18-Geol-A7 Applied Geophysics · December 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2016 — 04-Geol-A7 Applied Geophysics. Three-hour, closed-book exam; no 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 an all-essay paper with no numeric data, formula sheet or figure supplied. All ten questions are answered below.
Reference texts: Telford, Geldart & Sheriff, Applied Geophysics (2nd ed.) — the primary reference for every method touched in this paper (survey design, seismic reflection, well logging, gamma-ray spectrometry, electrical/EM methods, EM systems, data enhancement, forward/inverse modelling); Kearey, Brooks & Hill, An Introduction to Geophysical Exploration (3rd ed.) — survey planning, data display, case-history context; Blakely, Potential Theory in Gravity and Magnetic Applications — potential-field forward/inverse modelling theory (Q9); Selley & Sonnenberg, Elements of Petroleum Geology — well-logging context (Q3); Freeze & Cherry, Groundwater — hydrogeophysics context (Q10).
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.
Derivative filters (vertical and horizontal gradients). Concept: spatial derivatives amplify short-wavelength (shallow, high-wavenumber) content relative to long-wavelength (deep, regional) content, sharpening contacts and edges that a smoothly varying raw field obscures. Achieved: computed exactly as a multiplication by a power of wavenumber ($\propto k^n$) in the Fourier domain, then transformed back. Adjustable parameters: derivative order (first vs. higher order — higher orders sharpen more but amplify noise more aggressively) and an accompanying low-pass pre-filter cutoff wavenumber, chosen to suppress the noise amplification without removing the genuine short-wavelength signal of interest.
Upward continuation. Concept: mathematically projects the field to a higher observation level, which attenuates short-wavelength near-surface noise/clutter far more strongly than long-wavelength deep signal, isolating regional trends — the complementary operation to a derivative filter. Achieved: multiplication by $e^{-k\Delta z}$ in the wavenumber domain. Adjustable parameter: the continuation height $\Delta z$, chosen to match the wavelength of the noise/near-surface clutter to be suppressed — too small a height leaves noise in place, too large removes genuine shallow target signal as well.
Band-pass wavenumber filtering. Concept: isolates the specific range of anomaly wavelengths expected from a target at a known approximate depth, removing both shorter-wavelength noise and longer-wavelength regional trend simultaneously. Achieved: multiplying by a filter function that passes only a chosen wavenumber band. Adjustable parameters: the low and high corner wavenumbers and the filter's roll-off steepness (a very sharp cutoff risks ringing/Gibbs artifacts; a gentle roll-off passes more residual noise).
Directional (sun-shading / illumination) enhancement. Concept: an artificial oblique illumination of the gridded surface creates a pseudo-3-D shaded appearance that dramatically improves visual detection of subtle linear trends (faults, contacts, structural fabric). Achieved: a standard relief-shading algorithm applied to the gridded data treated as a topographic-like surface. Adjustable parameters: illumination azimuth and inclination — because features trending parallel to the illumination azimuth are strongly suppressed, the standard remedy is to generate several shaded views at different azimuths (e.g. every 30–45°) and compare, rather than relying on one.
Colour stretch and histogram equalization. Concept: re-maps data amplitude to a colour scale so that the eye can distinguish amplitude differences that are compressed or exaggerated under a naive linear stretch. Achieved: a non-linear (e.g. histogram-equalized or percentile-clipped) mapping from data value to colour, rather than a simple linear min-max stretch. Adjustable parameters: the clip percentiles and the colour palette itself, chosen so that the amplitude range containing the feature of interest occupies the greatest number of distinguishable colour steps.
Automatic gain control (AGC), for seismic/profile data. Concept: normalizes trace amplitude within a sliding time/space window so that both strong, shallow, and weak, deep or attenuated signal are made visually comparable on the same display. Achieved: dividing each sample by a locally computed RMS or average amplitude within the window. Adjustable parameter: window length — too short destroys genuine relative-amplitude information (useful for e.g. AVO analysis); too long fails to boost genuinely weak, deep signal.
