Objectives:
Within the earth sciences it is fundamental to obtain models that can explain our observed data. This process is called inversion. Before inversion it is often necessary to prepare and analyze the data.

A superior goal of the course is that the student shall attain a general overview of different analyses and inversion methods common in the earth sciences. As specific goals the student is expected to 1) conduct analysis/inversion on different types of geodata using MATLAB and other suitable computer software, 2) summarize observations, data, and methodological principles orally and in writing, 3) interpret and make decisions based on results from analysis and inversion

Content:
The course yields a general overview of different types of analyses and inversion methods common in the earth sciences. Moreover, the course goes into to depth within specific topics with associated applications (see list below). Topics and applications will be weighted according to the background of the students.

Data analysis
Topics and examples of methods/applications:

• Signal processing
  - Application of Fourier transformations on traces from reflection seismic and seismology
  - Processing of time series data from geology
• Automated recognition of data elements
  - Seismic interpretation of horizon data
  - Classic seismic velocity analysis
• Transformation of data between domains
  - Seismic imaging
• Parameterization of data and models
  - Preparing data and models for specific applications in modelling, data transformations, and inversion
  - Smoothing of attributes along geological surfaces

Inversion
Topics and examples of methods/applications:

• Explicit inversion
  - Time-to-depth conversion of reflection seismic data with joint velocity estimation
• Linear inversion
• Iterative linearized inversion
  - Classic transmission tomography in crosswell seismic and in global seismology
  - Seismic reflection tomography
  - Localization of earthquakes and determination of earthquake mechanisms
• Global optimization techniques
• Regularization and constraints

Exercises with MATLAB in combination with other computer software have a fundamental role in the teaching. The students are working with the exercises individually and in teams.

On completion of the course the student should have the following learning outcomes defined in terms of knowledge, skills and general competence:
Knowledge
The student can

• elaborate on different types of methodology that can be used for analysis and inversion on geodata
• explain fundamental concepts, definitions, and theories
• discuss types of analyses and inversion techniques that are appropriate for different types of data
• show insight with respect to how different computer applications may be combined for the purpose of analysis/inversion

Skills
The student

• can conduct analysis and inversion on different types of geodata, using MATLAB and other suitable computer software. In particular, the student shall be able to
  - code a small-scale linear inversion algorithm including regularization and constraints
  - do basic processing operations on time series data
• can summarize observations, data, and methodological principles orally and in writing
• can interpret and make decisions based on results from analysis and inversion

General competence
The student can

• communicate the importance of applying advanced methods and software, within a specialized work environment and in a general context
• apply and combine different types of computer programs to solve a complex task
• demonstrate ability to function well individually and in a team

• Linear algebra
• Calculus
• Computer programming (MATLAB or similar)

Mandatory participation in all classes assigned to exercises

Mandatory handing in of all exercises

Mandatory participation at seminar

The compulsory assignments are valid for a total of two semesters, including the teaching semester.

• Delivered exercises
• Seminar
• Written exam, 4 hours (counts 50% on the final grade)

The Faculty for Mathematics and Natural Sciences, Department of Earth Science has the administrative responsibility for the course and program