Signal analysis and inversion in the earth sciences

Undergraduate course

Course description

Objectives and Content


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 Python 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


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

Learning Outcomes

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


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


The student

  • can conduct analysis and inversion on different types of geodata, using Python 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
Required Previous Knowledge
The student is required to have basic skills in
  • Linear algebra
  • Calculus
  • Computer programming (Python or similar)
Recommended Previous Knowledge
It is preferable if the student has some previous knowledge within reflection seismic, seismology, and general computational algorithms.
Access to the Course
Access to the course requires admission to a program of study at The Faculty of Mathematics and Natural Sciences.
Teaching and learning methods
The teaching consists of lectures, exercises, and a seminar.
Compulsory Assignments and Attendance

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.

Forms of Assessment
The following forms of assessment are used in the course:
  • Delivered exercises (counts 35 % of the grade
  • Oral exam (counts 50% on the final grade)
  • Presentation (15 % of the final grade)
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.
Assessment Semester
Assessment is offered only in the actual semester in which teaching is given.
Reading List
The reading list will be available within July 1st for the autumn semester and December 1st for the spring semester.
Course Evaluation
The course will be evaluated by the students in accordance with the quality assurance system at UiB and the department
Examination Support Material
Programme Committee
The Programme Committee is responsible for the content, structure and quality of the study programme and courses.
Course Coordinator
The course coordinator and administrative contact person can be found on Mitt UiB, or you may contact
Course Administrator
The Faculty for Mathematics and Natural Sciences, Department of Earth Science has the administrative responsibility for the course and program