A Practical Understanding of Inversion for Exploration Geophysics

John Bancroft

The course will present the basic methods of seismic inversion in a simple manner and use diagrams and figures to illustrate the principles.  Some mathematics will be used and explained with images where possible.  The course will begin with simple examples of inversion processes and end with a short discussion on Full Waveform Inversion (FWI). Inversions are often approximated with processes that are referred to as transpose processes.

A number of related topics will be discussed that do affect the quality of seismic processes, e.g.,

  • Forward Modelling
  • Deconvolution
  • Statics analysis
  • Noise attenuation
  • Imaging
  • Time verses depth migration
  • Inversion verses migration

The mathematics with use linear algebra to discuss the relationship between transpose and inversions, and many examples will illustrate process using simple matrices.


8 hours

Intended Audience

The course is designed for all levels from entry to advanced.

Prerequisites (Knowledge/Experience/Education Required)

This course is designed to be followed by anyone with a broad knowledge of seismic processing. Basic knowledge of linear algebra will be an advantage, but is not necessary. Most of the principles will be presented with extensive illustrations.

Course Outline

It is the intent of this course to de-mystify inversion by relating the mathematics to simplifying examples and figures to identify and review many of the applications in exploration geophysics.

The course will identify what is meant by inversion and review the fundamentals of linear algebra with a visual emphasis on inversion techniques. The various applications of inversion follow: such as deconvolution, surface consistent methods, tomography, least-squares-migration (LSM), seismic inversion, and full waveform inversion (FWI).

  1. Objectives
  2. Introduction to Inversion
  3. Review of Matrix theory
  4. The forward Model
  5. The inverse process
  6. Common Inversion Processes in Geophysics
  7. Least Squares Migration
  8. Full Waveform Inversion

At the end of the course the participants will be able to identify and then communicate effectively with authority on the various inversion processes that are used in geophysics. Sufficient material is included as primers for those who desire to pursue and implement the various method of inversion.

Learner Outcomes

At the end of the course the participants will be able to

  • Identify the various geophysical application of inversion
  • Communicate effectively and with authority on the various inversion processes
  • Appreciate the mathematics behind inversion
  • Know how to pursue and then implement the various method of inversion

Instructor Biography

John Bancroft