Mathematical Methods in Geophysics is an introductory text focusing on the mathematics and statistical methods used by geophysicists. The book is aimed at upper level undergraduates, graduate students, and professionals in geophysics and related fields. The first half of the book introduces important mathematical concepts including tensor analysis, Fourier transforms, least squares fitting, and eigenvalue problems. The second half of the book introduces statistical concepts including probability theory, maximum likelihood theory, and Bayesian inference.

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Mathematical Methods in Geophysics

A concise introduction to modern mathematical methods applied to geophysical data and to the mathematical theory of geophysical processes. The book provides an introduction and a unified treatment of the main mathematical methods used in geophysics. Readers are assumed to have no knowledge of advanced mathematics beyond what is conventionally taught at high school level, with the exception of some elementary calculus. The book is written for undergraduate students who want to prepare for more advanced work, for graduate students who need a wider background than that provided by the courses they have taken, and for researchers who want a concise reference text. It is also useful for those working in other fields of science where similar mathematical methods are used.

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The emergence of machine learning as a field, and the rise of big data and related technologies, are transforming many aspects of science and society, with geoscience being no exception.

The goal of this blog is to provide some insights into the interplay between mathematics, statistics and machine learning, including their applications in geoscience.

Topics covered include:

- Applications of statistical learning methods in geoscience
- Mathematics underpinning key machine learning methods
- Interpretability and explainability of artificial neural networks (ANNs)
- Interpretation of deep learning models in earth sciences
- Transfer learning and domain adaptation for geosciences

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