04-Geol-B10 · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
EGBC National Exam — Geological Engineering, 04-Geol-B10-2 Electrical Methods, 2017-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, about half an hour each".
Reference texts: Telford, Geldart & Sheriff, Applied Geophysics, 2nd ed. (electrical properties of rocks ch.5; self-potential ch.6; induced polarization ch.9; resistivity ch.8; electromagnetic methods ch.7; magnetotellurics ch.10); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration, 3rd ed. (resistivity arrays, EM systems, MT surveying, ch.8–9); Simpson & Bahr, Practical Magnetotellurics (MT instrumentation and robust/remote-reference processing, ch.2–6).
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.
Inversion modelling is the process of estimating a subsurface physical-property model (e.g. resistivity, chargeability, density, susceptibility as a function of position) that, when the forward physics is applied to it, reproduces the field-observed data within their estimated uncertainty — the reverse of forward modelling, which predicts data from an assumed model. Because geophysical inversion is inherently non-unique (many different subsurface models can fit the same finite, noisy dataset equally well), practical inversion algorithms do not simply minimize data misfit; they minimize a combined objective function of data misfit PLUS a regularization (model-smoothness/reference-model) term, so that among all models fitting the data, the algorithm selects the smoothest, or the one closest to independent prior geological knowledge.
A widely used example is the UBC-Geophysical Inversion Facility's family of deterministic, regularized least-squares inversion codes (e.g. DCIP2D/3D for resistivity and IP, or an EM1D/EM3D code for TDEM/FDEM), which implement a Gauss–Newton/Occam-style iterative minimization of φ = φdata + βφmodel, where β is a regularization trade-off parameter progressively reduced ("cooling") as the iteration proceeds.
Inputs: the observed field data with estimated measurement uncertainties (apparent resistivity/chargeability/EM response values and their survey geometry); a discretized model mesh (cells whose physical property values are the unknowns to be solved for); a starting/reference model (often a uniform half-space, or informed by known geology/drill data); and inversion control parameters (regularization weighting, convergence/misfit tolerance, bound constraints if used). Outputs: the recovered subsurface property model (2-D section or 3-D volume), the predicted data corresponding to that model, a data-misfit statistic (e.g. normalized chi-squared, ideally ≈1 given accurate uncertainty estimates — underfitting leaves real signal unexplained, overfitting fits noise), and, in more advanced packages, model-resolution/uncertainty diagnostics.
A resistivity sounding (Wenner or Schlumberger) acquired over a suspected contaminant plume or to site a water well is routinely inverted from its raw apparent-resistivity-vs-spacing curve into a layered (or 2-D) true-resistivity-versus-depth model, which is then interpreted geologically (e.g. distinguishing a conductive clay aquitard from a resistive sand aquifer, or delineating a saline/leachate plume) — a decision-ready product that the raw apparent-resistivity curve alone cannot directly provide, since apparent resistivity is a smoothed, geometry-weighted average of the true subsurface distribution.
