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.     

Surface-wave analysis for static corrections in mineral exploration: A case study from central Sweden

In mineral exploration, increased interest towards deeper mineralizations makes seismic methods attractive. One of the critical steps in seismic processing workflows is the static correction, which is applied to correct the effect of the shallow, highly heterogeneous subsurface layers, and improve the imaging of deeper targets. We showed an effective approach to estimate the statics, based on the analysis of surface waves (groundroll) contained in the seismic reflection data, and we applied it to a legacy seismic line acquired at the iron-oxide mining site of Ludvika in Sweden. We applied surface-wave methods that were originally developed for hydrocarbon exploration, modified as a step-by-step workflow to suit the different geologic context of hard-rock sites. The workflow starts with the detection of sharp lateral variations in the subsurface, the existence of which is common at hard-rock sites. Their location is subsequently used, to ensure that the dispersion curves extracted from the data are not affected by strong lateral variations of the subsurface properties. The dispersion curves are picked automatically, windowing the data and applying a wavefield transform. A pseudo-2D time-average S-wave velocity and time-average P-wave velocity profile are obtained directly from the dispersion curves, after inverting only a reference curve. The time-average P-wave velocity profile is then used for the direct estimation of the one-way traveltime, which provides the static corrections. The resulting P-wave statics from the field data were compared with statics computed through conventional P-wave tomography. Their difference was mostly negligible with more than 91% of the estimations being in agreement with the conventional statics, proving the effectiveness of the proposed workflow. The application of the statics obtained from surface waves provided a stacked section comparable with that obtained by applying tomostatics.     

Deep reflection seismic imaging of iron-oxide deposits in the Ludvika mining area of central Sweden

Reflection seismic data were acquired within two field campaigns in the Blötberget, Ludvika mining area of central Sweden, for deep imaging of iron-oxide mineralization that were known to extend down to 800–850 m depth. The two surveys conducted in years 2015 and 2016, one employing a seismic landstreamer and geophones connected to wireless recorders, and another one using cabled geophones and wireless recorders, aimed to delineate the geometry and depth extent of the iron-oxide mineralization for when mining commences in the area. Even with minimal and conventional processing approaches, the merged datasets provide encouraging information about the depth continuation of the mineralized horizons and the geological setting of the study area. Multiple sets of strong reflections represent a possible continuation of the known deposits that extend approximately 300 m further down-dip than the known 850 m depth obtained from historical drilling. They show excellent correlation in shape and strength with those of the Blötberget deposits. Furthermore, several reflections in the footwall of the known mineralization can potentially be additional resources underlying the known ones. The results from these seismic surveys are encouraging for mineral exploration purposes given the good quality of the final section and fast seismic surveys employing a simple cost-effective and easily available impact-type seismic source.     

Intensity measures for the seismic response evaluation of buried steel pipelines under near-field pulse-like ground motions

Ground-motion Intensity Measures (IMs) are used to quantify the strength of ground motions and evaluate the response of structures. IMs act as a link between seismic demand and seismic hazard analysis and therefore, have a key role in performance-based earthquake engineering. Many studies have been carried out on the determination of suitable IMs in terms of efficiency, sufficiency and scaling robustness. The majority of these investigations focused on ordinary structures such as buildings and bridges, and only a few were about buried pipelines. In the current study, the optimal IMs for predicting the seismic demand of continuous buried steel pipelines under near-field pulse-like ground motion records is investigated. Incremental dynamic analysis is performed using twenty ground motion records. Using the results of the regression analysis, the optimality of 23 potential IMs are studied. It is concluded that specific energy density (SED) followed by \(\sqrt {VSI[{\omega _1}(PGD + RM{S_d})]} \) are the optimal IMs based on efficiency, sufficiency and scaling robustness for seismic response evaluation of buried pipelines under near-field ground motions.

     

b-value and fractal dimension variations in Iran

Iran sits on a region with a high intrinsic level of seismic activity due to its tectonic setting. Through statistical examination of the earthquakes listed in the catalogue from International Institute of Earthquake Engineering and Seismology (IIEES), this research attempted to calculate some seismicity factors and find correlation between them. A preliminary analysis indicated changes in the b-value of the Gutenberg-Richter relationship over the study region. Thus, the study area was divided into five zones (Alborz, Zagros, Azerbaijan, Central and East) and b-value was computed for each zone. Considering faulting mechanism styles and the b-values in the region, it was found that the lowest b-values belong to the thrust events and strike-slip faulting earthquakes have intermediate values. These findings support previous studies. Furthermore, results of b-value calculation were used for the estimation of accumulated differential stresses (σ₁–σ₂) over each zone. Overall, the b-value for Iran is averagely low which signifies the high stress tectonic regime in this region. Also, by having calculated fractal dimension (D) in each zone, a correlation obtained showing that in Iran region, the b-value correlates to fractal dimension by D = 4.2b–2 relation which does not support Aki's (1981) speculation of D = 3b/c.     

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.     

Evaluation of Land Surface Scheme SABAE-HW in Simulating Snow Depth,Soil Temperature and Soil Moisture within the BOREAS Site,Saskatchewan

The Soil Atmosphere Boundary, Accurate Evaluation of Heat and Water (SABAE-HW) model is a multilayered, one-dimensional, physically based version of the Canadian Land Surface Scheme (CLASS) and uses the same methodologies as CLASS, version 2.6. SABAE provides an improved interface for groundwater modelling to simulate soil moisture, soil temperature, energy fluxes and snow depth for a wide range of soil and vegetation. This paper reports the results of the first field comparison of SABAE-HW using an extensive ten-year dataset from the Boreal Ecosystem Atmosphere Study (BOREAS) and the Boreal Ecosystem Research and Monitoring Sites (BERMS) project, an area in central Saskatchewan, Canada, rich in terms of hydrological and meteorological data. The model is also independently tested and verified with the Simultaneous Heat and Water (SHAW) model, which is an unsaturated-zone transport model. Two boundary conditions are considered at the bottom of the soil profile: a water table boundary condition and a unit gradient boundary condition. There was substantial agreement between the results of the simulations and observations in terms of snow depth and soil temperature. Snow depth and soil temperature were simulated reasonably well by SABAE, with correlation values of 0.96 and 0.98, respectively. However, there were some discrepancies for simulated soil temperature in winter. General agreement was obtained in terms of unfrozen soil moisture results, especially at greater depths, but there were general similarities in observed and simulated soil moisture trends in winter. An average correlation of 0.55 was found for SABAE while the correlation for SHAW was much smaller (less than 0.30), which indicates a better fit between simulated and field data by SABAE. Although a unit gradient boundary condition does not influence soil moisture, it was found that unit gradient boundary runs resulted in increased bias towards overestimation of the soil temperature. Thus, a safer and more accurate approach, we believe, is to adopt a first type boundary (i.e., water table) condition at the bottom of the domain. This has implications for climate and weather modelling in general. The result of this field testing demonstrated the potential and high accuracy of SABAE-HW as a Canadian model capable of simulating snow depth, snow temperature, soil moisture, energy fluxes, and we believe it is now appropriate to include this land surface scheme with its counterparts.

R ésumé ?[Traduit par la rédaction] Le modèle Soil Atmosphere Boundary, Accurate Evaluation of Heat and Water (SABAE-HW) est une version multicouche, à une dimension, basée sur la physique du schéma CLASS (Canadian Land Surface Scheme) qui utilise les mêmes méthodologies que le CLASS version 2.6. Le SABAE offre une interface améliorée pour la modélisation des eaux sous-terraines permettant de simuler l'humidité du sol, la température du sol, les flux d'énergie et l'épaisseur de la neige pour une grande variété de sols et de végétation. Cet article présente les résultats de la première comparaison terrain du SABAE-HW en utilisant une base de données étendue de dix ans de l'Étude de l'atmosphère et des écosystèmes boréaux (BOREAS) et du projet des Sites de recherche et de surveillance des écosystèmes boréaux (BERMS), une région du centre de la Saskatchewan, au Canada, riche en données hydrologiques et météorologiques. Le modèle est aussi indépendamment testé et vérifié à l'aide du Simultaneous Heat and Water (SHAW), un modèle de transport en zone non saturée. Deux conditions aux limites sont supposées au fond du profil du sol : une condition aux limites de nappe phréatique et une condition aux limites de gradient unitaire. On a trouvé une concordance importante entre les résultats des simulations et les observations en ce qui a trait à l'épaisseur de la neige et à la température du sol. L'épaisseur de la neige et la température du sol ont été raisonnablement bien simulées par le modèle SABAE, avec des corrélations de 0,96 et 0,98, respectivement. Cependant, il y avait certaines divergences pour la température simulée du sol en hiver. Pour ce qui est des résultats concernant l'humidité du sol non gelé, ils s'accordaient généralement, surtout pour les plus grandes profondeurs, mais il y avait des similarités générales dans les tendances observées et simulées de l'humidité du sol en hiver. Nous avons trouvé une corrélation moyenne de 0,55 pour le SABAE alors que la corrélation pour le SHAW était beaucoup plus faible (0,30), ce qui indique un meilleur ajustement des données simulées aux données de terrain pour le SABAE. Même si une condition aux limites de gradient unitaire n'influence pas l'humidité du sol, il ressort que des passes faites avec un gradient unitaire aux limites ont produit un biais accru vers la surestimation de la température du sol. Donc, nous croyons qu'une approche plus sûre et plus précise serait d'adopter une condition aux limites de Dirichlet (c.-à-d. une nappe phréatique) au fond du domaine. Ceci a des répercussions sur la modélisation du climat et du temps en général. Le résultat de cet essai sur le terrain a démontré le potentiel et la grande exactitude du SABAE-HW en tant que modèle canadien capable de simuler l'épaisseur de la neige, la température du sol, l'humidité du sol et les flux d'énergie et nous croyons qu'il est maintenant approprié d'inclure ce schéma de surface avec ses contreparties.