Large-scale stochastic linear inversion using hierarchical matrices

Stochastic inverse modeling deals with the estimation of functions from sparse data, which is a problem with a nonunique solution, with the objective to evaluate best estimates, measures of uncertainty, and sets of solutions that are consistent with the data. As finer resolutions become desirable, the computational requirements increase dramatically when using conventional solvers. A method is developed in this paper to solve large-scale stochastic linear inverse problems, based on the hierarchical matrix (or ? ² matrix) approach. The proposed approach can also exploit the sparsity of the underlying measurement operator, which relates observations to unknowns. Conventional direct algorithms for solving large-scale linear inverse problems, using stochastic linear inversion techniques, typically scale as ??(n ² m+nm ²), where n is the number of measurements and m is the number of unknowns. We typically have n ? m. In contrast, the algorithm presented here scales as ??(n ² m), i.e., it scales linearly with the larger problem dimension m. The algorithm also allows quantification of uncertainty in the solution at a computational cost that also grows only linearly in the number of unknowns. The speedup gained is significant since the number of unknowns m is often large. The effectiveness of the algorithm is demonstrated by solving a realistic crosswell tomography problem by formulating it as a stochastic linear inverse problem. In the case of the crosswell tomography problem, the sparsity of the measurement operator allows us to further reduce the cost of our proposed algorithm from ??(n ² m) to $\mathcal {O}(n^{2} \sqrt {m} + nm)$ . The computational speedup gained by using the new algorithm makes it easier, among other things, to optimize the location of sources and receivers, by minimizing the mean square error of the estimation. Without this fast algorithm, this optimization would be computationally impractical using conventional methods.     

The causes of land-use and land-cover change: moving beyond the myths

Common understanding of the causes of land-use and land-cover change is dominated by simplifications which, in turn, underlie many environment-development policies. This article tracks some of the major myths on driving forces of land-cover change and proposes alternative pathways of change that are better supported by case study evidence. Cases reviewed support the conclusion that neither population nor poverty alone constitute the sole and major underlying causes of land-cover change worldwide. Rather, peoples’ responses to economic opportunities, as mediated by institutional factors, drive land-cover changes. Opportunities and constraints for new land uses are created by local as well as national markets and policies. Global forces become the main determinants of land-use change, as they amplify or attenuate local factors.     

Differentiation of planetesimals and the thermal consequences of melt migration

Abstract– We model the heating of a primordial planetesimal by decay of the short‐lived radionuclides ²⁶Al and ⁶⁰Fe to determine (1) the time scale on which melting will occur, (2) the minimum size of a body that will produce silicate melt and differentiate, (3) the migration rate of molten material within the interior, and (4) the thermal consequences of the transport of ²⁶Al in partial melt. Our models incorporate results from previous studies of planetary differentiation and are constrained by petrologic (i.e., grain‐size distributions), isotopic (e.g., ²⁰⁷Pb‐²⁰⁶Pb and ¹⁸²Hf‐¹⁸²W ages), and mineralogical properties of differentiated achondrites. We show that formation of a basaltic crust via melt percolation was limited by the formation time of the body, matrix grain size, and viscosity of the melt. We show that low viscosity (<1 Pa · s) silicate melt can buoyantly migrate on a time scale comparable to the mean life of ²⁶Al. The equilibrium partitioning of Al into silicate partial melt and the migration of that melt acts to dampen internal temperatures. However, subsequent heating from the decay of ⁶⁰Fe generated melt fractions in excess of 50%, thus completing differentiation for bodies that accreted within 2 Myr of CAI formation (i.e., the onset of isotopic decay). Migration and concentration of ²⁶Al into a crust results in remelting of that crust for accretion times less than 2 Myr and for bodies >100 km in size. Differentiation would be most likely for planetesimals larger than 20 km in diameter that accreted within approximately 2.7 Myr of CAI formation.     

Aqueous alteration of kamacite in CM chondrites

Abstract– The study of aqueous alteration of kamacite in CM chondrites provides insight on the conditions, products, and relative timing of aqueous alteration. We studied unaltered, partially altered, and fully altered kamacite grains from Murray, Murchison, Cold Bokkeveld, and Nogoya using optical microscopy, electron microprobe analysis, scanning electron microscopy, and Raman spectroscopy. From textual evidence and chemical analysis, we established three separate microchemical environments. 1) In a microchemical environment with a high S activity, kamacite alters to form tochilinite, P‐bearing sulfides, eskolaite, and schreibersite. Mass balance calculations show that 81% of the Fe in kamacite is removed from the alteration region, making it available for the formation of other minerals or Fe‐rich aureoles. The release of Fe can alter the mesostasis of type‐I chondrules forming cronstedtite. 2) In a microchemical environment with a high Si activity and a low S activity, kamacite alters to form cronstedtite with small accessory sulfide inclusions. 3) A microchemical environment with limited S and Si activity results in kamacite alteration forming magnetite. The resulting magnetite retains associated Ni that can distinguish it from precipitated magnetite. In addition, the accessory phases of pentlandite and apatite can be formed if S or Ca are present. Finally, we note that small tochilinite grains in the matrix lack typical Ni, P, and Co levels, suggesting that they did not form from kamacite but possibly by sulfidization of magnetite.     

Mass Flux Analysis of Abiotic Tetrachloroethene Dense Nonaqueous Phase Liquid Pool Dissolution in a Heterogeneous Flow Environment

Porous aquifer materials are often characterized by layered heterogeneities that influence groundwater flow and present complexities in contaminant transport modeling. Such flow variations also have the potential to impact the dissolution flux from dense nonaqueous phase liquid (DNAPL) pools. This study examined how these heterogeneous flow conditions affected the dissolution of a tetrachloroethene (PCE) pool in a two-dimensional intermediate-scale flow cell containing coarse sand. A steady-state mass-balance approach was used to calculate the PCE dissolution rate at three different flow rates. As expected, aqueous PCE concentrations increased along the length of the PCE pool and higher flow rates decreased the aqueous PCE concentration in the effluent. Nonreactive tracer studies at two flow rates confirmed the presence of a vertical flow gradient, with the most rapid velocity located at the bottom of the tank. These results suggest that flow focusing occurred near the DNAPL pool. Effluent PCE concentrations and pool dissolution flux rates were compared to model predictions assuming local equilibrium (LE) conditions at the DNAPL pool/aqueous phase interface and a uniform distribution of flow. The LE model did not describe the data well, even over a wide range of PCE solubility and macroscopic transverse dispersivity values. Model predictions assuming nonequilibrium mass-transfer-limited conditions and accounting for vertical flow gradients, however, resulted in a better fit to the data. These results have important implications for evaluating DNAPL pool dissolution in the field where subsurface heterogeneities are likely to be present.     

SPICES: spectro-polarimetric imaging and characterization of exoplanetary systems

SPICES (Spectro-Polarimetric Imaging and Characterization of Exoplanetary Systems) is a five-year M-class mission proposed to ESA Cosmic Vision. Its purpose is to image and characterize long-period extrasolar planets and circumstellar disks in the visible (450?C900 nm) at a spectral resolution of about 40 using both spectroscopy and polarimetry. By 2020/2022, present and near-term instruments will have found several tens of planets that SPICES will be able to observe and study in detail. Equipped with a 1.5 m telescope, SPICES can preferentially access exoplanets located at several AUs (0.5?C10?AU) from nearby stars (<25 pc) with masses ranging from a few Jupiter masses to Super Earths (??2 Earth radii, ??10 M_??) as well as circumstellar disks as faint as a few times the zodiacal light in the Solar System.     

The 2010 European Venus Explorer (EVE) mission proposal

The European Venus Explorer (EVE) mission described in this paper was proposed in December 2010 to ESA as an ‘M-class’ mission under the Cosmic Vision programme. It consists of a single balloon platform floating in the middle of the main convective cloud layer of Venus at an altitude of 55?km, where temperatures and pressures are benign (～25°C and ～0.5 bar). The balloon float lifetime would be at least 10 Earth days, long enough to guarantee at least one full circumnavigation of the planet. This offers an ideal platform for the two main science goals of the mission: study of the current climate through detailed characterization of cloud-level atmosphere, and investigation of the formation and evolution of Venus, through careful measurement of noble gas isotopic abundances. These investigations would provide key data for comparative planetology of terrestrial planets in our solar system and beyond.     

Initial Calibration of the Atmospheric Imaging Assembly (AIA) on the Solar Dynamics Observatory (SDO)

The Atmospheric Imaging Assembly (AIA) instrument onboard the Solar Dynamics Observatory (SDO) is an array of four normal-incidence reflecting telescopes that image the Sun in ten EUV and UV wavelength channels. We present the initial photometric calibration of AIA, based on preflight measurements of the response of the telescope components. The estimated accuracy is of order 25%, which is consistent with the results of comparisons with full-disk irradiance measurements and spectral models. We also describe the characterization of the instrument performance, including image resolution, alignment, camera-system gain, flat-fielding, and data compression.     

Devising stable geometrical reference frames for use in geodetic studies of vertical crustal motion

We present a method for constructing and assessing the stability of a geometrical reference frame for use in vertical crustal motion studies. Our approach exploits the fact that when we transform GPS velocity solutions from one reference frame (RF) to another one using a Helmert transformation, only the frame translation rate parameters produce significant changes in the vertical station velocities expressed in the final RF. Loosely speaking, one can select and impose a ‘vertical RF’ from an ensemble of candidate frames, without any reference to the ‘horizontal RF’ (which can be selected and imposed afterwards), by seeing how the frame translation rates vary as one moves across the ensemble of frames. We order this ensemble according to the number of stations, N, incorporated into the set VREF whose RMS vertical motion is minimized in order to realize each frame. The value of N controls the level of scatter in, and hence the degree of similarity between the vertical velocities of the stations composing VREF. We characterize a specific vertical RF as stable if all of the frames located in a large neighborhood of the ensemble which includes the specific frame are characterized by very small relative frame translation rates. In this case, the expression of vertical GPS station velocities in any of these frames would lead to very similar results. We present a case study using a very large global time series in which we find a large RF neighborhood in which vertical station velocities are globally stable at the $\sim $ 0.2 mm/year level, and a slightly smaller neighborhood in which vertical stability improves to $\sim $ 0.1 mm/year level in polar regions.     

An ontology-driven multi-agent system for nautical chart generalization

ABSTRACT

On nautical charts, undersea features are portrayed by sets of soundings (depth points) and isobaths (depth contours) from which map readers can interpret undersea features. Different techniques were developed for automatic sounding selection and isobath generalization. These methods are mainly used to generate a new chart from the bathymetric database or from a larger scale chart through selection and simplification. However, a part of the process consists in selecting and emphasizing undersea features formed by groups of soundings and isobaths on the chart according to their relevance to maritime navigation. Hence, automation of the process requires classification of features and their generalization through the application of a set of operators according not only to geometric constraints but also to their meaning.

The objective of this work is to conceive a multi-agent system (MAS) for nautical chart generalization that is driven by the knowledge on the generalization process and the undersea features and their relationships. First, this work provides a feature-centered ontology modeling of the generalization process. Then, the MAS structure is introduced where agents access cartographic knowledge stored in the ontology. The MAS makes use of measure algorithms to evaluate constraint violations on the chart in order to decide which generalization operators to apply. The whole model has been implemented to provide generalization plans on a real case study.