18-Geol-A7 Applied Geophysics · May 2018
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2018 — 04-Geol-A7 Applied Geophysics. Three-hour, closed-book exam; approved Casio or Sharp calculator permitted. The paper offers a choice of six of the following ten questions, each worth 16.66% of the total mark, and every question requires an essay-format answer — this is a genuinely all-essay sitting with no numeric data, formula sheet, or figure supplied in the source. All ten questions are answered below so the set stands as a complete study resource for choose-N-of-M exams.
Reference texts: Telford, Geldart & Sheriff, Applied Geophysics (2nd ed.) — the primary reference for every method touched in this paper (magnetics, seismic reflection, radiometrics, downhole resistivity, EM/IP, filtering, well logging, forward/inverse modelling); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration (3rd ed.) — survey planning, array geometry, data display; Blakely, Potential Theory in Gravity and Magnetic Applications — potential-field filtering and forward/inverse modelling (Q7, Q10); Selley & Sonnenberg, Elements of Petroleum Geology — well-logging tool context (Q8).
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.
Forward modelling starts from an assumed (hypothesized) subsurface model — geometry, physical property values — and computes the geophysical response that model would produce, using the governing physics directly (Newton's law of gravitation for gravity, Maxwell's equations for EM/magnetics, the wave equation for seismic). The modeller then compares the computed response with the observed data and manually adjusts the model, repeating (trial-and-error or "what-if" iteration) until an acceptable match is found.
Inverse modelling instead starts from the observed data and mathematically solves for the subsurface model (or model perturbation) that best explains it, automatically, using an optimization algorithm (typically minimizing a data-misfit objective function, often regularized/damped to control the well-known non-uniqueness of geophysical inversion) rather than manual trial-and-error.
Strengths and weaknesses of forward modelling. Strengths: the modeller retains full, direct control and geological judgement over every parameter, so a model can be built to honour specific known geological constraints (borehole intersections, mapped contacts) exactly and transparently; computation is straightforward (only the forward physics is needed, no optimization machinery). Weaknesses: slow and labour-intensive for complex 2-D/3-D models with many free parameters, since every adjustment is manual; the final model's quality depends heavily on the modeller's skill and is not guaranteed to be a best (or even a good) fit in any formal statistical sense.
Strengths and weaknesses of inverse modelling. Strengths: automated, efficient exploration of a large model-parameter space, and produces a formally "best-fit" (in a defined statistical sense) model along with some estimate of resolution/uncertainty; well suited to large, gridded 2-D/3-D data volumes where manual forward modelling would be impractical. Weaknesses: geophysical inverse problems are fundamentally non-unique (many different models can fit the same data equally well within noise), so the "best-fit" model is not necessarily the true or even the most geologically sensible one; requires careful choice of regularization/starting model/constraints to avoid physically or geologically implausible results, and can be a computational "black box" that obscures why a particular feature appears in the final model.
Example algorithms/programs. Forward modelling: GM-SYS/Oasis montaj 2-D gravity/magnetic forward modelling (interactive polygon-based models), Talwani's 2-D polygon gravity algorithm, finite-difference/finite-element forward EM or seismic modelling codes. Inverse modelling: the University of British Columbia UBC-GIF suite (GRAV3D, MAG3D, DCIP3D, E3D for smooth 3-D inversion of gravity/magnetics/resistivity-IP/EM respectively), Occam's-inversion 1-D MT/resistivity codes, seismic tomography and full-waveform inversion (FWI) packages.
Use in a geophysical study and example. The two approaches are complementary, not competing, and a typical study uses both in sequence: an initial inversion (e.g. UBC-GIF GRAV3D on a regional gravity dataset) produces a first, automated, unbiased 3-D density model highlighting candidate anomalous zones; the interpreter then builds a targeted forward model of the most promising zone, explicitly honouring known geology (an outcrop contact, a drill intersection, an assumed intrusion geometry) that the automated inversion could not directly incorporate as a hard constraint, refining the body's geometry/density by trial-and-error forward iteration until it matches both the observed anomaly and the known geological control — the inversion supplies the unbiased starting point and confirms nothing significant was missed regionally, while the forward model supplies the final, geologically-constrained, defensible target geometry used for a drill decision.
