LOWRIE Chs 1-2 (M827).qxd 28/2/07 11:18 AM Page 99 John John's G5:Users:john:Public:JOHN'S JOBS:10421 - CUP - LOWRIE (2nd edn): 2.7 ISOSTASY 99 Fig. 2.62 Observed and West East computed free-air gravity 100 anomalies across a 0 subduction zone. The density (a) – 100 observed model for the computed calculated anomaly is based on seismic, Free-air – 200 thermal and petrological data. anomaly (mgal) – 300 The profile crosses the Chile +5 Outer Chile Ande s trench and Andes mountains line Ridge Trench Sh ore at 23ЊS (after Grow and 0 Bowin, 1975). (b) (km) –5 vertical exaggeration = 10 × Elevation –10 – 2000 200 400 600 800 oceanic crust water 1030 2600–2900 0 UL 3240 2800 LL 3280 2900 3280 3560– 100 ASTHENO- 3340 3380 3340 3580 (c) SPHERE (km) Depth 3380 3380 200 3430 3440 3490 3440 300 densities in kg m–3 – 200 0 200 400 600 800 Distance (km) beneath the ridge, melts and accumulates in a shallow duction result in mass excesses. Peridotite in the upper magma chamber within the oceanic crust. lithosphere changes phase from plagioclase-type to the higher-density garnet-type. When oceanic crust is sub- 2.6.4.4 Gravity anomalies at subduction zones ducted to depths of 30–80 km, basalt changes phase to eclogite, which has a higher density (3560–3580 kg mϪ3) Subduction zones are found primarily at continental than upper mantle rocks. These effects combine to produce margins and island arcs. Elongate, narrow and intense the positive free-air anomaly. isostatic and free-air gravity anomalies have long been The Chile trench is more than 2.5 km deeper than the associated with island arcs. The relationship of gravity to ocean basin to the west. The sediments flooring the trench the structure of a subduction zone is illustrated by the have low density. The mass deficiency of the water and free-air anomaly across the Chile trench at 23ЊS (Fig. sediments in the trench cause a strong negative free-air 2.62). Seismic refraction data define the thicknesses of the anomaly, which parallels the trench and has an amplitude oceanic and continental crust. Thermal and petrological greater than Ϫ250 mgal. A small positive anomaly of data are integrated to give a density model for the struc- about ϩ20 mgal is present about 100 km seaward of the ture of the mantle and the subducting lithosphere. trench axis. This anomaly is evident also in the mean level The continental crust is about 65 km thick beneath the of the ocean surface as mapped by SEASAT (Fig. 2.28), Andes mountains, and gives large negative Bouguer which shows that the mean sea surface is raised in front of anomalies. The free-air gravity anomaly over the Andes is deep ocean trenches. This is due to upward flexure of the positive, averaging aboutϩ50 mgal over the 4 km high lithosphere before its downward plunge into the subduc- plateau. Even stronger anomalies up toϩ100 mgal are tion zone. The flexure elevates higher-density mantle rocks seen over the east and west boundaries of the Andes. This and thereby causes the small positive free-air anomaly. is largely due to the edge effect of the low-density Andean crustal block (see Fig. 2.44b and Section 2.5.6). A strong positive free-air anomaly of aboutϩ70 mgal 2.7 ISOSTASY lies between the Andes and the shore-line of the Pacific 2.7.1 The discovery of isostasy ocean. This anomaly is due to the subduction of the Nazca plate beneath South America. The descending slab is old Newton formulated the law of universal gravitation in 1687 and cool. Subduction exposes it to higher temperatures and confirmed it with Kepler’s laws of planetary motion. and pressures, but the slab descends faster than it can be However, in the seventeenth and eighteenth centuries the heated up. The increase in density accompanying greater law could not be used to calculate the mass or mean density depth and pressure outweighs the decrease in density due of the Earth, because the value of the gravitational con- to hotter temperatures. There is a positive density contrast stant was not yet known (it was first determined by between the subducting lithosphere and the surrounding Cavendish in 1798). Meanwhile, eighteenth century scien- mantle. Also, petrological changes accompanying the sub- tists attempted to estimate the mean density of the Earth LOWRIE Chs 1-2 (M827).qxd 28/2/07 11:18 AM Page 100 John John's G5:Users:john:Public:JOHN'S JOBS:10421 - CUP - LOWRIE (2nd edn): 100 Gravity, the figure of the Earth and geodynamics by various means. They involved comparing the attraction of the Earth with that of a suitable mountain, which could be calculated. Inconsistent results were obtained. During the French expedition to Peru in 1737–1740, direction to Pierre Bouguer measured gravity with a pendulum at a fixed star different altitudes, applying the elevation correction term local which now bears his name. If the density of crustal rocks deviation of local plumb-line is ␳ and the mean density of the Earth is ␳0,the ratio ofthe deviation of Bouguer-plate correction (see Section 2.5.4.3) for eleva- plumb-line N tion h to mean gravity for a spherical Earth of radius R is S ⌬gBP 2␲G␳h 3 ␳ h g ϭ ϭ ␳ (2.103) 4␲G␳ R 2 0 R 3 0 ΂ ΃΂ ΃ βN vertical at N β From the results he obtained near Quito, Bouguer esti- S α mated that the mean density of the Earth was about 4.5 N αS times the density of crustal rocks. The main method employed by Bouguer to determine vertical at S the Earth’s mean density consisted of measuring the deflection of the plumb-line (vertical direction) by the β mass of a nearby mountain (Fig. 2.63). Suppose the ele- vation of a known star is measured relative to the local D vertical direction at points N and S on the same meridian. R R The elevations should be ␣N and ␣S, respectively. Their sum is ␣, the angle subtended at the center of the Earth by the radii to N and S, which corresponds to the difference in latitude. If N and S lie on opposite sides of a large mountain, the plumb-line at each station is deflected by the attraction of the mountain. The measured elevations of the star are ␤N and ␤S, respectively, and their sum is ␤. The local vertical directions now intersect at the point D instead of at the center of the (assumed spherical) Earth. The difference ␦ϭ␤Ϫ␣ is the sum of the deviations of α the vertical direction caused by the mass of the mountain. C The horizontal attraction ƒ of the mountain can be calculated from its shape and density, with a method that Fig. 2.63 Deviations of the local plumb-line at N and S on opposite sides of a large mountain cause the local vertical directions to intersect resembles the computation of the topographic correction at the point D instead of at the center of the Earth. in the reduction of gravity measurements. Dividing the mountain into vertical cylindrical elements, the horizon- that the deflection of the vertical caused by the mountain tal attraction of each element is calculated and its compo- was much too small for its estimated mass. nent (G␳hi) towards the center of mass of the mountain is In 1774 Bouguer’s Chimborazo experiment was found. Summing up the effects of all the cylindrical ele- repeated in Scotland by Neville Maskelyne on behalf of ments in the mountain gives the horizontal attraction ƒ the Royal Society of London. Measurements of the eleva- towards its center of mass. Comparing ƒ with mean tions of stars were made on the north and south flanks of gravity g, we then write Mt. Schiehallion at sites that differed in latitude by 42.9Љ of arc. The observed angle between the plumb-lines was ␳ G hi hi 54.6Љ. The analysis gave a ratio ␳/␳ equal to 1.79, suggest- f ͚i ͚i ␳ 0 tan␦ϭ ϭ ϭ ( ) (2.104) Ϫ3 g 4 4 ␳0 ing a mean density for the Earth of 4500 kg m . This was 3␲G␳0R 3␲R more realistic than Bouguer’s result, which still needed For very small angles, tan␦ is equal to ␦, and so the explanation. deflection of the vertical is proportional to the ratio ␳/␳0 Further results accumulated in the first half of the of the mean densities of the mountain and the Earth. nineteenth century. From 1806 to 1843 the English geode- Bouguer measured the deflection of the vertical caused sist George Everest carried out triangulation surveys in by Mt. Chimborazo (6272 m), Ecuador’s highest moun- India. He measured by triangulation the separation of a tain. His results gave a ratio ␳/␳0 of around 12, which is site at Kalianpur on the Indo-Ganges plain from a site at unrealistically large and quite different from the values he Kaliana in the foothills of the Himalayas. The distance had obtained near Quito. The erroneous result indicated differed substantially from the separation of the sites LOWRIE Chs 1-2 (M827).qxd 28/2/07 11:18 AM Page 101 John John's G5:Users:john:Public:JOHN'S JOBS:10421 - CUP - LOWRIE (2nd edn): 2.7 ISOSTASY 101 computed from the elevations of stars, as in Fig. 2.63. The (a) Airy mountain discrepancy of 5.23Љ of arc (162 m) was attributed to h1 sea-level h2 deflection of the plumb-line by the mass of the d ocean Himalayas.