Seismic velocity estimation from post-critical wide-angle reflections in layered structures

The travel time inversion of wide-angle seismic data is a technique commonly used in the deep seismic sounding. We propose an application of this technique to a smaller scale of a sedimentary layer, where the characteristics of seismic observations changes significantly. Field observations confirmed by synthetic analysis recognize the dominant amplitudes of wide-angle post-critical reflections. A case study is presented in this paper, of a joint interpretation of conventional reflection seismic with reflection imaging, combined with the wide-angle travel time inversion of additional full-spread observations. A joint interpretation results in a precise recognition of the seismic velocity distribution, that is further used for the seismic depth conversion with the uncertainty analysis of the depth of the reflecting horizons. Despite the salt layer in the studied structure this method is able to precisely recognize the seismic velocities of the sub-salt structures.     

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.     

On accuracy of prediction of pre-failure deformations of granular soils

The problem of accuracy of predictions of pre-failure deformations of granular soils is considered. Firstly, the deterministic incremental equations describing qualitative character of such deformations are presented. These equations are based on extensive experimental data, obtained from the tri-axial compression tests. The parameters appearing in the incremental equations are assumed as random numbers, characterized by their mean values and standard deviations. The normal probability distribution is assumed. Then, such a model is applied to predict strains caused by some simple deterministic stress paths. The incremental equations are integrated for a large number of random coefficients, generated by a computer program. The final results are presented as either paths or points in the strain space, and respective density of probability distribution is calculated. The proposed method and results obtained show, that in mechanics of granular media we cannot expect “a good agreement” between predictions of theoretical models and experimental results, but only a kind of agreement measured by probability. The results presented should be important for both theoretical modellers and experimentalists.     

Shallow-generated damage within non-planar strike-slip fault zones: role of sedimentary rocks in slip accommodation,SW Holy Cross Mountains,Poland

International Journal of Earth Sciences - We investigated exhumed damage zones of dextral strike-slip faults dissecting the south-western part of the Mesozoic cover of the Late Palaeozoic Holy...     

Arbitrary order numerical solutions conserving the Jacobi constant in the motion near the equilibrium points

In the paper a modification of the polynomial extrapolation for solving the problem of motion nearby the equilibrium points is presented. It appears that the modification yields a better approximation of the exact solution than the convential polynomial extrapolation and other methods. Moreover, the modification conserves the Jacobi constant of motion. Computer examples for orbits nearby the equilibrium points of the Sun-Jupiter system are given.     

Diffraction by plane sectors and polygons

Time-domain theory of edge and edge-and-vertex diffraction is briefly reviewed and its applications to diffraction by polygons, pyramids and curved reflectors are discussed. The time-domain theory is based on canonical functions defined in terms of inverse trigonometric and algebraic functions, which ensures its numerical efficiency.     

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.     

An estimate of probabilistic seismic hazard for five cities in Greece by using the parametric-historic procedure

A probabilistic procedure was applied to assess seismic hazard for the sites of five Greek cities (Athens, Heraklion, Patras, Thessaloniki and Volos) using peak ground acceleration as the hazard parameter. The methodology allows the use of either historical or instrumental data, or a combination of both. It has been developed specifically for the estimation of seismic hazard at a given site and does not require any specification of seismic sources or/and seismic zones. A new relation for the attenuation of peak ground acceleration was employed for the shallow seismicity in Greece. The computations involved the area- and site-specific parts. When assessing magnitude recurrence for the areas surrounding the five cities, the maximum magnitude, m_max, was estimated using a recently derived equation. The site-specific results were expressed as probabilities that a given peak ground acceleration value will be exceeded at least once during a time interval of 1, 50 and 100 years at the sites of the cities. They were based on the maximum peak ground acceleration values computed by assuming the occurrence of the strongest possible earthquake (of magnitude m_max) at a very short distance from the site and using the mean value obtained with the help of the attenuation law. This gave 0.24 g for Athens, 0.53 g for Heraklion (shallow) and 0.39 g Heraklion (intermediate-depth seismicity), 0.30 g for Patras, 0.35 g for Thessaloniki and 0.30 g for Volos. In addition, the probabilities of exceedance of the estimated maximum peak ground acceleration values were calculated for the sites. The standard deviation of the new Greek attenuation law demonstrates the uncertainty and large variation of predicted peak ground acceleration values.     

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.     

Estimation of earthquake hazard parameters for incomplete and uncertain data files

The maximum likelihood estimation of earthquake hazard parameters (maximum regional magnitudem _max, activity rate λ, and theb parameter in the Gutenberg-Richter distribution) is extended to the cases of incomplete and uncertain data. The method accepts mixed data containing only large (extreme) events and a variable quality of complete data with different threshold magnitude values. Uncertainty of earthquake magnitude is specified by two values, the lower and upper magnitude limits. It is assumed that such an interval contains the real unknown magnitude. The proposed approach allows the combination of different quality catalog parts, e.g. those where the assignment of magnitude is questionable and those with magnitudes precisely determined. As an illustration of the method, the seismic hazard analysis for western Norway and adjacent sea area (4–8°E, 58–64°N) is presented on the basis of the strongest earthquakes felt during the period 1831–1889 and three complete catalog parts, covering the period 1890–1987.