Data analysis and model inversion in Python for Geosciences

Course Description

This course offers a theoretical and practical introduction to data analysis methods for geoscientific problem solving. It emphasizes two main areas: time series analysis, and model building through inverse theory. A short pre-recorded introduction to statistical analysis and statistical distributions will be provided. 

The first part focuses on time series analysis, a fundamental tool in geophysics for studying temporal or spatial sequences. Topics include spectral analysis and Fourier methods, with applications such as power spectral estimation, correlation, and deconvolution. Real data sets include DAS signals, global seismic and magnetic data.

The course follows with an introduction to model development and inverse theory. Students will learn how to construct idealized Earth models that generate synthetic data, and how to estimate model parameters from observations using least-squares methods with regularization and constraints.

Throughout the course, theoretical concepts are reinforced with hands-on practice. Students will work with real datasets, develop coding skills, and implement data analysis techniques in Python to interpret results in a geoscientific context.

Course Outline

Day 1

Part I

- Time Series Analysis

- Introduction to time (spatial) series 

- Fourier Methods

- Multitaper methods

Part 2

- Time Series Analysis

- Univariate spectral analysis

       - Power spectral density estimation

       - Confidence intervals

- Multivariable spectral analysis      

       - Correlation and Deconvolution      

       - Array processing

Day 2

Part 3

- Inverse Theory I

- Basic concepts of inverse theory

- Introduction to Linear Algebra

- Numerical solution to linear inverse problems

Part 3 

- Inverse Theory II

- Regularization

- Constrained inverse problems

- Non-linear inverse problems

Participants’ Profile

Geoscientists and geo-engineers that want to learn or improve their practical application of numerical methods to analyze earth science data sets, time or spatial series.

Prerequisites

Students should have a basic knowledge of Python, being able to load data, use Numpy arrays and make graphs. 

About the Instructor

German Prieto received his undergraduate degree in Geology at the Universidad Nacional de Colombia, later getting his MSc (2004) and PhD (2007) at UC San Diego, Scripps Institution of Oceanography.  Currently he is an Associate professor at Universidad Nacional (since 2017) with previous appointments as a Thompson Postdoctoral Fellow at Stanford University (2007-2009), an Assistant Professor at Universidad de los Andes (2009-2013) and later at MIT (2013-2016). 

Dr. Prieto's research interests include earthquake seismology, seismic tomography, subduction zones, earthquake engineering and tectonics of NW South America.  German Prieto has published more than 60 papers on various topics in geophysics and is developer of the Multitaper Spectrum Analysis codes that are often used in seismology. He is also Editor at Geophysical Research Letters.