Question 9 of 10: Forward and Inverse Modelling

Question 9: Forward and Inverse Modelling (16.66% of paper)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

The difference. Forward modelling starts from an assumed model — a specific geometry and set of physical-property values — and computes the geophysical response that model would produce, which is then compared by eye (or by a simple misfit measure) to the observed data, with the model adjusted by trial and error until an acceptable match is found. Inverse modelling works in the opposite direction: starting from the observed field data, an automated algorithm computes the model (or model perturbation) that best explains it, typically by iteratively minimizing an objective function combining data misfit with a regularization term that penalizes unrealistic model roughness or complexity.

Strengths and weaknesses of forward modelling. Strengths: direct and intuitive — the interpreter fully controls and understands every parameter in the model, and known geological constraints (drill intersections, mapped outcrop, a known structural style) can be built in exactly rather than only approximately honoured; well suited to testing a small number of specific geological hypotheses. Weaknesses: manual and time-consuming, especially in three dimensions or for a large dataset; inherently subjective (the interpreter's own prior assumptions strongly bias which models are even tried); provides no formal, quantitative measure of how well the final model actually fits the data relative to alternatives, nor any estimate of model uncertainty.

Strengths and weaknesses of inverse modelling. Strengths: objective and automated — capable of systematically searching a very large model space (voxel/3-D grid inversions with millions of cells) far beyond what manual forward modelling could attempt, and typically produces a quantitative data-misfit measure together with formal estimates of model resolution/uncertainty. Weaknesses: the underlying inverse problem is fundamentally NON-UNIQUE — many different models can fit the observed data equally well — so the result critically depends on the (somewhat arbitrary) choice of regularization, which tends to produce an overly SMOOTH model that under-resolves genuinely sharp geological boundaries; nonlinear inversions can also converge to a local, rather than the true global, minimum, and an interpreter who does not understand what constraints the chosen regularization is silently imposing risks treating an inversion artifact as real geology.

Example algorithms/programs. Forward: GM-SYS/Potent-style interactive 2-D/2.75-D gravity and magnetic forward-modelling packages, and EM plate-modelling programs such as Maxwell for time-domain EM anomalies. Inverse: the UBC-GIF voxel inversion codes (GRAV3D, MAG3D, DCIP3D) for potential-field and DC/IP data; RES2DINV/RES3DINV for resistivity/IP pseudosection inversion; and, for seismic data, velocity-model tomography and full-waveform inversion algorithms, alongside migration (itself a form of structural inversion).

Use in a geophysical program. The two approaches are most powerful used TOGETHER rather than as alternatives: an unconstrained inverse model is run first to obtain an objective, unbiased first image of the subsurface directly from the data with no prior geological assumption imposed; the interpreter then builds a simplified, geologically constrained FORWARD model informed both by that inverse image and by independent geological/drill constraints, iterating the forward model until it reproduces both the data and the known geology, which converts the inversion's mathematically valid but geologically generic result into a specific, defensible geological interpretation.