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   

Abrupt transition from fractional crystallization to magma mixing at Gorely volcano (Kamchatka) after caldera collapse     

Maxim Gavrilenko  Alexey Ozerov  Philip R. Kyle  Michael J. Carr  Alex Nikulin  Christopher Vidito  Leonid Danyushevsky 《Bulletin of Volcanology》2016,78(7):47

  相似文献   

Shifted hyperbola moveout approximation revisited     

Alexey Stovas  Sergey Fomel 《Geophysical Prospecting》2012,60(3):395-399

The shifted hyperbola approximation is widely used in seismic applications. Mostly, this approximation is applied to reflection moveout in multilayered media. The traditional domain for this application is the t ‐ x domain. In this paper, we discuss the use of this approximation in the τ ‐ p and t ‐ p domains. The accuracy of the shifted hyperbola approximation defined in different domains is illustrated by analytical and numerical examples.  相似文献   

Intercomparison between finite element and finite volume approaches to model North Sea tides     

Silvia Maßmann  Alexey Androsov  Sergey Danilov 《Continental Shelf Research》2010

  相似文献   

On shear‐wave triplications in a multilayered transeversely isotropic medium with vertical symmetry axis     

Yuriy Roganov  Alexey Stovas 《Geophysical Prospecting》2010,58(4):549-559

The presence of triplications (caustics) can be a serious problem in seismic data processing and analysis. The traveltime curve becomes multi‐valued and the geometrical spreading correction factor tends to zero due to energy focusing. We analyse the conditions for the qSV‐wave triplications in a homogeneous transversely isotropic medium with vertical symmetry axis. The proposed technique can easily be extended to the case of horizontally layered vertical symmetry axis medium. We show that the triplications of the qSV‐wave in a multilayered medium imply certain algebra. We illustrate this algebra on a two‐layer vertical symmetry axis model.  相似文献   

Remote mountain lakes of Eastern Siberia: a pattern of ecologically pure non-industrialised water-bodies     

Nina Bondarenko  Natalia Sheveleva  Natalia Rozhkova  Arkadiy Matveev  Vitaliy Samusenok  Alexey Vokin  Anatoliy Yuriev 《Environmental Earth Sciences》2017,76(10):378

A 3-year study of the biota of the remote mountain lakes of Amut, Balan-Tamur, and Yakondykon, situated in the Dzherginsky State Reserve in the Baikalian region of Eastern Siberia, was carried out from 2006 to 2008. Examining the biota of non-modern and non-industrialised mountain lakes allowed us to reveal its background in relation to the species composition of plankton, the main groups of benthos and fishes, production potential, and seasonal dynamics of the ecosystem’s basic links. Our data on pH and biota were compared with the findings of a previous study in 1986 in order to evaluate possible changes associated with probable acidification. We observed that the lakes of the Dzherginsky State Reserve have high species diversity. Despite this, they are classed as oligotrophic water-bodies with regard to the development level of their planktonic and benthic coenoses. These lakes are not polluted by anthropogenic activity and so could be considered as a pattern of ecologically pure water-bodies. It is important to add that high mountain lakes of Pribaikalye presently serve as refuges for species that were widespread during past geological epochs.  相似文献   

Duration,causes, and geodynamic significance of the Middle Cenozoic hiatus in sedimentation in the near-polar part of the Lomonosov Ridge (based on IODP-302-ACEX drilling data)     

A. A. Chernykh  A. A. Krylov 《Oceanology》2017,57(5):675-684

The paper analyzes the duration and causes of the Middle Cenozoic hiatus in sedimentation in the near-polar part of the Lomonosov Ridge, revealed during biostratigraphic research of ACEX borehole deposits. Arguments are presented against the existence of a long hiatus between sediments of lithological complexes 1/5 and 1/6. The Lomonosov Ridge naturally subsided in the Cenozoic as a result of cooling of the lithosphere after riftogenesis. However, the level of the Arctic Ocean in its isolation period (49(?)–36.6 Ma) could have been lower than the level of the World Ocean due to decelerated spreading in the Eurasian Basin. A brief hiatus in sedimentation was caused by opening of the Fram Strait around 36.6 Ma and the infiltration of intermediate Atlantic waters, which could have interacted with the Lomonosov Ridge, leading to the erosion or nondeposition of particles on its surface.  相似文献   

High resolution method of direct measurement of the magnetic field lines'' eigen frequencies     

L.N. Baransky  J.E. Borovkov  M.B. Gokhberg  S.M. Krylov  V.A. Troitskaya 《Planetary and Space Science》1985,33(12):1369-1374

The simultaneous observations of Pc4 geomagnetic pulsations at the two temporary stations, located along the geomagnetic meridian 50 km to the North and South from the observatory Borok (L = 2.8), have been used for the investigation of amplitude gradients of both H- and D-components of these pulsations. It has been discovered that the direction of a meridional component of the gradient H (grad_MH) depends on the frequency ƒ of a spectral component of pulsations. The grad_MD is directed more or less permanently northward independently from the frequency ƒ These results are the consequence of a local amplification of geomagnetic pulsations due to Alfvén waves resonance along the magnetic field lines. It has been demonstrated that the frequencies ƒ_R for which the northward direction of grad_MH is replaced by the southward one (with increasing ƒ) can be interpreted as the eigen frequencies of the field line which intersects the meridian in the middle between two temporary stations, i.e. in Borok.

The possible applications of a gradient method of measurement of the magnetic field lines' eigen frequencies are discussed.  相似文献   

Aluminous websterite and granulite xenoliths from the Chyulu Hills volcanic field, Kenya: gabbro–troctolitic cumulates subjected to lithospheric foundering     

Alexey Ulianov  Angelika Kalt  Thomas Pettke 《Contributions to Mineralogy and Petrology》2006,152(4):459-483

Whole rock major and trace element abundances in aluminous garnet–spinel websterite, sapphirine-bearing Mg–Al granulite and hibonite-bearing Ca–Al granulite xenoliths from the Chyulu Hills volcanic field, Kenya, suggest that the samples represent a meta-igneous suite linked by fractionation. The incompatible major element contents increase from the websterites to the Mg–Al granulites and further to the Ca–Al granulites. High bulk rock Mg#s and very low concentrations of most incompatible trace elements indicate that the rocks are cumulates rather than crystallized melts. Elevated Ni abundances, impoverishment in Cr and HFSE and high contents of normative plagioclase and olivine in the granulites indicate that their protoliths were similar to troctolite. The textures and metamorphic reaction paths recorded in the granulites suggest igneous emplacement in the crust and cooling from igneous to ambient crustal temperatures accompanied or followed by compression. For the websterite xenoliths, there is an apparent contradiction between the results of P–T calculations that suggest high P and T of crystallization of early generation pyroxenes and elevated P–T conditions during final equilibration (1.4–2.2 GPa/740–980°C) on the one hand and the positive Eu anomaly that suggests shallow-level plagioclase accumulation on the other hand. This contradiction can be reconciled by a model of compression of a plagioclase-bearing (gabbroic) protolith to mantle depths where it recrystallized to an ultramafic assemblage, which requires foundering of dense lower crustal material into the mantle.  相似文献   

Changing relationships between Religion, the State, and Society in Russia     

Alexey D. Krindatch 《GeoJournal》2006,67(4):267-282

This paper first traces the major changes in the relationship between the (Orthodox) Church and State in the different Russian polities, using Madeley’s framework of historic mono-confessional blocs and multi-confessional belts. Second, it outlines the recent tendencies and characteristic features of church–state relations in today’s Russia. Third, using data from sociological surveys, it analyses the current dominant popular perceptions and societal attitudes towards religion and the State, including religious freedom. Being part of the historic mono-confessional Orthodox bloc, the different Russian polities produced different models of church–state relations: from a symphony of religious and political powers, through a forced nationalization of the Orthodox Church (Russian Empire from the époque of Peter the Great until revolution of 1917), and forced secularisation (during the Soviet Union), to a return of mutual support of (Orthodox) Church and State despite a formal (constitutional) separation in Putin’s Russia.  相似文献