(a) Describe the types of radiometric dating techniques used to establish the age of the Earth. (20 marks) (b) Discuss the…

(a) Radiometric dating techniques used for the age of the Earth

Radiometric dating measures parent and daughter isotopes in minerals that have stayed closed systems since crystallisation, with age t = (1/λ) ln(1 + D/P). No Earth rock preserves the planet's formation, so its age of about 4.54 Ga is fixed from meteorites and the oldest terrestrial minerals.

(i) U–Pb and Pb–Pb. ²³⁸U decays to ²⁰⁶Pb (half-life 4.468 Ga) and ²³⁵U to ²⁰⁷Pb (0.704 Ga). Concordia–discordia plots separate crystallisation age from later Pb loss. Patterson's 1956 Pb–Pb isochron on Canyon Diablo and other meteorites gave about 4.55 Ga. Zircon holds Pb to above 900°C, so Jack Hills zircons (4.40 Ga) and the Acasta Gneiss (about 4.0 Ga) set the minimum age of the crust.

(ii) Rb–Sr. ⁸⁷Rb decays to ⁸⁷Sr (half-life 48.8 Ga) and is dated by whole-rock or mineral isochrons. It is used for granites and meteorites, but is reset at moderate temperatures.

(iii) Sm–Nd. ¹⁴⁷Sm decays to ¹⁴³Nd (106 Ga). Both elements are immobile, so it gives crust-formation model ages and mantle-extraction ages.

(iv) K–Ar and ⁴⁰Ar/³⁹Ar. ⁴⁰K (half-life 1.25 Ga) decays to ⁴⁰Ar, about 10.7% by electron capture, and to ⁴⁰Ca. Step-heating dates volcanic rocks such as the Deccan Traps (about 66 Ma), but Ar is lost on heating.

(v) Re–Os and Lu–Hf. Re–Os dates sulphides and mantle rocks; Lu–Hf dates zircon and garnet.

Isochron methods give both age and initial ratio, which tests closed-system behaviour. Agreement among U–Pb, Pb–Pb and Rb–Sr ages on meteorites is what fixes the 4.54 Ga value.

(b) Interaction of electromagnetic radiation with the atmosphere and its effect on images

Energy passing through the atmosphere is scattered, absorbed or refracted, so sensors record path radiance and attenuated surface signal.

(i) Rayleigh scattering. Particles much smaller than the wavelength scatter in proportion to λ⁻⁴. Blue light is scattered most, which makes the sky blue. In images it adds blue haze and lowers contrast in the short-wavelength bands.

(ii) Mie scattering. Particles of size comparable to the wavelength, such as dust, smoke and aerosols, scatter more in the forward direction and less selectively. It dominates in the lower atmosphere and lowers contrast.

(iii) Non-selective scattering. Droplets larger than about 10 µm, as in clouds and fog, scatter all visible and infrared wavelengths equally. Clouds look white and hide the ground.

(iv) Absorption. Water vapour, CO₂ and ozone absorb in particular bands: ozone in the ultraviolet, CO₂ and water vapour in the infrared. The spectral intervals of high transmission are atmospheric windows, namely the visible–near-infrared, the short-wave infrared, the thermal infrared window of 8–14 µm, and microwaves. Sensor bands are placed in these windows.

(v) Refraction. Bending of rays in layers of differing density causes small geometric errors.

Microwaves pass through cloud, so radar such as RISAT can image in the monsoon. Corrections include dark-object subtraction, radiative-transfer models (6S, MODTRAN, FLAASH) and geometric correction for refraction errors.

(c) Joints and their geometric and genetic classification

Joints are fractures in rock along which there has been no visible displacement; if there is displacement, they are faults. They occur in sets and control weathering, groundwater flow and the stability of slopes, dams and tunnels.

Geometric classification. Joints are named by their attitude relative to the bedding or the fold.

(i) Strike joints run parallel to the strike of the beds.

(ii) Dip joints run parallel to the dip direction of the beds.

(iii) Oblique (diagonal) joints cut the strike at an angle.

(iv) Bedding joints lie along the bedding planes.

In a fold, longitudinal joints are parallel and transverse joints perpendicular to the fold axis. Joints that recur at regular spacing and orientation are systematic; irregular, curved ones are non-systematic.

Genetic classification. It is based on the stress that produced the joint.

(i) Tension (extension) joints open perpendicular to the least principal stress σ₃. They have rough surfaces and are parallel to σ₁. Columnar joints in basalt arise from cooling contraction.

(ii) Shear joints form along planes at about 30° to σ₁, often as conjugate sets with about 60° between them, bisected by σ₁. They have smooth surfaces with slickensides.

(iii) Release (unloading) joints form when overburden is removed. Sheet or exfoliation joints in granite are an example.

Plumose structure and hackle marks on joint faces indicate tension joints.