A Practical Understanding of Inversion for Exploration Geophysics

by John Bancroft

Duration: Two days

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.


There is confusion in the exploration geophysics industry regarding inversion, and it is often surrounded in mystifying mathematics that obscures any meaning to the common geophysicist. Many of us have taken linear algebra courses that lead into inversion, but are never able to make the mystifying leap to understand the applications or usefulness of inversion. To compound the problem there are topics that appear to mean the same thing, but are unrelated such as least squares migration (LSM) and full waveform inversion (FWI).

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).

  • Objectives
  • Introduction to Inversion
  • Review of Matrix theory
  • The forward Model
  • The inverse process
  • Common Inversion Processes in Geophysics
  • Least Squares Migration
  • 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