Quantitative Methods for Earth Scientists
Period: first semester
Course unit contents:
1) Introduction to computer programming: Low-level and high-level programming languages. Introduction to MATLAB interface. Basic programming rules/syntax. For/While loops. IF/ELSE conditional statements. Relational, logical, arithmetic operators. Trigonometric, exp, log functions. Variable formats. Scalars, vectors, Tensors and their diagonalization (eigen vectors/values). Variables, Arrays, Structures
2) Data file format and processing: File formats (CSV, ascii, binary, HDF5, mat). File compression (zip, tarballs). File read and write in low-level and high-level file formats. Images/Videos format and processing
3) Statistical analysis: Univariate and bivariate methods for data analysis. Probabilistic treatment of geological data. Frequency and Probability Functions. Describing Datasets. Using statistics to summarize datasets. Fitting a Probability Distribution (on actual data provided by students and/or colleagues of other courses). Probability Distributions for relevant variables for earth scientists. Regression analysis (covariance and correlation, correlation coefficient, linear and non-linear regression). Time series analysis (Fast Fourier Transform and its applications)
4) AI/Machine Learning analysis: Cluster analysis with applications. Image recognition with applications.
5) Basics of numerical methods and applications: Resolution of linear systems of equations. Introduction to the numerical solution of ordinary and partial differential equations. Discretization methods (FDM, FEM, FVM, SM). Thermo-mechanical modeling. Petrological-geochemical modeling. Seismological Modeling. Solving a 1D diffusion problem with FDM.
Planned learning activities and teaching methods: Lectures complemented by tutorials, assignments, exercises and laboratory activities. Students are required to work on computer implementation of the techniques developed during the course lectures to solve practical problems suggested by the lecturer.
Frontal lectures (4 CFU = 32h)
Class laboratories (2 CFU = 16h)