Orbit uncertainty propagation and sensitivity analysis with separated representations

Most approximations for stochastic differential equations with high-dimensional, non-Gaussian inputs suffer from a rapid (e.g., exponential) increase of computational cost, an issue known as the curse of dimensionality. In astrodynamics, this results in reduced accuracy when propagating an orbit-state probability density function. This paper considers the application of separated representations for orbit uncertainty propagation, where future states are expanded into a sum of products of univariate functions of initial states and other uncertain parameters. An accurate generation of separated representation requires a number of state samples that is linear in the dimension of input uncertainties. The computation cost of a separated representation scales linearly with respect to the sample count, thereby improving tractability when compared to methods that suffer from the curse of dimensionality. In addition to detailed discussions on their construction and use in sensitivity analysis, this paper presents results for three test cases of an Earth orbiting satellite. The first two cases demonstrate that approximation via separated representations produces a tractable solution for propagating the Cartesian orbit-state uncertainty with up to 20 uncertain inputs. The third case, which instead uses Equinoctial elements, reexamines a scenario presented in the literature and employs the proposed method for sensitivity analysis to more thoroughly characterize the relative effects of uncertain inputs on the propagated state.     

Copper isotope fractionation in the Meiduk porphyry copper deposit,Northwest of Kerman Cenozoic magmatic arc,Iran

The Meiduk deposit possesses three different Cu reservoirs each with a unique Cu isotope signature. δ⁶⁵Cu for the leached cap minerals ranges from ?2.5 to +0.49‰ to ?0.45 to +0.3‰ for hypogene minerals and from +1.3 to +4.4‰ for supergene enrichment minerals. Oxidation of hypogene sulphides and effective trapping of copper (from solutions derived from the leached cap) in the supergene enrichment zone caused this relationship. A systematic pattern of low Cu isotope values close to the surface and higher isotope values with depth reveals a palaeo‐fluid pathway in the northwest–southeast direction over the deposit. Thus, the copper isotope data from leached cap and enrichment minerals can be used to monitor copper migration during supergene weathering at the Meiduk deposit.     

Monitoring and projection of climate change impact on 24-h probable maximum precipitation in the Southeast of Caspian Sea

Natural Hazards - Due to the impacts of climate change on probable maximum precipitation (PMP) and its importance in designing hydraulic structures, PMP estimation is crucial. In this study, the...     

Compounding effects of human activities and climatic changes on surface water availability in Iran

Climatic Change - By combining long-term ground-based data on water withdrawal with climate model projections, this study quantifies the compounding effects of human activities and climate change...     

Cost–benefit analyses to assess the potential of Operational Earthquake Forecasting prior to a mainshock in Europe

In the past couple of decades, Operational Earthquake Forecasting (OEF) has been proposed as a way of mitigating earthquake risk. In particular, it has the potential to reduce human losses (injuries and deaths) by triggering actions such as reinforcing earthquake drills and preventing access to vulnerable structures during a period of increased seismic hazard. Despite the dramatic increases in seismic hazard in the immediate period before a mainshock (of up to 1000 times has been observed), the probability of a potentially damaging earthquake occurring in the coming days or weeks remains small (generally less than 5%). Therefore, it is necessary to balance the definite cost of taking an action against the uncertain chance that it will mitigate earthquake losses. In this article, parametric cost–benefit analyses using a recent seismic hazard model for Europe and a wide range of inputs are conducted to assess when potential actions for short-term OEF are cost–beneficial prior to a severe mainshock. Ninety-six maps for various combinations of input parameters are presented. These maps show that low-cost actions (costing less than 1% of the mitigated losses) are cost–beneficial within the context of OEF for areas of moderate to high seismicity in the Mediterranean region. The actions triggered by OEF in northern areas of the continent are, however, unlikely to be cost–beneficial unless very large increases in seismicity are observed or very low-cost actions are possible.

     

Seismic imaging and potential field modelling to delineate structures hosting VHMS deposits in the Skellefte Ore District, northern Sweden

The Skellefte District in northern Sweden is a roughly 150 by 50 km² large early Proterozoic massive sulphide belt. Based on high-resolution reflection seismic data along two parallel seismic profiles, potential field modeling has been carried out and two geologic cross sections have been constructed that are consistent with the available geophysical data as well as surface geologic observations. The combined modelling suggests that the Kristineberg deposit occurs on the northern limb of a regional E–W striking syncline. The interpretations help to identify new prospective areas, both down-plunge from known ores, and on the ore-bearing horizon on the southern limb of the syncline. The new results suggest that the post-orogenic Revsund granites can be divided into two major types of intrusives, those which are intruded as domes/stokes with a maximum present day thickness of about 3–3.5 km and those which are intruded as thin sheets, with a maximum thickness of a few hundred meters. The margins of the intrusions are generally inclined inwards, suggesting that the current erosion level is near the middle, or toward the base, of the granites. The contact between the Skellefte volcanic rocks and the Bothnian Basin has been interpreted as a thrust fault. We also suggest that crustal thickening predates the Skellefte volcanism and that the interpreted Bothnian Basin rocks are either a structural basement or a separate terrane to the Skellefte volcanism. Diffraction patterns in the reflection seismic data can be interpreted as originating from either a mafic–ultramafic intrusion or a mineralization zone, similar to observations elsewhere in the world. The results obtained in this study have greatly improved our understanding of the tectonostratigraphic framework and architecture of the poly-deformed c. 1.9 Ga Skellefte VHMS belt and is a key step towards building a 3D geological model in the area.     

Dynamic Positioning System Design for A Marine Vessel with Unknown Dynamics Subject to External Disturbances Including Wave Effect

China Ocean Engineering - In this paper, a new control system is proposed for dynamic positioning (DP) of marine vessels with unknown dynamics and subject to external disturbances. The control...     

A multiple-point statistics algorithm for 3D pore space reconstruction from 2D images

Fluid flow behavior in a porous medium is a function of the geometry and topology of its pore space. The construction of a three dimensional pore space model of a porous medium is therefore an important first step in characterizing the medium and predicting its flow properties. A stochastic technique for reconstruction of the 3D pore structure of unstructured random porous media from a 2D thin section training image is presented. The proposed technique relies on successive 2D multiple point statistics simulations coupled to a multi-scale conditioning data extraction procedure. The Single Normal Equation Simulation Algorithm (SNESIM), originally developed as a tool for reproduction of long-range, curvilinear features of geological structures, serves as the simulation engine. Various validating criteria such as marginal distributions of pore and grain, directional variograms, multiple-point connectivity curves, single phase effective permeability and two phase relative permeability calculations are used to analyze the results. The method is tested on a sample of Berea sandstone for which a 3D micro-CT scanning image is available. The results confirm that the equi-probable 3D realizations obtained preserve the typical patterns of the pore space that exist in thin sections, reproduce the long-range connectivities, capture the characteristics of anisotropy in both horizontal and vertical directions and have single and two phase flow characteristics consistent with those of the measured 3D micro-CT image.