A Student's Guide to Geophysical Equations

A Student's Guide to Geophysical

The advent of accessible student computing packages has meant that geophysics students can now easily manipulate datasets and gain first-hand modeling experience - essential in developing an intuitive understanding of the physics of the Earth. Yet to gain a more in-depth understanding of physical theory, and to develop new models and solutions, it is necessary to be able to derive the relevant equations from first principles. This compact, handy book fills a gap left by most modern geophysics textbooks, which generally do not have space to derive all of the important formulae, showing the intermediate steps. This guide presents full derivations for the classical equations of gravitation, gravity, tides, earth rotation, heat, geomagnetism and foundational seismology, illustrated with simple schematic diagrams. It supports students through the successive steps and explains the logical sequence of a derivation - facilitating self-study and helping students to tackle homework exercises and prepare for exams.

  • ASIN: 0521183774

Full Seismic Waveform Modelling and Inversion (Advances in Geophysical and Environmental Mechanics and Mathematics Book 2)

Full Seismic Waveform Modelling and Inversion (Advances in

Recent progress in numerical methods and computer science allows us today to simulate the propagation of seismic waves through realistically heterogeneous Earth models with unprecedented accuracy. Full waveform tomography is a tomographic technique that takes advantage of numerical solutions of the elastic wave equation. The accuracy of the numerical solutions and the exploitation of complete waveform information result in tomographic images that are both more realistic and better resolved. This book develops and describes state of the art methodologies covering all aspects of full waveform tomography including methods for the numerical solution of the elastic wave equation, the adjoint method, the design of objective functionals and optimisation schemes. It provides a variety of case studies on all scales from local to global based on a large number of examples involving real data. It is a comprehensive reference on full waveform tomography for advanced students, researchers and professionals.

  • ASIN: B00F76R6ZE

Geophysical Data Analysis: Discrete Inverse Theory

Geophysical Data Analysis: Discrete Inverse

Geophysical Data Analysis: Diverse Inverse Theory, Fourth Edition is a revised and expanded introduction to inverse theory and tomography as it is practiced by geophysicists. It demonstrates the methods needed to analyze a broad spectrum of geophysical datasets, with special attention to those methods that generate images of the earth. Data analysis can be a mathematically complex activity, but the treatment in this volume is carefully designed to emphasize those mathematical techniques that readers will find the most familiar and to systematically introduce less-familiar ones. Using problems and case studies, along with MATLAB computer code and summaries of methods, the book provides data scientists and engineers in geophysics with the tools necessary to understand and apply mathematical techniques and inverse theory.Includes material on probability, including Bayesian influence, probability density function and metropolis algorithmOffers detailed discussion of the application of inverse theory to tectonic, gravitational and geomagnetic studiesContains numerous examples, color figures and end-of-chapter homework problems to help readers explore and further understand presented ideas Includes MATLAB examples and problem setsUpdated and refined throughout to bring the text in line...

  • ASIN: 0128135557

Shallow Geophysical Mass Flows down Arbitrary Topography: Model Equations in Topography-fitted Coordinates, Numerical Simulation and Back-calculations ... Environmental Mechanics and Mathematics)

Shallow Geophysical Mass Flows down Arbitrary Topography: Model

Geophysical mass flows, such as landslides, avalanches or debris flows, are frequent mass movement processes in mountain areas and often cause disastrous damage. This book lays a foundation for formulating the depth-averaged equations describing the shallow geophysical mass flows over non-trivial topography. It consists of the detailed derivation of the model equations. The stimulating numerical examples demonstrate how the proposed models are applied. All this make this book accessible to a wide variety of readers, especially senior undergraduate and graduate students of fluid mechanics, civil engineering, applied mathematics, engineering geology, geophysics or engineers who are responsible for hazard management.


Global Optimization Methods in Geophysical Inversion

Global Optimization Methods in Geophysical

Providing an up-to-date overview of the most popular global optimization methods used in interpreting geophysical observations, this new edition includes a detailed description of the theoretical development underlying each method and a thorough explanation of the design, implementation and limitations of algorithms. New and expanded chapters provide details of recently developed methods, such as the neighborhood algorithm, particle swarm optimization, hybrid Monte Carlo and multi-chain MCMC methods. Other chapters include new examples of applications, from uncertainty in climate modeling to whole earth studies. Several different examples of geophysical inversion, including joint inversion of disparate geophysical datasets, are provided to help readers design algorithms for their own applications. This is an authoritative and valuable text for researchers and graduate students in geophysics, inverse theory and exploration geoscience, and an important resource for professionals working in engineering and petroleum exploration.

  • ASIN: 1107011906

Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models

Geophysical Fluid Dynamics: Understanding (almost) everything with rotating

Geophysical fluid dynamics examines the dynamics of stratified and turbulent motion of fluids in the ocean and outer core, and of gases in the atmosphere. This book explains key notions and fundamental processes of the dynamics of large- and medium-scale atmospheric and oceanic motions from the unifying viewpoint of the rotating shallow water model. The model plays a distinguished role in geophysical fluid dynamics. It has been used for about a century for conceptual understanding of various phenomena, for elaboration of approaches and methods to be used later in more complete models, for development and testing of numerical codes, and for many other purposes. In spite of its simplicity, the model grasps essential features of the complete "primitive equations" models, being their vertically averaged version, and gives an intuitive representation and clear vision of principal dynamical processes.This book is a combination of a course on geophysical fluid dynamics (Part 1), with explanations and illustrations of fundamentals, and problems, as well as a more advanced treatise of a range of principal dynamical phenomena (Part 2), including recently arisen approaches and applications (Part 3). Mathematics and physics underlying dynamical phenomena are explained, with necessary demonst...

  • ASIN: 0198804334

Fluid and Thermodynamics: Volume 1: Basic Fluid Mechanics (Advances in Geophysical and Environmental Mechanics and Mathematics)

Fluid and Thermodynamics: Volume 1: Basic Fluid Mechanics

This first volume discusses fluid mechanical concepts and their applications to ideal and viscous processes. It describes the fundamental hydrostatics and hydrodynamics, and includes an almanac of flow problems for ideal fluids. The book presents numerous exact solutions of flows in simple configurations, each of which is constructed and graphically supported. It addresses ideal, potential, Newtonian and non-Newtonian fluids. Simple, yet precise solutions to special flows are also constructed, namely Blasius boundary layer flows, matched asymptotics of the Navier-Stokes equations, global laws of steady and unsteady boundary layer flows and laminar and turbulent pipe flows. Moreover, the well-established logarithmic velocity profile is criticised.

  • ASIN: 3319336320

Analysis of the Navier-Stokes Equations for Geophysical Boundary Layers

Analysis of the Navier-Stokes Equations for Geophysical Boundary

The Navier-Stokes equations are the fundamental model for the mathematical analysis of incompressible viscous fluids. In this text, a modification of this system of partial differential equations representing the situation of geophysical flows is investigated. An important mathematical model of geophysical boundary layers is the Ekman spiral, which is a stationary solution of the modified Navier-Stokes equations. Its long-time behaviour is of certain interest in natural sciences. Here, the stability of the Ekman spiral is shown in three-dimensional halfspaces and infinite layers in the case of a small Reynolds number of the according hydrodynamical system. The problem of maximal regularity of the Stokes operator in bounded and exterior domains with smooth boundary is also discussed

  • ASIN: 3832523049

Geophysical Data Analysis: Discrete Inverse Theory, Volume 45: MATLAB Edition (International Geophysics)

Geophysical Data Analysis: Discrete Inverse Theory, Volume 45:

Since 1984, Geophysical Data Analysis has filled the need for a short, concise reference on inverse theory for individuals who have an intermediate background in science and mathematics. The new edition maintains the accessible and succinct manner for which it is known, with the addition of: MATLAB examples and problem setsAdvanced color graphicsCoverage of new topics, including Adjoint Methods; Inversion by Steepest Descent, Monte Carlo and Simulated Annealing methods; and Bootstrap algorithm for determining empirical confidence intervalsAdditional material on probability, including Bayesian influence, probability density function, and metropolis algorithmDetailed discussion of application of inverse theory to tectonic, gravitational and geomagnetic studiesNumerous examples and end-of-chapter homework problems help you explore and further understand the ideas presentedUse as classroom text facilitated by a complete set of exemplary lectures in Microsoft PowerPoint format and homework problem solutions for instructors

  • Brand: Brand: Academic Press
  • ASIN: 0123971608

The Boundary Element Method in Geophysical Survey (Innovation and Discovery in Russian Science and Engineering)

The Boundary Element Method in Geophysical Survey (Innovation

This volume is devoted to the application of the integral equations method (IEM) and boundary elements method (BEM) to problems involving the sounding of geological media using direct current (DC). Adaptive mesh generation algorithms and numerical methods for solving a system of integral equations are discussed. Integral equations for the media, which contains piecewise linear contact boundaries, immersed local inclusions, and subsurface relief, are derived and solved numerically. Both 2.5D and 3D models with ground surface relief are considered. For 2D conductivity distributions, the influence of the relief on the interpretation of results is shown.  Search solutions of the direct problem with ground surface relief are compared using the appropriate interpretation of results based on different inversion programs. 

  • ASIN: 3319729071
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