EES215

Lecture 2

Determination of ages

• Geological approach - comparison of sequence of events (layered structure; presence of fossils etc.): relative ages
• Radiometric approach - decay of radioactive isotopes and build-up of radiogenic isotopes (e.g. decay of ⁸⁷Rb into ⁸⁷Sr with half-life of 48.9 GA): N = N_oe^-lt - absolute ages
• Half-life indicates the time it takes for a given number of isotopes to diminish by half, it is related to the decay constant l by l = ln2/T_1/2 Both half-life and decay constant are characteristic for a specific isotope and are independent of any other parameters (such as temperature or pressure).
• The isochron equation: ( ⁸⁷Sr/⁸⁶Sr)_t = ( ⁸⁷Sr/⁸⁶Sr)_o + ( ⁸⁷Rb/⁸⁶Sr)_t (e ^{+l t} – 1) which is of a form y = a + bx
• The subscript t indicates present-day isotope ratios, which can be determined in mass spectrometers. Once these ratios have been measured in a set of samples, the isochron can be established and the angle with the horizontal is then (e ^{+l t} – 1), the intercept with the y-axis gives the initial ratio ( ⁸⁷Sr/⁸⁶Sr)_o

Fig. 1

• Fig. 1 shows the development of an isochron, Fig.2 gives an example of an actual age determination (from Faure and Mensing, Isotopes)

Geologic and radiometric approaches together give the established age system for the earth Fig. 3

Time scale for processes

Turn-over of mantle	1 GA
Opening of oceans basin	100 MA
Turn-over of oceans	1 KA
Residence time in geothermal reservoir	100 A
Rotation of earth around sun	1 A
Turn-over of atmosphere	1 month
Rotation of earth around its axis	1 day
Human time scale - generation	30 A

Forces important for present state of earth
 What determines the shape of the earth?

First order:	Gravitation
Second order:	Rotation è flattening
Third order:	Heat from earth?s interior: Plate tectonics; formation of topography
Fourth order:	Solar energy - erosion and sedimentation due to movement in hydrosphere and atmosphere (driven by solar energy). Heat generation and formation of crust tends to build up topography, solar forces tends to level topography (erosion of mountain tops; filling of lakes and ocean)

Gravity - Basic principle: Newton's Law F = Gm₁m₂/r²
Gravitational constant G = 6.67x10^-11 m³ kg^-1 s^-2
Gravitational potential - principles of derivation: calculate expected gravity value for given location: take into account latitude (g = 9.7803185 (1 + 5.278895x10^-3 sin²l - 2.3462x10^-5 sin⁴l)) and altitude and compare to measured value: difference is gravity anomaly, which indicates the presence of material with higher (positive anomaly) or lower (negative anomaly) density in crust
Free air correction: correct for altitude of measurement
Bouguer correction: correct for excess (or missing) mass between location of measurement and sealevel

Geoid - shape of rotating sphere composed of perfect liquid                                    Fig. 4
Deviations from geoid: differences in altitude; bimodal distribution of altitudes - two types of crust; formation of crust; principles of plate tectonics

Plate tectonics:

Crust is made up of number of plates, which move independently from each other.
Consequence: existence of three basic types of boundaries:

· diverging boundary: formation of crust è Mid-ocean Ridges

· converging boundary: subduction of crust è Subduction zones

· tangential boundary: neither formation nor subduction of crust

· Examples                                                                                             Fig. 5

Additional features: island arcs; back arc spreading; marginal sea; hot spots

A consequence of plate tectonics is that the configuration of continents has changed dramatically with time (Fig.6)