04-Geol-B10 · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 04-Geol-B10-1 Gravity and Magnetic Fields, 2016-May. Closed book; no calculator permitted. All ten questions require an answer in essay format, with diagrams used wherever appropriate. The exam instructs "choose six (6) of the following ten (10) questions, the first six as they appear in the answer book will be marked, each of equal value".
Reference texts: Telford, Geldart & Sheriff, Applied Geophysics, 2nd ed. (physical properties ch.2 & 5; gravimeters and gravity reduction ch.2; magnetometers and magnetic surveying ch.4–5; forward/inverse modelling throughout); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration, 3rd ed. (survey design, data processing and interpretation workflow ch.6 & 7); Blakely, Potential Theory in Gravity and Magnetic Applications (potential-field theory, Fourier-domain filters, reduction-to-pole ch.2, 9 & 12).
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 geological model — a geometry (e.g. a dipping polygonal body) and its physical property (density or susceptibility contrast) — and computes the anomaly that model would produce, which the interpreter then compares to the observed data and adjusts by hand (or by automated curve-fitting) until an acceptable match is achieved. Inverse modelling works in the opposite direction: starting from the observed data, an algorithm automatically computes the physical-property distribution (or, for parametric inversion, the model geometry) that best reproduces the observations, subject to constraints and a regularization scheme that keeps the solution geologically reasonable.
Forward modelling is geologically intuitive and gives the interpreter complete, direct control over the assumed geometry, so complex, realistic shapes (dipping sheets, multiple adjacent bodies, known stratigraphy) can be incorporated directly from mapped/drilled information, and the interpreter can immediately see why a particular geometry does or does not fit the data. Its weakness is that it is essentially subjective, iterative trial-and-error: there is no guarantee the chosen model is the best (or only) fit, the process can be slow for complex 3D geometries, and the result depends heavily on the interpreter's starting assumptions.
Inverse modelling is objective and can process large, complex 3D grids automatically, converging to a best-fit model by a defined, quantitative misfit criterion, and modern algorithms can incorporate independent constraints (a reference/starting model from drilling, bound constraints on property values) via regularization. Its weakness is the fundamental non-uniqueness of potential-field inversion — by Gauss's theorem, infinitely many different subsurface property distributions can reproduce the same surface field exactly — so an unconstrained inversion tends to produce an overly smooth, minimum-structure model that is mathematically valid but need not be geologically realistic; inversion is also computationally expensive for large 3D voxel models and is sensitive to the choice of regularization parameters, model parameterization and data noise.
Forward: Talwani's method (the classical algorithm for computing the 2D gravity/magnetic field of an arbitrary polygonal cross-section by line-integrating around its boundary), implemented in interactive packages such as GM-SYS (Geosoft/Oasis montaj), Potent, and ModelVision, which let an interpreter build and adjust 2D/2.75D cross-sections against observed profiles in real time.
Inverse: Euler deconvolution (a fast, semi-automated method that solves Euler's homogeneity equation over a moving window to estimate source location and depth given an assumed structural index, useful for rapid regional scanning, Question 8); parametric non-linear least-squares inversion (e.g. Marquardt–Levenberg) for fitting a small number of geometric parameters to an anomaly; and large-scale 3D voxel (Tikhonov-regularized) inversion such as UBC-GIF's GRAV3D/MAG3D (Li & Oldenburg's minimum-structure inversion), which produces a smooth 3D density or susceptibility model of a whole survey volume; global optimization methods (simulated annealing, genetic algorithms) are also used for strongly non-unique, multi-parameter problems where gradient-based methods risk local minima.
Early in a program, quick forward modelling of isolated, well-defined anomalies tests specific geological hypotheses cheaply (Question 8) and helps rank targets for follow-up before committing to drilling. As independent constraints (drill intersections, downhole logs, seismic horizons) accumulate, they are fed into inverse modelling as a reference model or bound constraints, narrowing the otherwise non-unique inversion toward a geologically consistent result; the resulting 3D property model is then used to guide further drill targeting, refine resource/structural models, and, ultimately, to integrate the geophysics quantitatively into the overall 3D geological model of the deposit or region.
