Seismic Tomography by Monte Carlo Sampling

The paper discusses the performance and robustness of the Bayesian (probabilistic) approach to seismic tomography enhanced by the numerical Monte Carlo sampling technique. The approach is compared with two other popular techniques, namely the damped least-squares (LSQR) method and the general optimization approach. The theoretical considerations are illustrated by an analysis of seismic data from the Rudna (Poland) copper mine. Contrary to the LSQR and optimization techniques the Bayesian approach allows for construction of not only the “best-fitting” model of the sought velocity distribution but also other estimators, for example the average model which is often expected to be a more robust estimator than the maximum likelihood solution. We demonstrate that using the Markov Chain Monte Carlo sampling technique within the Bayesian approach opens up the possibility of analyzing tomography imaging uncertainties with minimal additional computational effort compared to the robust optimization approach. On the basis of the considered example it is concluded that the Monte Carlo based Bayesian approach offers new possibilities of robust and reliable tomography imaging.     

Advantages and limitations of an α-plasticity model for sand

Acta Geotechnica - The stress–strain response of sand was observed to depend on its material state, i.e., pressure and density. Successful modelling of such state-dependent response of sand...     

Generation and propagation of transient nonlinear waves in a wave flume

A semi-analytical nonlinear wavemaker model is derived to predict the generation and propagation of transient nonlinear waves in a wave flume. The solution is very efficient and is achieved by applying eigenfunction expansions and FFT. The model is applied to study the effect of the wavemaker and its motion on the generation and propagation of nonlinear waves. The results indicate that the linear wavemaker theory may be applied to predict only the generation of waves of low steepness for which the nonlinear terms in the kinematic wavemaker boundary condition and free-surface boundary conditions are of secondary importance. For waves of moderate steepness and steep waves these nonlinear terms have substantial effects on wave profile and wave spectrum just after the wavemaker. A wave spectrum corresponding to a sinusoidally moving wavemaker possesses a multi-peak form with substantial nonlinear components, which disturbs or may even exclude physical modeling in wave flumes. The analysis shows that the widely recognized weakly nonlinear wavemaker theory may only be applied to describe the generation and propagation of waves of low steepness. This is subject to further restrictions in shallow and deep waters because the kinematic wavemaker boundary condition as well as the nonlinear interaction of wave components and the evolution of wave energy spectrum is not properly described by weakly nonlinear wavemaker theory. Laboratory experiments were conducted in a wave flume to verify the nonlinear wavemaker model. The comparisons show a reasonable agreement between predicted and measured free-surface elevation and the corresponding amplitudes of Fourier series. A reasonable agreement between theoretical results and experimental data is observed even for fairly steep waves.     

Distribution of compact object mergers around galaxies

Compact object mergers are one of the currently favoured models for the origin of gamma-ray bursts (GRBs). The discovery of optical afterglows and identification of the nearest, presumably host, galaxies allow the analysis of the distribution of burst sites with respect to these galaxies. Using a model of stellar binary evolution we synthesize a population of compact binary systems which merge within the Hubble time. We include the kicks in the supernovae explosions and calculate orbits of these binaries in galactic gravitational potentials. We present the resulting distribution of merger sites and discuss the results in the framework of the observed GRB afterglows.     

Anisotropic Kepler and anisotropic two fixed centres problems

In this paper we show that the anisotropic Kepler problem is dynamically equivalent to a system of two point masses which move in perpendicular lines (or planes) and interact according to Newton’s law of universal gravitation. Moreover, we prove that generalised version of anisotropic Kepler problem as well as anisotropic two centres problem are non-integrable. This was achieved thanks to investigation of differential Galois groups of variational equations along certain particular solutions. Properties of these groups yield very strong necessary integrability conditions.     

Non‐normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study

In this paper, an implementation of fractional plastic flow rule in the framework of implicit and explicit procedures is under consideration. The fractional plastic flow rule is obtained from a generalisation of the classical plastic flow rule utilising fractional calculus. The key feature of this new concept is that in general, the non‐associative flow is obtained without necessity of additional potential assumption. If needed, the model can cover the anisotropy induced by plastic deformation. Illustrative examples showing the unusual flexibility of this model are also presented. Copyright © 2015 John Wiley & Sons, Ltd.     

A Model to Simulate Pumping Tests in Wells with High Loss and Backflow

Traditional methods of analyzing pumping tests in single wells fail when the well loss is very high due to a low transmissivity skin. Because of the restricted rate at which water can enter a high loss well from the aquifer, well casing storage becomes a significant factor. Additionally, if a slug of water enters the well from the pump column immediately after the pump is switched off, it has a long‐lasting significant effect on the recovering water level in the well because it cannot be absorbed rapidly by the aquifer. A theoretical model is derived here that simulates the water level in a well in these circumstances. In the model, the continuously changing rate of water inflow from the aquifer to the well is approximated by a step function with a finite difference time step. It is demonstrated by a real example that the model can be applied easily to analyze pumping tests, including tests with a varying pumping rate. The analysis confirms suspected high well loss, calculates the unknown rate of backflow, and determines the aquifer's transmissivity.     

Sedimentary anatomy and hydrological record of relic fluvial deposits in a karst cave conduit

This case study from the renowned Demänová Cave System in the Carpathians of Slovakia demonstrates that the conventional methods of fluvial sedimentology, combined with an allostratigraphic mapping and speleothem U‐series isotopic dating, can give unprecedented insights into the hydrological history of underground karst conduit. The deposits studied are a relic compound sidebar ranging from gravel to mud and encapsulating the conduit’s hydrological history from the middle Pleistocene to the present time. A succession of 10 allostratigraphic units, time‐constrained by speleothems, are recognized in the sidebar deposits, and the corresponding morphodynamics of an evolving cave‐floor sedimentation are reconstructed in considerable detail. The subterranean river water stages recognized from the deposits, time‐constrained by flowstone layers and stalagmites, correlate with and add to the regional record of climate changes. Two distinct episodes of flow ponding (high‐stage slackwater conditions) are recognized and attributed to the independently documented downstream cave‐roof collapses, probably triggered by the Carpathian post‐orogenic earthquakes. This multidisciplinary study may serve as a useful methodological guide for the analysis of fluviokarstic deposits in speleological research and reconstruction of their hosting cave hydrological history.     

Modelling of hydrogeochemical potential of three lake catchments in Polesie region (Eastern Poland)

Total dissolved solids (TDS) in lake and catchment water is a result of geological structure, as well as duration of rock and water contact and human activity. In this paper, a potential dissolved solids (PtDS) in three ??czna–W?odawa Lake catchments was determined using extraction and computer software (GIS and AquaChem). Human pressure on water quality was estimated as a difference of the TDS and a catchment hydrogeochemical potential (TPtDS, total potential dissolved solids). TPtDS coefficient included hydrogeological features of the aquifer, soil cover impact on infiltrated water quality, and sediments susceptibility to denudation. The main advantage of the model is a possibility of its employment for every catchment or other areas (e.g. administrative) on both microscale and mesoscale. The highest TPtDS occurred in the catchment, favoured with underground supply, which was located in the vicinity of the Cretaceous mesoregional unit (Che?m Hills). The lowest value was observed in the catchment built with organogenic sediments and coarse material. A seasonal constancy of TPtDS values proved a stability of the lake‐catchment systems under study. Copyright © 2012 John Wiley & Sons, Ltd.