(a) Lead (Pb) mineralization zone is drawn in the given diagram with nomenclature. The related data is also provided in the…

(a) Average grade of lead

The zones of influence differ in area, so the grade is weighted by area (W × L), not averaged simply.

Areas: 21.00, 18.75, 30.00 and 43.75 ft², total 113.50 ft².

Area × grade: S-1 21.00 × 7.1 = 149.10; S-2 18.75 × 7.5 = 140.625; S-3 30.00 × 6.9 = 207.00; S-4 43.75 × 8.9 = 389.375. Sum = 886.10.

Average grade = 886.10 / 113.50 = 7.81% Pb. The simple mean of the four assays would be 7.60%, which understates the grade because the richest sample, S-4, represents the largest area.

(b) Jharia coalfield

Jharia, in the Damodar Valley of Jharkhand, is an east-west elongated, faulted synclinal basin of about 450 km² within the Gondwana rift basins. The coal measures are the Lower Gondwana Barakar Formation (Early Permian), with sandstone, shale and about 18 seams, separated by the barren Barren Measures; the Raniganj Formation lies above in the Gondwana succession. The basin is bounded on the south by a major boundary fault and cut by faults and by Mesozoic mica-peridotite dykes and sills that have locally devolatilised coal.

Economically, Jharia holds India's principal prime coking coal, essential for blast-furnace steel, and also non-coking coal for power. Its potential is limited by underground fires, first noted in 1916, by subsidence and by deep, old, congested mining, so safe extraction and fire control decide the recoverable reserves.

(c) Geophysical methods and gravity method

Geophysical methods map the subsurface from measured contrasts in physical properties: gravity (density), magnetic (susceptibility), electrical and electromagnetic (conductivity), induced polarisation (chargeability), seismic (velocity) and radiometric methods.

The gravity method measures small variations in gravitational acceleration with a gravimeter, in milligals. Drift, latitude, free-air, Bouguer and terrain corrections give the Bouguer anomaly. Massive sulphides, chromite and iron ore are denser than host rock, so they give local positive residual anomalies; the anomaly shape and amplitude give ore-body depth, extent and approximate tonnage. It cannot separate ore from other dense rocks, so it is combined with magnetic and electrical surveys and then confirmed by drilling.

(d) Trace elements and their entry

A trace element is one present at less than 0.1% (1,000 ppm) by weight in a rock or mineral and not part of the stoichiometric formula.

It enters a mineral mainly by diadochic substitution, replacing a major ion of similar charge and radius. Goldschmidt's rules describe it: a trace ion is captured if its charge is higher than the host's, admitted if lower, and camouflaged if similar. Examples are Rb⁺ for K⁺ in feldspar, Sr²⁺ for Ca²⁺ in plagioclase and U⁴⁺ for Zr⁴⁺ in zircon.

It can also occupy interstitial sites or lattice vacancies and defects, or sit in tiny inclusions, when no suitable lattice site exists.

(e) Late Pleistocene sea-level changes

Sea level fell during glacial advances and rose in interglacials, mainly because ice sheets stored or released water (glacio-eustasy). At the Last Glacial Maximum, about 20,000 years ago, it stood about 120 m below the present. Melting then raised it rapidly to near present level by about 6,000–7,000 years ago. Thermal expansion of warming ocean water, glacio-isostatic adjustment and local tectonics add to or modify the signal.

In the last two centuries, global sea level has risen about 20 cm since 1900. Human-caused warming from fossil-fuel CO₂ drives thermal expansion and melting of glaciers and ice sheets. Groundwater withdrawal and dams alter land-water storage, and extraction of groundwater or hydrocarbons causes local subsidence, raising relative sea level in deltas.