Applied Mathematics in EM Studies with Special Emphasis on an Uncertainty Quantification and 3-D Integral Equation Modelling   总被引：1，自引：0，他引：1  

Oleg Pankratov  Alexey Kuvshinov 《Surveys in Geophysics》2016,37(1):109-147

Despite impressive progress in the development and application of electromagnetic (EM) deterministic inverse schemes to map the 3-D distribution of electrical conductivity within the Earth, there is one question which remains poorly addressed—uncertainty quantification of the recovered conductivity models. Apparently, only an inversion based on a statistical approach provides a systematic framework to quantify such uncertainties. The Metropolis–Hastings (M–H) algorithm is the most popular technique for sampling the posterior probability distribution that describes the solution of the statistical inverse problem. However, all statistical inverse schemes require an enormous amount of forward simulations and thus appear to be extremely demanding computationally, if not prohibitive, if a 3-D set up is invoked. This urges development of fast and scalable 3-D modelling codes which can run large-scale 3-D models of practical interest for fractions of a second on high-performance multi-core platforms. But, even with these codes, the challenge for M–H methods is to construct proposal functions that simultaneously provide a good approximation of the target density function while being inexpensive to be sampled. In this paper we address both of these issues. First we introduce a variant of the M–H method which uses information about the local gradient and Hessian of the penalty function. This, in particular, allows us to exploit adjoint-based machinery that has been instrumental for the fast solution of deterministic inverse problems. We explain why this modification of M–H significantly accelerates sampling of the posterior probability distribution. In addition we show how Hessian handling (inverse, square root) can be made practicable by a low-rank approximation using the Lanczos algorithm. Ultimately we discuss uncertainty analysis based on stochastic inversion results. In addition, we demonstrate how this analysis can be performed within a deterministic approach. In the second part, we summarize modern trends in the development of efficient 3-D EM forward modelling schemes with special emphasis on recent advances in the integral equation approach.  相似文献   

Solar Occultation Measurements of the Martian Atmosphere on the Phobos Spacecraft: Water Vapor Profile,Aerosol Parameters,and Other Results     

Korablev  O. I. 《Solar System Research》2002,36(1):12-34

The Auguste experiment onboard the Phobos spacecraft was devoted to solar occultation spectroscopy of the Martian atmosphere in the ultraviolet through infrared wavelength region. Despite the short duration of the space mission and problems associated largely with a fault in the solar pointing system, data have been obtained on the chemical composition and aerosol content in the atmosphere of Mars at sunset early in the summer at equatorial latitudes (in the northern hemisphere). This paper presents a somewhat detailed review of the experiment performed, the data obtained, and their interpretation, and compares these data with new results. Ozone traces were detected at altitudes of 40–60 km, and, in one case, an ozone profile was obtained. Nine profiles of water vapor content at altitudes between 12 and 50 km were obtained from absorption data in the 1.87-m band. At altitudes of 23–25 km, the mean H₂O concentration profile falls steeply to the value of 3 ppm, but at lower altitudes the relative H₂O content is approximately constant (130 ppm). The overall content of water vapor is estimated as 8.3^+2.5 _-1.5 m of settled water. The temperature profile for the saturated atmosphere yields a cooling rate of 2 ± 1 K/km at altitudes from 25 to 35 km. The atmospheric extinction profiles were measured at altitudes from 10 to 50 km at the wavelengths 1.9 and 3.7 m. The atmosphere is transparent up to 25–33 km; below this level radiation is attenuated by dust; it is also possible that a layer of water ice clouds is present at altitudes of 20–25 km. High-altitude transparent ( 0.03) clouds consisting supposedly of water ice were observed in 5 of 38 cases at altitudes z 50 km. The optical depth ₀ of the atmosphere was estimated to be 0.2 ± 0.1, and constraints on the form of the size distribution of dust particles were established. Spectral features in the 3.7 m range have been previously attributed to formaldehyde; its content is substantially higher than the limits deduced from new ground-based observations. The spectrum in the 3.7 m range is discussed and other unsettled problems are pointed out.  相似文献   

Karibibite,a new FeAs mineral from South West Africa     

Oleg V Knorring  Th.G Sahama  Pentti Rehtijärvi 《Lithos》1973,6(3):265-271

Karibibite (ideally, Fe₂As₄O₉) occurs in vugs in massive loellingite of the Karibib pegmatite area, South West Africa. It is brownish yellow and finely fibrous. The thickness of the soft, single fibers is less than 1 micron, unsuitable for single-crystal X-ray study. Electron diffraction and X-ray powder pattern indicate that the mineral is orthorhombic, with $\text{a}{}_0\text{= 27.91}\text{A}\text{?}\text{, b}{}_0\text{= 6.53}\text{A}\text{?}\text{and c}{}_0\text{(}\text{fiber axis}\text{) = 7.20}\text{A}\text{?}$. The space group cannot be given. The mineral is paramagnetic with yellow fluorescence and is pleochroic with γ > 2.10, α = 1.96, 2V_α large, d = 4.07. It is soluble in acids and alkali hydroxide. Decomposition starts around 320 °C. The infra-red absorption spectrum indicates absence of AsO₄ groups. The mineral is classified tentatively as an oxide or arsenite.  相似文献   

Designing laboratory wind simulations using artificial neural networks     

Josip Križan  Goran Gašparac  Hrvoje Kozmar  Oleg Antonić  Branko Grisogono 《Theoretical and Applied Climatology》2015,120(3-4):723-736

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