Relevant bibliographies by topics / Mathematical geophysics

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Mathematical geophysics'

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Published: 4 June 2021
Last updated: 10 March 2023

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Journal articles on the topic "Mathematical geophysics"

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Temirbekova, L. N., N. M. Temirbekov, V. L. Los, Ye I. Imangaliyev, D. R. Baigereyev, and M. B. Nurmangalieva. "A MODULE OF A GEOINFORMATION SYSTEM BASED ON NUMERICAL MODELING OF INVERSE PROBLEMS OF GEOCHEMISTRY BY REGULARIZING ALGORITHMS." Bulletin Series of Physics & Mathematical Sciences 75, no. 3 (September 15, 2021): 15–28. http://dx.doi.org/10.51889/2021-3.1728-7901.02.

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Currently, due to the rapid development of computer technology in geology, methods and approaches of scientific visualization based on additional data analysis are being intensively developed. The general concept is that the main data field on the daily surface and additional conditions are set at the input. Further, methods of mathematical geophysics are used for their analysis and processing, as a result of which new information is obtained for deep surveys. Then, in the information system, visualization tools are applied to the new information received and to the main data field. Thus, the information system is based on the synthesis of visual representation methods and methods of mathematical geophysics, computational mathematics from different branches of knowledge. This paper presents a description of the software module of the geoinformation system, based on the methods of intelligent detection of anomalies of hidden deposits, for deep predictive and search modeling of deposits. The functioning of the software module is based on the application of the theory of inverse problems of mathematical geophysics with elements of artificial intelligence using geological data on the earth's surface, geophysical measurements and geochemical analyses as input data. The program module for the inverse problem of the continuation of potential fields in the direction of disturbing masses is used for real data of a specific mineral deposit.
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Gurefe, Yusuf, Yusuf Pandir, and Tolga Akturk. "On the Nonlinear Mathematical Model Representing the Coriolis Effect." Mathematical Problems in Engineering 2022 (September 26, 2022): 1–12. http://dx.doi.org/10.1155/2022/2504907.

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In this study, the traveling wave solutions of a nonlinear partial differential equation (NPDE) called as Geophysics Korteweg-de Vries (GpKdV) equation are obtained using the modified exponential function method (MEFM). Coriolis effect is stated with the help of this model used in geophysics. The nonlinear model has a Coriolis coefficient representing this effect.
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Kogan, L. I. "EXPEDITIONS AND RESEARCHES OF MARINE GEOPHYSICS YU.P. NEPROCHNOV." Journal of Oceanological Research 48, no. 2 (August 28, 2020): 208–24. http://dx.doi.org/10.29006/1564-2291.jor-2020.48(2).16.

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This article is dedicated to the anniversary of geophysicist, doctor of physical and mathematical sciences, Professor Yuri Pavlovich Neprochnov, who would turn 90 years old this year. Prof. Neprochnov created a school of seismic marine geologists. He had numerous students, who prepared and successfully defended 12 Ph.D., and D.Sc. dissertations under his leadership. He is the author and co-author of more than 400 scientific articles and 18 monographs. Neprochnov was a Member of the Second World War, a Member of the Scientific Council of the Russian Academy of Sciences on the problems of the oceans, where he led the working group on seismic and integrated geophysics; Coordinator of International projects for scientific cooperation with India, China and Finland, a Member of the Editorial board of the Journal «Oceanology», was elected a full Member of the Russian Academy of Natural Sciences and a Member of the New York Academy of Sciences, and in 2002 for his labor successes and a great contribution to strengthening friendship and cooperation between peoples he was awarded the title of Honored Scientist of the Russian Federation. His friend and colleague in scientific geophysical research L.I. Kogan recalls years of teamwork and expresses his appreciation for professional friendships throughout his life.
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Moorkamp, Max. "Research resource review: Mathematical methods for geophysics and space physics." Progress in Physical Geography: Earth and Environment 41, no. 2 (April 2017): 243–44. http://dx.doi.org/10.1177/0309133317704051.

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Buchen, P. W. "Seismic Migration And Mathematical Mapping." Exploration Geophysics 22, no. 1 (March 1991): 55–58. http://dx.doi.org/10.1071/eg991055.

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Løseth, Lars O., Hans M. Pedersen, Bjørn Ursin, Lasse Amundsen, and Svein Ellingsrud. "Low-frequency electromagnetic fields in applied geophysics: Waves or diffusion?" GEOPHYSICS 71, no. 4 (July 2006): W29—W40. http://dx.doi.org/10.1190/1.2208275.

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Low-frequency electromagnetic (EM) signal propagation in geophysical applications is sometimes referred to as diffusion and sometimes as waves. In the following we discuss the mathematical and physical approaches behind the use of the different terms. The basic theory of EM wave propagation is reviewed. From a frequency-domain description we show that all of the well-known mathematical tools of wave theory, including an asymptotic ray-series description, can be applied for both nondispersive waves in nonconductive materials and low-frequency waves in conductive materials. We consider the EM field from an electric dipole source and show that a common frequency-domain description yields both the undistorted pulses in nonconductive materials and the strongly distorted pulses in conductive materials. We also show that the diffusion-equation approximation of low-frequency EM fields in conductive materials gives the correct mathematical description, and this equation has wave solutions. Having considered both a wave-picture approach and a diffusion approach to the problem, we discuss the possible confusion that the use of these terms might lead to.
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Peng, Liangrong, and Liu Hong. "Recent Advances in Conservation–Dissipation Formalism for Irreversible Processes." Entropy 23, no. 11 (October 31, 2021): 1447. http://dx.doi.org/10.3390/e23111447.

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The main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF’s physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker–Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.
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Kubáčková, Ludmila. "Mathematical geophysics. A survey of recent developments in seismology and geodynamics." Tectonophysics 172, no. 3-4 (February 1990): 370–71. http://dx.doi.org/10.1016/0040-1951(90)90044-9.

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Shore, K. Alan. "Mathematical methods for geophysics and space physics, by William I. Newman." Contemporary Physics 58, no. 1 (November 23, 2016): 113–14. http://dx.doi.org/10.1080/00107514.2016.1259256.

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Li, Zhenhua, and Mirko van der Baan. "Tutorial on rotational seismology and its applications in exploration geophysics." GEOPHYSICS 82, no. 5 (September 1, 2017): W17—W30. http://dx.doi.org/10.1190/geo2016-0497.1.

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Traditionally, seismological interpretations are based on the measurement of only translational motions, such as particle displacement, velocity, and/or acceleration, possibly combined with pressure changes; yet theory indicates that rotational motions should also be observed for a complete description of all ground motions. The recent and ongoing development of rotational sensors renders a full analysis of the translational and rotational ground motion possible. We have developed the basic mathematical theory related to rotational motion. And we also evaluated several instruments used to directly measure the rotational ground motion, which may be applicable for exploration geophysics. Finally, we made several applications of rotational motion in exploration geophysics, namely, (1) P- and S-wavefield separation, (2) wavefield reconstruction, (3) ground-roll removal, (4) microseismic event localization and reflection seismic migration by wavefield extrapolation, and (5) moment tensor inversion. The cited research shows that in particular, the information on the spatial gradient of the wavefield obtained by rotational sensors is beneficial for many purposes. This tutorial is meant to (1) enhance familiarity with the concept of rotational seismology, (2) lead to additional applications, and (3) fast track the continued development of rotational sensors for global and exploration geophysical use.
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Dissertations / Theses on the topic "Mathematical geophysics"

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Cocks, David. "Mathematical modelling of dune formation." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442818.

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This study is concerned with the mathematical modelling of the formation and subsequent evolution of sand dunes, both beneath rivers (fluvial) and in deserts (Aeolian). Dunes are observed in the environment in many different shapes and sizes; we begin by discussing qualitatively how and why the different forms exist. The most important aspect of a successful model is the relationship between the bed shape and the shear stress that the flow exerts on the bed. We first discuss a simple model for this stress applied to fluvial dunes, which is able to predict dune-like structures, but does not predict the instability of a flat bed which we would hope to find. We therefore go on to look at improved models for the shear stress based on theories of turbulent flow and asymptotic methods, using assumptions of either a constant eddy viscosity or a mixing length model for turbulence. Using these forms for the shear stress, along with sediment transport laws, we obtain partial integrodifferential equations for the evolution of the bed, and we study these numerically using spectral methods. One important feature of dunes which is not taken into account by the above models is that of the slip face - a region of constant slope on the downwind side of the dune. When a slip face is present, there is a discontinuity in the slope of the bed, and hence it is clear that flow separation will occur. Previous studies have modelled separated flow by heuristically describing the boundary of the separated region with a cubic or quintic polynomial which joins smoothly to the bed at each end. We recreate this polynomial form for the wake profile and demonstrate a method for including it into an evolution system for dunes. The resulting solutions show an isolated steady-state dune which propagates downstream. From the asymptotic framework developed earlier with a mixing length model for turbulence, we are able, using techniques of complex analysis, to model the shape of the wake region from a purely theoretical basis, rather than the heuristic one used previously. We obtain a Riemann-Hilbert problem for the wake profile, which can be solved using well-known techniques. We then use this method to calculate numerically the wake profile corresponding to a number of dune profiles. Further, we are able to find an exact solution to the wake profile problem in the case of a sinusoidally shaped dune with a slip face. Having found a method to calculate the shear stress exerted on the dune from the bed profile in the case of separated flow, we then use this improved estimate of the shear stress in an evolution system as before. In order to do this efficiently, we consider an alternative method for calculating the wake profile based on the spectral method used for solving the evolution system. We find that this system permits solutions describing an isolated dune with a slip face which propagates downstream without changing shape. All of the models described above are implemented in two spatial dimensions; the wind is assumed to blow in one direction only, and the dunes are assumed to be uniform in a direction perpendicular to the wind flow. While this is adequate to explain the behaviour of transverse dunes, other dune shapes such as linear dunes, barchans, and star dunes are by nature three-dimensional, so in order to study the behaviour of such dunes, the extension of the models to three dimensions is essential. While most of the governing equations generalize easily, it is less obvious how to extend the model for separated flow, due to its reliance on complex variables. We implement some three-dimensional evolution models, and discuss the possibility of modelling three-dimensional flow separation.
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Hewitt, Ian. "Mathematical modelling of geophysical melt drainage." Thesis, University of Oxford, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.509957.

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Fluid flows involving transport of a liquid phase in close proximity with its solid phase involve continuous transfer of mass and heat, which can influence the nature of the drainage that occurs. We consider mathematical models for two such situations; magma flow in the mantle and water flow beneath glaciers. In part I, we derive a model for porous flow within a partially molten column of mantle undergoing decompression melting. By ignoring composition effects, and by scaling the equations appropriately, approximate analytical solutions can be found for one-dimensional upwelling, which allow the region and extent of melting to be determined. We study the dynamics of open channels of melt flow in the same situation, and find that such channels would have low pressure compared to the surrounding porous flow, and therefore draw in melt from a region of the size of a compaction length. We suggest that such channels could form through the unstable effects of melting caused by heat transfer by the upwelling melt. We emphasise the similarity with channels of meltwater that are known to exist beneath ice. In part II we pose a generalised model for subglacial water flow, which is described as an effective porous medium, the pore space being determined from an evolution equation. This is used to investigate the flow into a channel, which is found to be drawn from a surrounding region whose size, we suggest, determines the spacing between major drainage channels beneath ice sheets. These are compared to the observed spacing of eskers. A critical condition on the discharge necessary to sustain a channel is found, which may provide a criteria to decide where and when channelised drainage occurs. Lastly, a simple drainage model is used to explain seasonal variations in the velocity of a valley glacier.
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Cassidy, Nigel John. "The application of mathematical modelling in the interpretation of near-surface archaeological ground-penetrating radar." Thesis, Keele University, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.344057.

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Ng, F. S. L. "Mathematical modelling of subglacial drainage and erosion." Thesis, University of Oxford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.244772.

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The classical theory of channelized subglacial drainage,due orginally to Röthlisberger (1972) and Nye (1976), considers water flow in an ice channel overlying a rigid, impermeable bed. At steady flow, creep closure of the channel walls is counteracted by melt-back due to heat dissipation, and this leads to an equilibrium relation between channel water pressure and discharge. More generally, such a balance exhibits an instability that can be used to describe the mechanics of catastrophic flood events known as `jökulhlaups'. In this thesis, we substantiate these developments by exploring a detailed model where the channel is underlain by subglacial till and the flow supports a sediment load. Attention is given to the physics of bed processes and its effect on channel morphology. In particular, we propose a theory in which the channel need not be semi-circular, but has independently evolving depth and width determined by a local balance between melting and closure, and in which sediment erosion and deposition is taken into account. The corresponding equilibrium relation indicates a reverse dependence to that in the classical model, justifying the possibility of the subglacial canals envisaged by Walder and Fowler (1994). Theoretical predictions for sediment discharge are also derived. Regarding time-dependent flood drainage, we demonstrate how rapid channel widening caused by bank erosion can explain the abrupt recession observed in the flood hydrographs. This allows us to produce an improved simulation of the 1972 jökulhlaup from Grímsvötn, Iceland, and self-consistently, a plausible estimate for the total sediment yield. We also propose a mechanism for the observed flood initiation lake-level at Grímsvötn. These investigations expose the intimate interactions between drainage and sediment transport, which have profound implications on the hydrology, sedimentology and dynamics of ice masses, but which have received little attention.
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Schoof, C. "Mathematical models of glacier sliding and drumlin formation." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.249325.

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One of the central difficulties in many models of glacier and ice sheet flow lies in the prescription of boundary conditions at the bed. Often, processes which occur there dominate the evolution of the ice mass as they control the speed at which the ice is able to slide over the bed. In part I of this thesis, we study two complications to classical models of glacier and ice sheet sliding. First, we focus on the effect of cavity formation on the sliding of a glacier over an undeformable, impermeable bed. Our results do not support the widely used sliding law $u_b = C\tau_b^pN^{-q}$, but indicate that $\tau_b/N$ actually decreases with $u_b/N$ at high values of the latter, as suggested previously for simple periodic beds by Fowler (1986). The second problem studied is that of an ice stream whose motion is controlled by bed obstacles with wavelengths comparable to the thickness of ice. By contrast with classical sliding theory for ice of constant viscosity,the bulk flow velocity does not depend linearly on the driving stress. Indeed, the bulk flow velocity may even be a multi-valued function of driving stress and ice thickness. In the second part of the thesis, attention is turned to the formation of drumlins. The viscous till model of Hindmarsh (1998) and Fowler (2000) is analysed in some detail. It is shown that the model does not predict the formation of three-dimensional drumlins, but only that of two-dimensional features, which may be interpreted as Rogen moraines. A non-linear model allows the simulation of the predicted bedforms at finite amplitude. Results obtained indicate that the growth of bedforms invariably leads to cavitation. A model for travelling waves in the presence of cavitation is also developed, which shows that such travelling waves can indeed exist. Their shape is, however, unlike that of real bedforms, with a steep downstream face and no internal stratification. These results indicate that Hindmarsh and Fowler's model is probably not successful at describing the processes which lead to the formation of streamlined subglacial bedforms.
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Fay, Gemma Louise. "Mathematical modelling of turbidity currents." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:62bb9382-1c50-47f3-8f59-66924cc31760.

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Turbidity currents are one of the primary means of transport of sediment in the ocean. They are fast-moving, destructive fluid flows which are able to entrain sediment from the seabed and accelerate downslope in a process known as `ignition'. In this thesis, we investigate one particular model for turbidity currents; the `Parker model' of Parker, Pantin and Fukushima (1986), which models the current as a continuous sediment stream and consists of four equations for the depth, velocity, sediment concentration and turbulent kinetic energy of the flow. We propose two reduced forms of the model; a one-equation velocity model and a two-equation shallow-water model. Both these models give an insight into the dynamics of a turbidity current propagating downstream and we find the slope profile to be particularly influential. Regions of supercritical and subcritical flow are identified and the model is solved through a combination of asymptotic approximations and numerical solutions. We next consider the dynamics of the four-equation model, which provides a particular focus on Parker's turbulent kinetic energy equation. This equation is found to fail catastrophically and predict complex-valued solutions when the sediment-induced stratification of the current becomes large. We propose a new `transition' model for turbulent kinetic energy which features a switch from an erosional, turbulent regime to a depositional, stably stratified regime. Finally, the transition model is solved for a series of case studies and a numerical parameter study is conducted in an attempt to answer the question `when does a turbidity current become extinct?'.
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Yang, Xin-She. "Mathematical modelling of compaction and diagenesis in sedimentary basins." Thesis, University of Oxford, 1997. http://ora.ox.ac.uk/objects/uuid:0bdc6c43-4534-4f08-97e2-8a33d6b13e61.

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Sedimentary basins form when water-borne sediments in shallow seas are deposited over periods of millions of years. Sediments compact under their own weight, causing the expulsion of pore water. If this expulsion is sufficiently slow, overpressuring can result, a phenomenon which is of concern in oil drilling operations. The competition between pore water expulsion and burial is complicated by a variety of factors, which include diagenesis (clay dewatering), and different modes (elastic or viscous) of rheological deformation via compaction and pressure solution, which may also include hysteresis in the constitutive behaviours. This thesis is concerned with models which can describe the evolution of porosity and pore pressure in sedimentary basins. We begin by analysing the simplest case of poroelastic compaction which in a 1-D case results in a nonlinear diffusion equation, controlled principally by a dimensionless parameter lambda, which is the ratio of the hydraulic conductivity to the sedimentation rate. We provide analytic and numerical results for both large and small lambda in Chapter 3 and Chapter 4. We then put a more realistic rheological relation with hysteresis into the model and investigate its effects during loading and unloading in Chapter 5. A discontinuous porosity profile may occur if the unloaded system is reloaded. We pursue the model further by considering diagenesis as a dehydration model in Chapter 6, then we extend it to a more realistic dissolution-precipitation reaction-transport model in Chapter 7 by including most of the known physics and chemistry derived from experimental studies. We eventually derive a viscous compaction model for pressure solution in sedimentary basins in Chapter 8, and show how the model suggests radically different behaviours in the distinct limits of slow and fast compaction. When lambda << 1, compaction is limited to a basal boundary layer. When lambda >> 1, compaction occurs throughout the basin, and the basic equilibrium solution near the surface is a near parabolic profile of porosity. But it is only valid to a finite depth where the permeability has decreased sufficiently, and a transition occurs, marking a switch from a normally pressured environment to one with high pore pressures.
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Silva, Maria Gabriela Melo. "Preservação da amplitude na migração da equação da onda." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307300.

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Orientadores: Joerg Schleicher, Amelia Novais
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-06T21:47:51Z (GMT). No. of bitstreams: 1 Silva_MariaGabrielaMelo_M.pdf: 824279 bytes, checksum: 86fc870083d29ff7d1c834bea8c9f983 (MD5) Previous issue date: 2006
Resumo: Em meios homogêneos, o operador diferencial da equação da onda cheia pode ser substituído pelo produto de dois operadores diferenciais. Cada um destes operadores gera uma equação da onda de sentido único. As soluções destas equações descrevem a propagação de uma onda para baixo e uma para cima, respectivamente. Estas soluções possuem os mesmos tempos de trânsito e amplitudes que a onda cheia, uma vez que satisfazem as mesmas equações iconal e de transporte. No entanto, em meios heterogêneos, estas ondas de sentido único satisfazem somente a mesma equação iconal que a onda cheia. Zhang et al. (2003) mostraram como obter equações da onda de sentido único de amplitude verdadeira de modo que estas possuam tanto os mesmos tempos de trânsito como as mesmas amplitudes da onda cheia. Com base nestas equações, desenvolveram uma migração da equação da onda de amplitude verdadeira para seções de fonte comum. Nosso objetivo neste trabalho é modificar a migração de Gazdag (1980), de tal maneira que esta passe a utilizar as equações da onda de sentido único de amplitude verdadeira ao invés das equações de sentido único padrão, para realizar uma migração da equação da onda em amplitude verdadeira para seções de afastamento nulo
Abstract: In homogeneous media, the two-way wave operator can be substituted by the product of two one-way wave operators each of which generates a one-way wave equation. One of these equations has a downgoing wave and the other has an upgoing wave as a solution. Those oneway waves have the same travei time and amplitudes as the full wave since they satisfy the same eikonal and transport equation. However, in heterogeneous media, the standard one-way waves satisfy only the same eikonal equation as the full wave. Thus, in this case, the amplitudes of the migrated section obtained through a migration method based on the standard wave equations are incorrect. Zhang et al. (2003) described how to modify the standard one-way waves in order to produce the true amplitude one-way waves, which not only have the same travei times but also the same amplitudes as the full wave. They use these true amplitudes one-way wave equations to preserve the amplitudes in common-shot wave-equation migration. Our goal is to modify Gazdag migration (Gazdag, 1980) in such a way that it uses the true amplitude one-way wave equations instead of the standard ones, in order to realize a true amplitude wave equation migration for zero-offset data
Mestrado
Geofisica
Mestre em Matemática Aplicada
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Nicholson, Lindsey. "Modelling melt beneath supraglacial debris : implications for the climatic response of debris-covered glaciers." Thesis, University of St Andrews, 2005. http://hdl.handle.net/10023/10264.

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Understanding how debris-covered glaciers respond to climate is necessary in order to evaluate future water resources and glacier flood hazard potential, and to make sense of the glacier chronology in mountain regions, In order achieve this, it is necessary to improve the current understanding of how surface debris affects glacier ablation rate, and to develop methods by which the ablation of debris-covered glaciers can be predicted under various climatic scenarios. This thesis develops a numerical surface energy balance model that uses simple meteorological data to calculate melt beneath a debris layer of given thickness and thermal characteristics. Field data from three contrasting sites demonstrate that the assumptions made within the model concerning the thermal properties of supraglacial debris are valid during most ablation conditions and that model performance is considerably better than previous models. Model results indicate that the effect of debris on melt rate is highly dependent on meteorological conditions. Under colder climates, thin debris can accelerate ice melt by extending the ablation period at both diurnal and seasonal scales. However, in milder mid- summer conditions, even a very thin debris cover inhibits melt rate compared to that of exposed ice. The new melt model is applied to produce the first quantified ablation gradients for debris- covered glaciers, and to model the evolution of ice surfaces under a debris layer of variable thickness. Modelled ablation gradients are qualitatively similar to hypothetical ones outlined previously, and quantitatively similar to those measured in the field. The ablation gradients are used to explore the factors affecting the response of debris-covered glaciers to climate change. Beneath a debris layer of variable thickness, the melt model produced ablation topography, as observed in the field, which underwent topographic inversion over time in response to debris redistribution. Debris thickness variability was found to cause calculated ablation rate to increase compared to that calculated using a mean debris thickness by one to two orders of magnitude, suggesting that melt calculations made on the basis of spatially averaged debris thickness may be inaccurate.
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Wijns, Christopher P. "Exploring conceptual geodynamic models : numerical method and application to tectonics and fluid flow." University of Western Australia. School of Earth and Geographical Sciences, 2005. http://theses.library.uwa.edu.au/adt-WU2005.0068.

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Geodynamic modelling, via computer simulations, offers an easily controllable method for investigating the behaviour of an Earth system and providing feedback to conceptual models of geological evolution. However, most available computer codes have been developed for engineering or hydrological applications, where strains are small and post-failure deformation is not studied. Such codes cannot simultaneously model large deformation and porous fluid flow. To remedy this situation in the face of tectonic modelling, a numerical approach was developed to incorporate porous fluid flow into an existing high-deformation code called Ellipsis. The resulting software, with these twin capabilities, simulates the evolution of highly deformed tectonic regimes where fluid flow is important, such as in mineral provinces. A realistic description of deformation depends on the accurate characterisation of material properties and the laws governing material behaviour. Aside from the development of appropriate physics, it can be a difficult task to find a set of model parameters, including material properties and initial geometries, that can reproduce some conceptual target. In this context, an interactive system for the rapid exploration of model parameter space, and for the evaluation of all model results, replaces the traditional but time-consuming approach of finding a result via trial and error. The visualisation of all solutions in such a search of parameter space, through simple graphical tools, adds a new degree of understanding to the effects of variations in the parameters, the importance of each parameter in controlling a solution, and the degree of coverage of the parameter space. Two final applications of the software code and interactive parameter search illustrate the power of numerical modelling within the feedback loop to field observations. In the first example, vertical rheological contrasts between the upper and lower crust, most easily related to thermal profiles and mineralogy, exert a greater control over the mode of crustal extension than any other parameters. A weak lower crust promotes large fault spacing with high displacements, often overriding initial close fault spacing, to lead eventually to metamorphic core complex formation. In the second case, specifically tied to the history of compressional orogenies in northern Nevada, exploration of model parameters shows that the natural reactivation of early normal faults in the Proterozoic basement, regardless of basement topography or rheological contrasts, would explain the subsequent elevation and gravitationally-induced thrusting of sedimentary layers over the Carlin gold trend, providing pathways and ponding sites for mineral-bearing fluids.
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Books on the topic "Mathematical geophysics"

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Vlaar, N. J., G. Nolet, M. J. R. Wortel, and S. A. P. L. Cloetingh, eds. Mathematical Geophysics. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2.

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Chiappini, Massimo, and Vincenzo Vespri, eds. Applied Mathematical Problems in Geophysics. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-05321-4.

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Roy, K. K. Potential theory in applied geophysics. Berlin: Springer, 2008.

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Siamak, Hassanzadeh, Society of Photo-optical Instrumentation Engineers., and Society of Exploration Geophysicists, eds. Mathematical methods in geophysical imaging V: 20-21 July, 1998, San Diego, California. Bellingham, Wash: SPIE, 1998.

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D, Schertzer, ed. Nonlinear variability in geophysics 3. Singapore: World Scientific, 1996.

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N, Strakhov V., and Obʺedinennyĭ institut fiziki Zemli im. O.I︠U︡. Shmidta., eds. Metody reshenii︠a︡ t︠s︡entralʹnoĭ vychislitelʹnoĭ zadachi gravimetrii, magnitometrii, geodezii i geoinformatiki: Sbornik nauchnykh stateĭ. Moskva: Institut fiziki Zemli im. O.I︠U︡. Shmidta RAN, 2007.

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N, Strakhov V., and Obʺedinennyĭ institut fiziki Zemli im. O.I︠U︡. Shmidta., eds. Metody reshenii︠a︡ t︠s︡entralʹnoĭ vychislitelʹnoĭ zadachi gravimetrii, magnitometrii, geodezii i geoinformatiki: Sbornik nauchnykh stateĭ. Moskva: Institut fiziki Zemli im. O.I︠U︡. Shmidta RAN, 2007.

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Kubáčková, Ludmila. Probability and statistics in geodesy and geophysics. Amsterdam: Elsevier, 1987.

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Andreas, Vogel, ed. Model optimization in exploration geophysics. Braunschweig: Vieweg, 1988.

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Zhdanov, Mikhail Semenovich. Integral transforms in geophysics. Berlin: Springer-Verlag, 1988.

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Book chapters on the topic "Mathematical geophysics"

1

Masters, Guy, and Michael Ritzwoller. "Low frequency seismology and three-dimensional structure — observational aspects." In Mathematical Geophysics, 1–30. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_1.

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Jarvis, G. T., and W. R. Peltier. "Long wavelength features of mantle convection." In Mathematical Geophysics, 209–26. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_10.

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Quareni, Francesca, and David A. Yuen. "Mean-field methods in mantle convection." In Mathematical Geophysics, 227–64. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_11.

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Machetel, Philippe, and David A. Yuen. "Infinite Prandtl number spherical-shell convection." In Mathematical Geophysics, 265–90. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_12.

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Forte, A. M., and W. R. Peltier. "Lateral heterogeneity and the geoid: the importance of the surface kinematic constraints." In Mathematical Geophysics, 291–323. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_13.

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Peltier, W. R. "Lithospheric thickness, Antarctic deglaciation history, and ocean basin discretization effects in a global model of postglacial sea level change." In Mathematical Geophysics, 325–46. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_14.

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Nakada, Masao, and Kurt Lambeck. "Non-uniqueness of lithospheric thickness estimates based on glacial rebound data along the east coast of North America." In Mathematical Geophysics, 347–61. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_15.

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Cloetingh, S. A. P. L., and M. J. R. Wortel. "On the mechanics of plate boundary formation." In Mathematical Geophysics, 363–87. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_16.

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Angevine, C. L., S. R. Linneman, and P. L. Heller. "Supercontinent breakup: effect on eustatic sea level and the oceanic heat flux." In Mathematical Geophysics, 389–99. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_17.

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Park, Jeffrey. "Free-oscillation coupling theory." In Mathematical Geophysics, 31–52. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-2857-2_2.

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Conference papers on the topic "Mathematical geophysics"

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Vîlceanu, Clara –. Beatrice, Carmen Grecea, and Cosmin Muşat. "Relevancy of mathematical support for geophysics determinations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992604.

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Temirbekov, Nurlan, and Laura Temirbekova. "Using the conjugate equations method for solving inverse problems of mathematical geophysics and mathematical epidemiology." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040264.

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Aksѐnov, V. V. "Fifteen theorems of mathematical geophysics. Wording, evidence, links to publications." In SCIENCE OF RUSSIA: TARGETS AND GOALS. ЦНК МОАН, 2020. http://dx.doi.org/10.18411/sr-10-04-2020-28.

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Balkov, E. V., M. I. Epov, and A. K. Manstein. "Mathematical apparatus for shallow-depth electromagnetic scanning device." In Geophysics of the 21st Century - The Leap into the Future. European Association of Geoscientists & Engineers, 2003. http://dx.doi.org/10.3997/2214-4609-pdb.38.f123.

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Prigara, A. M., V. N. Aptukov, R. I. Tsarev, V. A. Voroshilov, and A. A. Zhukov. "Investigation of the Wave Propagation Process under Seismoacoustic Impacts in a Rock Mass Using Mathematical Modeling Methods." In Engineering and Mining Geophysics 2020. European Association of Geoscientists & Engineers, 2020. http://dx.doi.org/10.3997/2214-4609.202051054.

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Soares*, Átila Saraiva Quintela, and Wilson Mouzer Figueiró. "Some mathematical and numerical developments for improvements in computational efficiency applied to geophysics." In 15th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 31 July-3 August 2017. Brazilian Geophysical Society, 2017. http://dx.doi.org/10.1190/sbgf2017-071.

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Aleinikov, A. L., V. T. Belikov, and L. V. Eppelbaum. "Investigation of Mountainous Rock Destruction: A New Physico‐Mathematical Conception." In Symposium on the Application of Geophysics to Engineering and Environmental Problems 1999. Environment and Engineering Geophysical Society, 1999. http://dx.doi.org/10.4133/1.2922658.

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Martynova, Y. V., and S. P. Mikhailov. "Application of A Mathematical Model of the Capillary Curve to Elaboration of the Water Saturation of Rocks." In Engineering and Mining Geophysics 2019 15th Conference and Exhibition. European Association of Geoscientists & Engineers, 2019. http://dx.doi.org/10.3997/2214-4609.201901684.

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Sharafutdinov, R. F., R. A. Valiullin, A. S. Ramazanov, A. A. Sadretdinov, T. R. Khabirov, and A. M. Sharipov. "The Use of Mathematical Models in the Control Environment of Underground Gas Storage." In Near Surface Geoscience 2015 - 21st European Meeting of Environmental and Engineering Geophysics. Netherlands: EAGE Publications BV, 2015. http://dx.doi.org/10.3997/2214-4609.201413682.

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Titov, K., B. Mehalli, G. Gurin, and A. Tarasov. "Induced Polarization of ion-conducting porous media: A review of mathematical models. Pt.2. Granular and capillary models." In NSG2021 27th European Meeting of Environmental and Engineering Geophysics. European Association of Geoscientists & Engineers, 2021. http://dx.doi.org/10.3997/2214-4609.202120247.

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Reports on the topic "Mathematical geophysics"

1

Perdigão, Rui A. P. Earth System Dynamic Intelligence - ESDI. Meteoceanics, April 2021. http://dx.doi.org/10.46337/esdi.210414.

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Earth System Dynamic Intelligence (ESDI) entails developing and making innovative use of emerging concepts and pathways in mathematical geophysics, Earth System Dynamics, and information technologies to sense, monitor, harness, analyze, model and fundamentally unveil dynamic understanding across the natural, social and technical geosciences, including the associated manifold multiscale multidomain processes, interactions and complexity, along with the associated predictability and uncertainty dynamics. The ESDI Flagship initiative ignites the development, discussion and cross-fertilization of novel theoretical insights, methodological developments and geophysical applications across interdisciplinary mathematical, geophysical and information technological approaches towards a cross-cutting, mathematically sound, physically consistent, socially conscious and operationally effective Earth System Dynamic Intelligence. Going beyond the well established stochastic-dynamic, information-theoretic, artificial intelligence, mechanistic and hybrid techniques, ESDI paves the way to exploratory and disruptive developments along emerging information physical intelligence pathways, and bridges fundamental and operational complex problem solving across frontier natural, social and technical geosciences. Overall, the ESDI Flagship breeds a nascent field and community where methodological ingenuity and natural process understanding come together to shed light onto fundamental theoretical aspects to build innovative methodologies, products and services to tackle real-world challenges facing our planet.
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Perdigão, Rui A. P. New Horizons of Predictability in Complex Dynamical Systems: From Fundamental Physics to Climate and Society. Meteoceanics, October 2021. http://dx.doi.org/10.46337/211021.

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Discerning the dynamics of complex systems in a mathematically rigorous and physically consistent manner is as fascinating as intimidating of a challenge, stirring deeply and intrinsically with the most fundamental Physics, while at the same time percolating through the deepest meanders of quotidian life. The socio-natural coevolution in climate dynamics is an example of that, exhibiting a striking articulation between governing principles and free will, in a stochastic-dynamic resonance that goes way beyond a reductionist dichotomy between cosmos and chaos. Subjacent to the conceptual and operational interdisciplinarity of that challenge, lies the simple formal elegance of a lingua franca for communication with Nature. This emerges from the innermost mathematical core of the Physics of Coevolutionary Complex Systems, articulating the wealth of insights and flavours from frontier natural, social and technical sciences in a coherent, integrated manner. Communicating thus with Nature, we equip ourselves with formal tools to better appreciate and discern complexity, by deciphering a synergistic codex underlying its emergence and dynamics. Thereby opening new pathways to see the “invisible” and predict the “unpredictable” – including relative to emergent non-recurrent phenomena such as irreversible transformations and extreme geophysical events in a changing climate. Frontier advances will be shared pertaining a dynamic that translates not only the formal, aesthetical and functional beauty of the Physics of Coevolutionary Complex Systems, but also enables and capacitates the analysis, modelling and decision support in crucial matters for the environment and society. By taking our emerging Physics in an optic of operational empowerment, some of our pioneering advances will be addressed such as the intelligence system Earth System Dynamic Intelligence and the Meteoceanics QITES Constellation, at the interface between frontier non-linear dynamics and emerging quantum technologies, to take the pulse of our planet, including in the detection and early warning of extreme geophysical events from Space.
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