Three-Point Problem in a Bhima Basin Limestone Deposit
A cement company drills exploration boreholes for a limestone bed in the Bhima basin near Sedam. Coordinates are on a local grid (x east, y north, in metres) and collar elevations are surveyed. Each hole records the elevation at which it entered the same flaggy limestone, recognised by a persistent stromatolitic marker band: A (0, 0), collar 512 m, top of bed 480 m; B (900, 0), collar 500 m, top 480 m; C (0, 600), collar 470 m, top 420 m. Borehole D (1800, 0) logged the bed at 505 m. The contractor wants to move the rig to a fifth site at (600, 900), where the ground surface is 490 m, and the mine planner asks two things before signing: how deep the bed will be there, and whether the bed is folded, since hole D 'does not fit'. Only bed-top elevations are to be used.
1. Compute the strike, true dip and the depth to the bed at (600, 900), showing the construction.
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Strike. A and B both intersect the bed top at 480 m, so the line joining them is a structure contour at 480 m. A–B runs east–west along y = 0, therefore strike = E–W (090°–270°).
Dip. From the 480 m contour, the bed falls to 420 m at C, which lies 600 m due north. Horizontal distance between the 480 m and 420 m contours is 600 m.
tan δ = 60 / 600 = 0.10 → δ = 5.7° dipping due north.
(Structure contours are parallel to A–B, spaced 600 m per 60 m of fall, i.e. 100 m of bed elevation per 1,000 m.)
Depth at (600, 900). The point is 900 m north of the 480 m contour, i.e. 9 structure-contour intervals down-dip. Bed elevation = 480 − (0.10 × 900) = 480 − 90 = 390 m. Surface is 490 m, so depth = 490 − 390 = 100 m.
Judgement: a 100 m hole to reach a bed under 100 m of overburden is a poor exploration target. Before moving the rig, note that stepping along strike costs nothing in depth; the same bed is only ~10 m deep where the ground surface is near 400 m further west.
2. Hole D gives 505 m on the same strike line. Give the competing interpretations and the cheapest test that separates them.
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Along y = 0, the planar model predicts the bed at 480 m everywhere. D gives 505 m, i.e. 25 m higher. Two explanations:
1. Mispick (first to eliminate). The marker is identified by stromatolite morphology - a bioherm in one core can mimic the band. Re-log the D core, compare the stromatolite form, bed thickness and the beds immediately above and below. If they do not match, D is not on the marker and the planar model stands.
2. Real structure. The bed is not a perfect plane: a broad, low-amplitude N–S warp, or a fault between B and D with about 25 m throw (east side up). A fault would leave gouge, slickensides, drag or an abrupt change in bed thickness in the core.
Cheapest test: drill one confirmation hole halfway between B and D (about x = 1350, y = 0). If elevation changes gradually, it is a fold; if it jumps between two adjacent holes, it is a fault. Also re-compute dip using A, B and the new hole. Until then, do not extend structure contours east of B and do not quote a single dip figure for the deposit.
3. How does the 5.7° dip change the drilling and pit-design strategy?
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5.7° looks trivial but it accumulates: over the 1.8 km between A/B and D the bed swings about 180 m in elevation. Consequences:
Drilling. Holes sunk along strike (east–west) will all meet the bed at nearly the same elevation and will suggest a flat-lying deposit - an apparent dip of 0°. The true dip appears only in north–south sections. Fence the deposit with holes laid out across strike (N–S), not along it, or half the deposit will be mis-modelled.
Pit design. A pit planned as if the bed were flat will find the ore body plunging away northwards; stripping ratio rises sharply at the northern end while the southern part is already shallow. Design benches and the pit outline around the 5.7° northerly dip, and calculate reserves on structure contours, not on average thickness.
Water. The bedding and any karst will transmit groundwater down-dip to the north; expect inflow to increase toward the down-dip margin of the pit, and site sumps accordingly. A single average dip quoted for the whole lease would mislead both the driller and the planner.