Abstract Characterisation of crustal magnetic anomalies can yield valuable insights into the current state and history of a planet’s interior. Such characterisation often involves inversion modelling, which relies on mathematical expressions that relate the observable magnetic field to the geometry and magnetisation of the obscured source bodies. Here, I revisit the magnetised rectangular prism—a natural building block for crustal source modelling. Although the core expressions can be found in previous work, I offer a more generalised, matrix-based formulation for computing the 3D vector magnetic field while also emphasising a geometric interpretation that can be helpful for building physical intuition. This approach allows for arbitrary prism orientation and magnetisation direction while separating the roles of the source geometry and the magnetisation vector. This separation clarifies the mathematical relationships and can improve computational efficiency in inversion studies. I focus on the relationships between source geometry, magnetisation direction, and the resulting magnetic field structure in both two and three dimensions, highlighting symmetries, simplifications, and diagnostic features that can aid in the interpretation of survey data. The accompanying open-source Matlab software (MagTools) provides a transparent implementation of this framework.
D J Hemingway (Thu,) studied this question.