MIT12_009S11_lec17_21

MIT12_009S11_lec17_21 - 6 Spectral analysis References:...

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Unformatted text preview: 6 Spectral analysis References: Bracewell [33], Muller and MacDonald [29], Berge et al. [4]. Astronomically forced phenomena such as glacial cycles give rise to signals in which periodic phenomena are superimposed on other types of variations. One often seeks to measure the frequency of the various periodic components along with their relative amplitude. To do so, we compute power spectra , using Fourier transforms . These lectures are intended to provide a theoretical understanding of power spectra. But we first consider some typical data. 6.1 Climatic signals Reference: Emerson and Hedges [12], Muller and Macdonald [29]. Ocean sediments and ice cores contain within them a great many signals of climate change, e.g. Isotopic composition of oxygen, which is sensitive to global ice volume and temperature, obtained from entrapped air in ice cores; and carbonate shells of planktic (sea surface) and benthic (sea bottom) organisms. Deuterium/hydrogen ratios (D/H), D = 2 H ( 1 H with a neutron), sensi- tive to temperature, in ice cores. Carbon isotopic compositions. Dust content, etc. 103 Perhaps the most studied signal is 18 O = 18 O / 16 O sample 1 1000 ( 18 O / 16 O) std Heres an example, from entrapped air in the Vostok (Antarctica) ice core ( data from Petit et al. [1]):-4-3-2-1-0.5 0.5 1 1.5 time [10 5 yr] 18 O [permil] Note the clear occurrence of the precession signal, with a period of about 23 Kyr. Many processes cause 18 O to change. The two most important are the following: The vapor pressure (related to evaporation rate) of water containing 16 O is higher than that of water containing 18 O. Thus 16 O evaporates more readily, and evaporated water is depleted in 18 O. Conversely, precipitated water is enriched in 18 O. In other words, H 2 18 O condenses at a faster rate than H 2 16 O. The combined effect of these two processes leads to an enrichment of 18 O of air as the global volume of ice grows. 104 Heres why: Take ocean water to be at . Evaporated water is typically about 9 lighter (at 20 C) than liquid water. Conversely condensate is about 9 heavier than vapor. So a cloud forming from recently evaporated seawater has cloud = 9 . And the first rain from this cloud is 9 is heavier, so that rain = 0 . However the remaining water in the cloud must be isotopically lighter than it was originally, and the rain out of it will therefore also become lighter. As the cloud moves to higher elevations or higher latitudes, it loses more vapor to condensate, and the resulting rain or snow becomes lighter and lighter. This process, in which a particular masshere a cloudis progressively milked of the heavy isotope so that it becomes lighter and lighter (or vice- versa), is an example of Rayleigh distillation ....
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This note was uploaded on 01/13/2012 for the course GEOLOGY 12.001 taught by Professor Staff during the Fall '11 term at MIT.

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MIT12_009S11_lec17_21 - 6 Spectral analysis References:...

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