary conditions is established for the three models. Regularity properties of the three models are examined.     

Differential calibration of seismometers for measurement of rotation and strain

A method of correcting the seismometers’ responses discrepancy for differential measurements of strains and rotations in the seismic far field is proposed. The method concerns differential calibration of the whole seismometers’ array by electric current. A model of corrective filtering of the obtained differential signals in the Z domain is given. Two methods of the filter parameters’ estimation are introduced; they are based on the seismometers response to the calibration. A practical test of the methods — an analysis of a recorded seismic event — is added. Significant reduction of differences between simultaneous seismic recordings was obtained, which is interpreted as cleaning of differential signal from spurious elements.     

New model simulations of the global atmospheric electric circuit driven by thunderstorms and electrified shower clouds: The roles of lightning and sprites

Several processes acting below, in and above thunderstorms and in electrified shower clouds drive upward currents which close through the global atmospheric electric circuit. These are all simulated in a novel way using the software package PSpice. A moderate negative cloud-to-ground lightning discharge from the base of a thunderstorm increases the ionospheric potential above the thundercloud by 0.0013%. Assuming the ionosphere to be an equipotential surface, this discharge increases the current flowing in the global circuit and the fair-weather electric field also by 0.0013%. A moderate positive cloud-to-ground lightning discharge from the bottom of a thunderstorm decreases the ionospheric potential by 0.014%. Such a discharge may trigger a sprite, causing the ionospheric potential to decrease by . The time scales for the recovery of the ionospheric potential are shown to be , which is of the same order as the CR time constant for the global circuit. Knowing the global average rate of lightning discharges, it is found that negative cloud-to-ground discharges increase the ionospheric potential by only 4%, and that positive cloud-to-ground discharges reduce it by 3%. Thus, overall, lightning contributes only 1%—an almost insignificant proportion—to maintaining the high potential of the ionosphere. It is concluded that the net upward current to the ionosphere due to lightning is only . Further, it is concluded that conduction and convection currents associated with “batteries” within thunderclouds and electrified shower clouds contribute essentially equally ( each) to maintaining the ionospheric potential.     

Features of the ionosphere behavior before the Kythira 2006 earthquake

In this paper we present specific features of TEC (total electron content of the ionosphere) behavior as possible precursors of Kythira (Southern Greece) earthquake of January 8, 2006 (M6.8). For this purpose, we used both the TEC data of GPS-IGS stations nearest to the epicenter, and TEC maps over Europe. The favorable circumstance for this analysis was the quiet geomagnetic situation during the period prior to the earthquake. One day before the earthquake, a characteristic anomaly was found out as the day-time significant increase of TEC at the nearest stations, up to the value of 50% relative to the background condition. To estimate the spatial dimensions of seismo-ionospheric anomaly, the differential mapping method was used. The ionosphere modification as a cloud-like increase of electron concentration situated in the immediate vicinity of the forthcoming earthquake epicenter has been revealed. The amplitude of modification reached the value of 50% relative to the non-disturbed condition and was in existence from 10:00 till 22:00 UT. The area of significant TEC enhancement had a size of about 4000 km in longitude and 1500 km in latitude.     

New Methods for Modeling Laterolog Resistivity Corrections

The paper presents methods for laterolog response modeling. In Coulomb’s charges method, Laplace’s equation is solved for the electric field distribution in rock medium with internal boundaries between different resistivity layers. There, the boundary problem is reduced to Fred-holm integral equation of the second kind. The second method uses a finite element array to model apparent resistivity from laterolog. The task is treated as DC problem and the Laplace equation is solved numerically. The presented methods were applied to borehole data covering a typical stratigraphie section of the Fore-Sudetic Monocline in southwestern Poland. Apparent resistivity was calculated using the Coulomb’s charges method and alternatively modeled using a finite element method which gave similar results. Then, a series of linear corrections for borehole, shoulder bed, and filtration effects for apparent resistivity obtained by the Coulomb’s charges method demonstrated the feasibility of calculating true resistivity of virgin and invaded zones. The proposed methods provide a flexible solution in modeling which can be adapted to other logs.