Content

Earth Sciences is particularly rich in data. To infer processes from this data, advanced processing and optimization techniques are required. Raw data can hide the specific information one is interested in and data processing becomes necessary. We will review the fundamentals of geophysical data processing, starting with a detailed description of sampling continuous functions and progressing to the corresponding discrete Fourier transform. We will introduce the important concept of convolution and present linear filter theory. In the following, simple linear inverse and optimization theory will be discussed and the classical techniques will be introduced. We will show how to design optimal filters using basic inverse theory. The lectures will finish with a small introduction to machine learning. During the course and especially in the computer practicals, examples will be taken from various fields of geophysics.

Course notes and books

I will not follow any particular book. All you'll need are your class notes (my notes are available on 'Blackboard'). However, most of what I will cover can be found in 'Fundamentals of Geophysical Data Processing' from Jon Claerbout's web page and in the book 'Inverse Problem Theory' from Albert Tarantola's web page. I have PowerPoint files on the data processing part and notes on inverse theory part, which will be made available through Blackboard.

Lectures and practicals

We will meet twice a week, Tuesdays from 9h00-11h00 and Thursdays from 13h15-15h15 in various rooms assigned to us. The course will be followed by a 2 hour computer class where you will learn to put theory into practice. All computer exercises are in Python. Below is a provisional planning of the topics I will cover. The schedule and room planning can be found on 'MyTimetable'.

Week 37: Properties of the continuous Fourier transform, convolution and correlation Week 38: Sampling of continuous functions and discrete Fourier transform
Week 39: Linear filters, Z-transform and filter design
Week 40: Deconvolution and predictive filters. Time-frequency analysis
Week 41: Least-squares / minimum norm solutions to inverse problems
Week 42: Generalised least-squares
Week 43: Singular value decomposition
Week 44: Introduction to machine learning

Previous exams

You might want to try and answer questions from previous exams (see 'Blackboard'). An extra class will be organised in week 45 dedicated to general questions and solutions to the previous exam questions. The exam will be in week 45 (check room and time in 'MyTimetable' !) and will count for 70% of the mark. You will have to hand in reports concerning the computer classes. You will get an overall mark for your practical work, which will count for 30% of the final mark. Additional information on this course can be found in the study guide available on 'Blackboard'.