Geophysical Data Analysis: Discrete Inverse Theory

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 with current understanding and improved examples and case studiesExpanded sections to cover material, such as second-derivation smoothing and chi-squared tests not covered in the previous edition

1. Describing Inverse Problems 2. Some Comments on Probability Theory 3. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 1: The Length Method 4. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 2: Generalized Inverses 5. Solution of the Linear, Gaussian Inverse Problem, Viewpoint 3: Maximum Likelihood Methods 6. Nonuniqueness and Localized Averages 7. Applications of Vector Spaces 8. Linear Inverse Problems and Non-Gaussian Statistics 9. Nonlinear Inverse Problems 10. Factor Analysis 11. Continuous Inverse Theory and Tomography 12. Sample Inverse Problems 13. Applications of Inverse Theory to Solid Earth Geophysics