18-Geol-A7 Applied Geophysics · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2014 — 04-Geol-A7 Applied Geophysics. Three-hour, open-book exam; any non-communicating calculator permitted. The NOTES state that SIX questions constitute a complete paper, but eight numbered questions are printed on the exam — all eight, and every lettered/numbered sub-part, are solved below. Two figures (the CMP gather of Q6 and the reversed-refraction time-distance plot of Q8) carry real numeric data that is only given graphically on the printed page; both were read from the printed figures, calibrated against each figure's own printed axes, and the reading tolerance is given in a check callout beside each calculation.
Reference texts: Telford, Geldart & Sheriff, Applied Geophysics (2nd ed.) — the primary reference for every method in this paper (gravity, magnetics, seismic refraction and reflection, electrical resistivity, induced polarization, electromagnetics); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration (3rd ed.) — survey design and interpretation context; Blakely, Potential Theory in Gravity and Magnetic Applications — the dipole/sphere anomaly shapes used in Q2–Q3.
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.
(i) 2-layer and 3-layer sounding curves. A vertical electrical sounding (VES) plots apparent resistivity $\rho_a$ against electrode spacing (e.g. $AB/2$) on log-log axes, because the ratio of successive spacings, not their absolute difference, is what controls depth of investigation. For a simple 2-layer earth, $\rho_a$ starts at small spacing reading close to the TOP layer's true resistivity $\rho_1$, and as spacing increases the current samples progressively more of layer 2, so the curve smoothly transitions to an asymptote at $\rho_2$ — an ASCENDING curve if $\rho_2>\rho_1$ (as sketched below) or a DESCENDING curve if $\rho_2<\rho_1$. A 3-layer earth adds a second transition, producing one of four classic type-curve shapes depending on the relative order of $\rho_1,\rho_2,\rho_3$: H-type ($\rho_1>\rho_2<\rho_3$, a trough), K-type ($\rho_1<\rho_2>\rho_3$, a hump — sketched below), A-type (ascending throughout, $\rho_1<\rho_2<\rho_3$) or Q-type (descending throughout, $\rho_1>\rho_2>\rho_3$).
For a depth-sounding survey the Schlumberger array is recommended (as already justified in Question 1(iii)): it needs far fewer electrode moves per sounding than Wenner (only the outer current electrodes are expanded, the inner potential pair stays fixed except for occasional repositioning), it is less sensitive to shallow lateral inhomogeneity near any one electrode, and it is the standard array used to build the master/type-curve catalogues that 2- and 3-layer soundings are traditionally matched against.
(ii) Dipole-dipole pseudo-section over the given model. The model is a thin, vertical, CONDUCTIVE body ($\rho=5$) reaching the surface in a resistive host ($\rho=50$). In a dipole-dipole pseudo-section each reading is plotted midway between the current dipole and the potential dipole, at a pseudo-depth that increases with the separation level $n$. A reading is strongly lowered whenever EITHER dipole sits over the conductor: at the current dipole, current is drawn into the conductor; across the potential dipole, the conductor short-circuits the field and the measured voltage drops. The plotting points for those electrode positions lie along two lines running down and outward at about $45^\circ$ from the top of the body. The low apparent resistivities therefore form the classic inverted-V, or "pant-leg", pattern: two diagonal legs of low $\rho_a$ that spread apart with increasing $n$. Between the legs, where the two dipoles lie on opposite sides of the body, the effect is much weaker and values return to about background or slightly above; outside the legs values are near the 50 Ωm background.
Utility and limitations of pseudo-sections. A pseudo-section is fast to produce directly from raw field readings (no inversion required) and gives an immediately useful QUALITATIVE picture of where conductive/resistive structure is located along a line, making it valuable for quick-turnaround target identification in the field. Its major LIMITATION is that the pseudo-depth axis is only a plotting convention, not a true depth — pseudo-section anomalies are systematically distorted in shape, smeared, and the diagonal legs described above look like two dipping bodies when there is only one vertical one; a pseudo-section should never be read as a true depth cross-section without inversion.
(iii) Inverse modelling ("inversion") of resistivity/IP data. Forward modelling computes the theoretical apparent-resistivity (or IP) response of an ASSUMED subsurface model; inversion runs this process in reverse — starting from the observed field data, an iterative algorithm (e.g. a smoothness-constrained least-squares scheme) automatically adjusts a grid of model resistivity cells so that the model's FORWARD-predicted response converges to match the observed pseudo-section data, typically minimizing a combination of data misfit and a model-smoothness (regularization) penalty to avoid an unstable, over-fit result. The output is a genuine resistivity-vs-TRUE-depth cross-section (not a pseudo-section), often called a "real section" or, when many overlapping soundings/profiles are combined into a dense 2-D or 3-D image, Electrical Resistivity Tomography (ERT). The utility of inversion is exactly that it removes the pseudo-section's depth distortion and flanking artifacts, producing a directly interpretable geometric image of the true subsurface resistivity distribution that can be compared quantitatively with borehole or other independent control, at the cost of requiring a computer inversion (non-unique, and dependent on the regularization/starting-model choices) rather than a same-day field plot.
