Computational Geosciences with Mathematica is the only book written by a geologist specifically to show geologists and geoscientists how to use Mathematica to formulate and solve problems. It spans a broad range of geologic and mathematical topics, which are drawn from the author's extensive experience in research, consulting, and teaching. The reference and text leads readers step-by-step through geologic applications such as custom graphics programming, data input and output, linear and differential equations, linear and nonlinear regression, Monte Carlo simulation, time series and image analysis, and the visualization and analysis of geologic surfaces. It is packed with actual Mathematica output and includes boxed Computer Notes with tips and exploration suggestions.

Shows geologists and geoscientists how to use Mathematica to formulate and solve problems. Leads step-by-step through geologic applications such as custom graphics programming, data input and output, linear and differential equations, linear and nonlinear regression, Monte Carlo simulation, time series and image analysis, and the visualization and analysis of geologic surfaces. Includes Mathematica output and boxed Computer Notes with tips and exploration suggestions. The accompanying CD-ROM contains notebooks of all text and graphics, plus an appendix on color graphics and specialized functions.

This book showcases powerful new hybrid methods that combine numerical and symbolic algorithms. Hybrid algorithm research is currently one of the most promising directions in the context of geosciences mathematics and computer mathematics in general. One important topic addressed here with a broad range of applications is the solution of multivariate polynomial systems by means of resultants and Groebner bases. But that’s barely the beginning, as the authors proceed to discuss genetic algorithms, integer programming, symbolic regression, parallel computing, and many other topics. The book is strictly goal-oriented, focusing on the solution of fundamental problems in the geosciences, such as positioning and point cloud problems. As such, at no point does it discuss purely theoretical mathematics. "The book delivers hybrid symbolic-numeric solutions, which are a large and growing area at the boundary of mathematics and computer science." Dr. Daniel Li chtbau

This monograph aims to provide state-of-the-art numerical methods, procedures and algorithms in the field of computational geoscience, based on the authors’ own work during the last decade. Although some theoretical results are provided to verify numerical ones, the main focus of this monograph is on computational simulation aspects of the newly-developed computational geoscience discipline. The advanced numerical methods, procedures and algorithms presented are also applicable to a wide range of problems in both geological length-scales and engineering length-scales. In order to broaden the readership, common mathematical notations are used to describe the theoretical aspects of geoscience problems, making it either an invaluable textbook for postgraduate students or an indispensable reference book for computational geoscientists, mathematicians, engineers and geoscientists.

Computational Challenges in the Geosciences addresses a cross-section of grand challenge problems arising in geoscience applications, including groundwater and petroleum reservoir simulation, hurricane storm surge, oceanography, volcanic eruptions and landslides, and tsunamis. Each of these applications gives rise to complex physical and mathematical models spanning multiple space-time scales, which can only be studied through computer simulation. The data required by the models is often highly uncertain, and the numerical solution of the models requires sophisticated algorithms which are mathematically accurate, computationally efficient and yet must preserve basic physical properties of the models. This volume summarizes current methodologies and future research challenges in this broad and important field.

MATLAB® is used in a wide range of geoscientific applications, e.g. for image processing in remote sensing, for creating and processing digital elevation models, and for analyzing time series. This book introduces readers to MATLAB-based data analysis methods used in the geosciences, including basic statistics for univariate, bivariate and multivariate datasets, time-series analysis, signal processing, the analysis of spatial and directional data, and image analysis. The revised and updated Fifth Edition includes seven new sections, and the majority of the chapters have been rewritten and significantly expanded. New sections include error analysis, the problem of classical linear regression of log-transformed data, aligning stratigraphic sequences, the Normalized Difference Vegetation Index, Aitchison’s log-ratio transformation, graphical representation of spherical data, and statistics of spherical data. The book also includes numerous examples demonstrating how MATLAB can be used on datasets from the earth sciences. The supplementary electronic material (available online through SpringerLink) contains recipes that include all the MATLAB commands featured in the book and the sample data.

MATLAB® is used in a wide range of applications in geosciences, such as image processing in remote sensing, generation and processing of digital elevation models and the analysis of time series. This book introduces methods of data analysis in geosciences using MATLAB such as basic statistics for univariate, bivariate and multivariate datasets, jackknife and bootstrap resampling schemes, processing of digital elevation models, gridding and contouring, geostatistics and kriging, processing and georeferencing of satellite images, digitizing from the screen, linear and nonlinear time-series analysis and the application of linear time-invariant and adaptive filters. The revised and updated Second Edition includes new subchapters on windowed Blackman-Tukey, Lomb-Scargle and Wavelet powerspectral analysis, statistical analysis of point distributions and digital elevation models, and a full new chapter on the statistical analysis of directional data. The text includes a brief description of each method and numerous examples demonstrating how MATLAB can be used on data sets from earth sciences. All MATLAB recipes can be easily modified in order to analyse the reader's own data sets.