Question 1 of 8: Short Answers Across Methods

Question 1: Short Answers Across Methods (equal value)

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) Latitude dependence of gravimeter readings. A stationary gravimeter's reading depends on latitude because the Earth is an oblate spheroid rotating about its polar axis: the equatorial radius exceeds the polar radius by about 21 km, so a station at the equator sits farther from the Earth's centre of mass (weaker attraction) and also experiences the largest centrifugal acceleration from rotation (which acts opposite to gravity), while a station at the pole is closer to the centre of mass and has zero centrifugal correction. Both effects make normal gravity increase smoothly from about 978,032 mGal at the equator to about 983,218 mGal at the poles — the International Gravity Formula, $g_t=g_o(1+\alpha\sin^2\phi+\beta\sin^2 2\phi)$ (given on the formula sheet), reproduces exactly this latitude trend and is subtracted from every observed reading (the "theoretical" or "normal" gravity correction) before any residual is interpreted geologically; for a small survey the same effect is handled with the formula sheet's latitude gradient $\Delta g_L=0.811\sin2\phi$ mGal/km applied to each station's north-south distance from a base station. A gravimeter in motion (shipborne or airborne) additionally reads a spurious signal from the platform's own velocity relative to the rotating Earth — the Eötvös effect — because an eastward-moving vehicle adds to the Earth's own rotational velocity and increases the outward centrifugal acceleration (reducing apparent gravity), while a westward-moving vehicle reduces it (increasing apparent gravity); the Eötvös correction, $E=7.503\,V\cos\phi\sin\alpha+0.004154\,V^2$ mGal ($V$ in knots, $\alpha$ = heading from true north, $\phi$ = latitude; positive for an eastward heading, so it is added to the reading), must be logged from continuous GPS/INS velocity and heading and removed in addition to the ordinary latitude correction, or a survey line flown in one direction will show a systematic gravity gradient that has nothing to do with subsurface geology.

(ii) Induced field over a buried anomaly at low vs. high latitude. Induced magnetization is always parallel to the inducing field, so the sketch below shows the two limiting inclinations. At the equator the Earth's field is nearly horizontal (inclination $I\approx0^\circ$); the induced dipole in the buried body is therefore also horizontal, and its own dipole field directly above the body points in the OPPOSITE sense to the regional field (the classic bar-magnet field: above a horizontal dipole's centre the dipole's own field points back toward the body, i.e. anti-parallel to $B$), so the total field measured at the surface is reduced — the anomaly is negative or has a strong negative lobe. At the poles the field is nearly vertical ($I\approx90^\circ$); the induced dipole is vertical, and directly above a vertical dipole the dipole's own field points in the SAME sense as the inducing field, so the two add and the anomaly is a simple positive peak.

(iii) Schlumberger array for depth profiling (resistivity). The Schlumberger array keeps the two potential (M,N) electrodes close together and fixed near the centre while only the current (A,B) electrodes are progressively expanded outward. Because $\rho_a=2\pi k\,\Delta V/I$ with the Schlumberger geometric factor $k_{Schl}\approx \pi (AB/2)^2/MN$, and $\Delta V$ falls off rapidly with electrode spacing, keeping MN small (only moved occasionally, when the signal gets too weak to resolve) keeps $\Delta V$ measurable at large AB while requiring far fewer electrode relocations than an array (like Wenner) that expands every electrode simultaneously — this makes Schlumberger both faster to execute for a vertical electrical sounding (VES) and less sensitive to small lateral inhomogeneities near a single moved electrode (since three of the four electrodes stay fixed most of the time). The larger the AB spacing, the deeper the current penetrates, so a Schlumberger sounding with AB/2 stepped out logarithmically directly builds a depth profile of apparent resistivity vs. current-electrode spacing at one fixed sounding location, which is exactly the 1-D layered-earth interpretation the method targets.

(iv) Time-domain vs. frequency-domain EM. In time-domain EM (TDEM) the transmitter current is switched off abruptly and the decaying secondary (eddy-current) field is measured during the transmitter's OFF time, when the (much larger) primary field is absent; because there is no primary field to null out, TDEM systems can use a single coincident or overlapping transmit/receive loop, they measure the secondary field's full time-decay (which maps directly to $\sigma/\text{depth}$ through the diffusion of the eddy currents, giving good depth resolution from one sounding), and they are relatively insensitive to induction from a shallow conductive overburden overwhelming a deeper target, since early time gates see shallow structure and late time gates see progressively deeper structure. Frequency-domain EM (FDEM) must instead measure a small secondary field superimposed on (and often orders of magnitude smaller than) an always-present primary field, requiring precise transmitter-receiver geometry (bucking coils / fixed separation) to null the primary; it is generally faster for reconnaissance profiling (continuous readout while walking or flying) but gives comparatively poorer depth discrimination from a single frequency, and multiple frequencies are needed to approximate the depth information a single TDEM transient already contains.

(v) Shot gather vs. common midpoint (CMP) gather. A shot gather is the set of all seismic traces recorded by every receiver in the spread for ONE source (shot) location — it is the natural raw-acquisition unit, showing direct, reflected, refracted and surface-wave arrivals all sharing one common source point. A common midpoint gather is instead assembled by sorting traces AFTER acquisition (from many different shots and receivers) so that every trace in the gather shares the same midpoint between its own source and receiver, even though the individual source and receiver positions differ from trace to trace; with a horizontal reflector, all traces in a CMP gather sample the same subsurface reflection point (hence "common midpoint"), so after normal-moveout (NMO) correction they can be summed (stacked) to boost signal-to-noise — the CMP gather, not the shot gather, is what Question 6's normal-moveout/Dix analysis below is built from.

(vi) Hidden-layer effects in seismic refraction. A layer can fail to produce its own first-arrival refraction branch (and so be invisible to a first-arrivals-only refraction survey) in two distinct ways. Velocity inversion / blind zone: if a layer's velocity is LOWER than (or only marginally higher than) the velocity of the layer immediately above it, no head wave can critically refract along its top (Snell's law $\sin\theta_c=v_1/v_2$ has no real solution when $v_2\le v_1$, or the critical angle is so large the refracted arrival never outruns the direct/overlying refracted wave as a first arrival) — the layer is "hidden" and the refraction interpretation will silently skip straight from the layer above to whatever lies below it. Thin-layer (blind-zone) effect: even when the velocity DOES increase, if the layer is too thin, its refracted branch's crossover distance is so short that it is never the first arrival at any offset actually recorded — the branch exists mathematically but is masked by the overlying or underlying layer's refraction over the entire practical offset range, so the layer's thickness (and sometimes its existence) cannot be resolved from first arrivals alone.