Multiple-point statistics using multi-resolution images

Stochastic Environmental Research and Risk Assessment - Multiple-point statistics (MPS) is a simulation technique allowing to generate images that reproduce the spatial features present in a...     

Fast and Interactive Editing Tools for Spatial Models

Mathematical Geosciences - Multiple point statistics (MPS) algorithms allow generation of random fields reproducing the spatial features of a training image (TI). Although many MPS techniques offer...     

Pc3–4 ULF waves at polar latitudes

A search for Pc3–4 wave activity was performed using data from a trans-Antarctic profile of search-coil magnetometers extending from the auroral zone through cusp latitudes and deep into the polar cap. Pc3–4 pulsations were found to be a ubiquitous element of ULF wave activity in all these regions. The diurnal variations of Pc3 and Pc4 pulsations at different latitudes have been statistically examined using discrimination between wave packets (pulsations) and noise. Daily variations of the Pc3–4 wave power differ for the stations at the polar cap, cusp, and auroral latitudes, which suggests the occurrence of several channels of propagation of upstream wave energy to the ground: via the equatorial magnetosphere, cusp, and lobe/mantle. An additional maximum of Pc3 pulsations during early-morning hours in the polar cap has been detected. This maximum, possibly, is due to the proximity of the geomagnetic field lines at these hours to the exterior cusp. The statistical relation between the occurrence of Pc3–4 pulsations and interplanetary parameters has been examined by analyzing normalized distributions of wave occurrence probability. The dependences of the occurrence probability of Pc3–4 pulsations on the IMF and solar wind parameters are nearly the same at all latitudes, but remarkably different for the Pc3 and Pc4 bands. We conclude that the mechanisms of high-latitude Pc3 and Pc4 pulsations are different: Pc3 waves are generated in the foreshock upstream of the quasi-parallel bow shock, whereas the source of the Pc4 activity is related to magnetospheric activity. Hourly Pc3 power has been found to be strongly dependent on the season: the power ratio between the polar summer and winter seasons is 8. The effect of substantial suppression of the Pc3 amplitudes during the polar night is reasonably well explained by the features of Alfven wave transmission through the ionosphere. Spectral analysis of the daily energy of Pc3 and Pc4 pulsations in the polar cap revealed the occurrence of several periodicities. Periodic modulations with periods 26, 13 and 8–9 days are caused by similar periodicities in the solar wind and IMF parameters, whereas the 18-day periodicity, observed during the polar winter only, is caused, probably, by modulation of the ionospheric conductance by atmospheric planetary waves. The occurrence of the narrow-band Pc3 waves in the polar cap is a challenge to modelers, because so far no band-pass filtering mechanism on open field lines has been identified.     

Statistical relations between the probability of occurrence of Pc3-4 pulsations at high latitudes in the antarctic regions and the solar wind and IMF parameters

Geomagnetic pulsation in the Pc3-4 bands have been studied at high Antarctic latitudes during the local summer. The statistical relation between the occurrence probability of Pc3 and Pc4 pulsations and the solar wind (SW) and IMF parameters has been revealed by verifying the hypothesis that an indication is identical in two distributions. Different dependences of the occurrence probability of high-latitude Pc3 and Pc4 pulsations on the IMF value and orientation and SW density and velocity have been found out. It has been indicated that these dependences remain unchanged in the range of geomagnetic latitudes from 66° to 87°. It has been established that the Pc3 observation probability at small (20°–50°) IMF cone angles (θ = cos^?1(B _x/|B|)) is a factor of 1.5 higher than the average statistical probability and depends on the IMF value, which confirms the hypothesis that the Pc3 source is the turbulent region upstream of the magnetospheric quasiparallel low shock. On the contrary, the probability of occurrence of Pc4 weakly depends on the IMF cone angle and is maximal at θ ～ 0° and ～90°. With increasing negative B _z values, the generation probability increases in the Pc4 band and tends to decrease in the Pc3 band. It has been found out for the first time that the dependence of the Pc4 occurrence probability on the IMF clock angle (? = tan^?2 (B/B _z) is identical in the regions of projections of closed and open field lines, whereas this dependence is different for Pc3. In the region of projections of closed field lines, the Pc3 occurrence probability increases at B _z < 0 and B _y > 0 (the condition under which the cusp shifts on the dawn side) and at B _y < 0 and B _z > 0 (which is typical of the formation of the low-latitude boundary plasma sheet). In the region of projections of open field lines such a probability increases at B _y < 0 and B _z < 0 (which results in the formation of the high-latitude boundary plasma sheet). Based on the discovered regularities, the conclusion has been made that the sources of generation of high-latitude Pc3 and Pc4 pulsations are different.     

The development of the urban settlement system in Belgorod oblast

We have investigated the urbanization processes in the region. The study revealed the characteristics of evolution of urban systems and of the urbanization development stages as well as ascertaining the current formation tendencies for large cities and their suburban zones.     

Statistical characteristics of the spatial distribution of Pc3-4 geomagnetic pulsations at high latitudes in the antarctic regions

The diumal variations in the parameters of Pc3 (20–60 mHz) and Pc4 (10–19 mHz) pulsations at latitudes of the dayside cusp and polar cap have been studied using data of the magnetic stations of the trans-Antarctic meridional profile for the time interval from January to March 1997 (local summer) under weakly disturbed geomagnetic conditions (AE ≤ 250 nT). The technique for estimating pulsation parameters is based on the separation of the wave packets and noise. The diumal variations in the hourly average parameters of the wave packets in the Pc3 and Pc4 bands and noise in the Pc3-4 band (10–60 mHz)—the average number of wave packets, energy of wave packets and noise, and energy of a single wave packet—turned out to be different for the stations located deep in the polar cap (Φ ～ 87°) and at the latitudes of the dayside polar cusp (Φ ～ 70°) and auroral oval (Φ ～ 66°). Several sources of pulsations caused by different channels of wave energy penetration into the magnetosphere through the dayside cusp, dayside magnetopause, and dawn flank of the magnetotail apparently exist at high latitudes.     

Multiple-Point Simulations Constrained by Continuous Auxiliary Data

An important issue of using the multiple-point (MP) statistical approach for reservoir modeling concerns the integration of auxiliary constraints derived, for instance, from seismic information. There exist two methods in the literature for these non-stationary MP simulations. One is based on an analytical approximation (the “τ-model”) of the conditional probabilities that involve auxiliary data. The degree of approximation with this method depends on the parameter τ, whose inference is difficult in practice. The other method is based on the inference of these conditional probabilities directly from training images. This method classifies the auxiliary data into a few classes. This classification is in general arbitrary and therefore inconvenient in practice, especially in the case of continuous auxiliary constraints. In this paper, we propose an alternative method for performing non-stationary MP simulations. This method accounts for the data support in the modeling procedure and allows, in particular, continuous auxiliary data to be integrated into MP simulations. This method avoids the major limitations of the previous methods, namely the use of an approximate analytical model and the reduction of the auxiliary data into a limited number of classes. This method can be easily implemented in the existing MP simulation codes. Numerical tests show good performance of this method both in reproducing the geometrical features of the training image and in honouring the auxiliary data.     

Explicit Fracture Network Modelling: From Multiple Point Statistics to Dynamic Simulation

This paper addresses the problem of explicit fractured media modelling in an operational case. On one side, realistic fracture models are mainly used for research purposes in order to investigate better the flow behaviour impacted by the complex multi-scale fracture network. Often, a very fine grid and hence an increased computation time are needed. On the other hand, an operational fractured reservoir is still generally modelled using an implicit fracture media representation. The upscaled petrophysical properties and dual media are defined on a coarse grid to limit the computational time of dynamic simulation. The challenge of this work is to demonstrate that an explicit fracture modelling is not reserved only for the research domain, but can be applied to an operational case study. The static model is constructed using a multiple point statistics approach in order to represent complex interaction patterns of fractures and faults observed at the analogue outcrop. The dynamic behaviour is simulated based on this spatial fracture network representation.     

Periodic modulation of Pc3 and Pc4 pulsations in the polar cap by interplanetary and atmospheric processes

The variations in the daily average energy of geomagnetic pulsations and noise in the Pc3 (20–60 mHz) and Pc4 (10–19 mHz) frequency bands in the polar cap have been studied based on the data from P5 Antarctic station (corrected geomagnetic latitude ?87°) from November 1998 to November 1999. The daily average pulsation energy has been calculated using the method for detecting the wave packets, the spectral amplitude of which is higher than the threshold level, from the dynamic spectrum. A spectral analysis of the energy of pulsations and noise in the Pc3 and Pc4 bands, performed using the maximal entropy method, has revealed periodicities of 18 days in the local winter and 26, 13, and 7–9 days during the local summer. The simultaneous and coherent variations with periods of 26, 13, and 7–9 days in the solar wind velocity and IMF orientation indicate that the variations in the Pc3–4 wave energy in the polar cap at a sunlit ionosphere are mainly controlled by the parameters of the interplanetary medium. The variations in the Pc3–4 wave energy with a period of 18 days are observed only during the local winter and are supposedly related to the variations in the ionospheric conductivity modulated by planetary waves.