Most of our knowledge about the physical structure and the chemical composition of the Earth's deep interior is inferred from seismic data. The interpretation of seismic waves generally follows the assumption that the Earth's physical structure is grossly layered and that fluctuations of the physical parameters within individual layers are smooth in structure and small in magnitude. While this view greatly facilitates the analytic and interpretative procedure, it is clearly at odds with evidence from outcrops and boreholes, which indicates that compositional, structural and petrophysical heterogeneity in the Earth prevails over a wide range of scales.

This book is the first to unify three different views of crustal and upper mantle heterogeneity. It brings together the geological view, which is derived from the analysis of crustal exposures and deep boreholes; the stochastic view, which attempts to find order and structure in these seemingly chaotic data; and the seismological view, which considers the end product of the complex interaction of seismic energy with the heterogeneous structure at depth. John Goff and Klaus Holliger have compiled chapters that explore and quantify the relationship between geological and petrophysical heterogeneity and its seismic response, and use seismic data to probe the fabric of the Earth's interior. Geologists, geostaticians, and geophysicists alike will benefit from the integrative perspective presented in Heterogeneity in the Crust and Upper Mantle: Nature, Scaling, and Seismic Properties, making this text an unparalleled reference for professionals and students in Earth science fields.

Most of our knowledge about the physical structure and the chemical composition of the Earth's deep interior is inferred from seismic data. The interpretation of seismic waves generally follows the assumption that the Earth's physical structure is grossly layered and that fluctuations of the physical parameters within individual layers are smooth in structure and small in magnitude. While this view greatly facilitates the analytic and interpretative procedure, it is clearly at odds with evidence from outcrops and boreholes, which indicates that compositional, structural and petrophysical heterogeneity in the Earth prevails over a wide range of scales. This book is the first to unify three different views of crustal and upper mantle heterogeneity. It brings together the geological view, which is derived from the analysis of crustal exposures and deep boreholes; the stochastic view, which attempts to find order and structure in these seemingly chaotic data; and the seismological view, which considers the end product of the complex interaction of seismic energy with the heterogeneous structure at depth. John Goff and Klaus Holliger have compiled chapters that explore and quantify the relationship between geological and petrophysical heterogeneity and its seismic response, and use seismic data to probe the fabric of the Earth's interior. Geologists, geostaticians, and geophysicists alike will benefit from the integrative perspective presented in Heterogeneity in the Crust and Upper Mantle: Nature, Scaling, and Seismic Properties, making this text an unparalleled reference for professionals and students in Earth science fields.

B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory:* Aapproximation methods (mathematics).* Modeling techniques (engineering).* Geometric algorithms (computer science). supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.

The finite element method (FEM) has become the most widely accepted general-purpose technique for numerical simulations in engineering and applied mathematics. Principal applications arise in continuum mechanics, fluid flow, thermodynamics, and field theory. In these areas, computational methods are essential and benefit strongly from the enormous advances in computer technology. B-splines play an important role in approximation and geometric modeling. They are used in data fitting, computer-aided design (CAD), automated manufacturing (CAM), and computer graphics. Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for B-splines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples. The text is essentially self-contained and easily accessible to graduate students in mathematics, engineering, and computer sciences. The new concepts are also of interest to academic researchers and to scientists in industry who are developing finite element software. Some basic facts on functional analysis and partial differential equations, which are required, are listed in the appendix.

Dieses Buch bietet Ihnen eine UEbersicht aller fundamentalen Problemstellungen in UEbungs- und Klausuraufgaben der Mathematikgrundvorlesungen fur Ingenieure, Natur- und Wirtschaftswissenschaftler. Es enthalt eine Auswahl von mehr als 400 typischen Aufgaben, gegliedert in 50 Themengebiete, mit detaillierten Loesungsskizzen und Beschreibungen der relevanten mathematischen Methoden. Zusatzliche Beispiele und Erlauterungen finden Sie in einer auf das Buch abstimmten internetbasierten Sammlung von Lehrmaterialien, die auch von Dozenten in ihren Vorlesungen verwendet werden kann. Im E-Book sind zu den Aufgaben passende Inhalte verlinkt; mit einem Klick koennen Sie unmittelbar auf benoetigte Definitionen und Formeln zugreifen. Des Weiteren stehen im Internet-Portal Mathematik-Online Aufgabenvarianten zur Verfugung, um die Beherrschung der erlernten Techniken online zu uberprufen und sich in Verbindung mit dem Buch optimal auf Prufungen vorzubereiten.