Physics for Geologists, Second edition

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108 Acoustics: sound and other waves velocity of the source. (The red shift is also a Doppler effect, where lines in the spectra of stars that are receding from the Earth are shifted towards the red - a reduction of frequency, lengthening of wavelength. The light is also transmitted in all directions at speed co, unaffected by the velocity of the source.) Earthquakes Elastic waves in the solids and porous solids of the Earth are of much longer wavelength than audible waves in air, but they must still be considered as sound waves. The frequencies of waves from earthquakes are principally in the range Hz to 1 Hz. Consider the Earth. With the appropriate 'listening' devices, there is a constant noise in the Earth punctuated, from time to time, by earthquakes of variable magnitude. There are four main types of waves generated by earthquakes, and they come under three headings, P, S and L waves. P waves oscillate in the direction of propagation by compression and dilation (you can think of them as push-pull waves). These waves are the same as sound waves transmitted through fluids - water and air, for example - but not the same as surface water waves. They are propagated at a speed or velocity of [(K + 4 ~/3)/~]'/~ = [(X + 2~)/p]'/~ and travel at different speeds in different media and so may be refracted. S waves are shear waves that oscillate normal to the direction of propagation (like a violin string). These waves can only be propagated through solids because fluids are incapable of sustaining a shear stress. They are propagated at a speed of [~/p]'/~, which is also different in different media, and so can be refracted. In fluids, G is sensibly zero, as we have noted. S waves travel at about half the speed of P waves. In the context of the Earth, there is another set of waves called L waves that travel in the surface layers. They have very long periods and travel more slowly than P or S waves (remember, c = h/T). There are two types of L waves. There are Rayleigh waves, in which the particles move in elliptical orbits; and Love waves, with horizontal oscillation normal to the direction of propagation. Surface waves exhibit dispersion, in that their velocity is a function of wavelength, much as sea waves are dispersed according to their wavelength. These different waves travel with different speeds; and the speed of each wave is a function of the density, porosity and elastic properties of the rock through which it passes. At surfaces of density contrast, a proportion of the energy of the wave is refracted, a proportion reflected. P and S waves can be identified on a seismograph and, as a first approximation, the difference in time between the arrival of the first P wave and the first S wave is proportional to the distance the waves have travelled from their source. This is the basis of earthquake location. The severity of earthquakes is measured on two scales, the Richter scale and the Mercalli scale. The Richter scale is a measurement of the energy Copyright 2002 by Richard E. Chapman
Acoustics: sound and other waves 109 of the earthquake at the epicentre of the earthquake, a measurement of its magnitude. The Mercalli scale is a measure of the effect of the earthquake, its local intensity, and it is an arbitrary scale rather like the Beaufort wind scale. The Mercalli scale runs from I (capital roman numerals), for those that are so weak that they are only detected by instruments, to XI1 where there is total destruction and visible waves at the surface. The Mercalli scale can be used to map the intensity of an earthquake over the area affected by it. The Richter scale has been much modified since its introduction in 1935 for Californian earthquakes measured by stations with identical seismometers. Knowing the epicentre of an earthquake in California, the amplitude recorded on the seismometer was plotted against the distance of the station from the epicentre. Because the range of amplitudes was so large, the log- arithm (to the base 10) of the amplitudes was taken, and this led to the comparison of the magnitude of earthquakes by considering the difference of the logarithms (to the base 10) of measured amplitudes - in particular, the comparison with the weakest. The modern Richter scale is an open-ended scale of general application that estimates the total energy of the source, E, from the magnitude, M, by a formula of the form Although the scale is open-ended (it is not a scale from 0 to lo), no earthquake has yet reached 9. What are the units of E? They are considered to be ergs, which are 100 x lop9 joules. See Richter (1984) for a description of the scale that bears his name. There is no convincing correlation between the Mercalli and Richter scales. Local geology has a very important influence on the local effects of earthquakes, as does the geology of the track from the epicentre. Seismic surveys The basis of seismic surveys is to create waves from surface explosions at shot points and time and record their return to the ground or water surface after reflection or refraction from surfaces in the subsurface. Seismic reflection is similar in principle to the echo-sounder in boats, the total time taken by the signal being converted to depth if the velocity of the signal in the water is known. Seismic reflection surveys differ from the echo-sounder in having an array of receivers, called seismometers or geophones, from which multiple echoes from surfaces give multiple points on the surface and so improve the accuracy of the results. The wave from the shot-point is propagated in a hemispherical form that becomes distorted by the different seismic properties of the sedimentary layers it encounters. The velocity of the wave increases with compaction and consolidation and changes with some lithological changes. It is the first arrival at the geophone that is recorded. During the propagation of the wave, its energy is dissipated and the signal attenuated, but there are Copyright 2002 by Richard E. Chapman
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Physics for Geologists Second editi
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Copyright 2002 by Richard E. Chapma
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... vlii Contents Polarization 47 L
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Figures Copyright 2002 by Richard E
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Tables Copyright 2002 by Richard E.
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xiv Preface waves diminishes with d
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xvi Preface provides. This book is
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xviii Acknowledgements to K. Whaler
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xx Symbols mass refractive index bu
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2 Basic concepts Table 1.1 Dimensio
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4 Basic concepts Table 1.2 Basic SI
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6 Basic concepts pascal (Pa) and si
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8 Basic concepts all the relevant d
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10 Basic concepts relating them by
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2 Force The dimensions of force are
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14 Force The ratio of the Moon's ac
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16 Force Figure 2.1 The sum of the
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18 Force When a motorcycle takes a
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20 Force Figure 2.3 Torque is the p
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22 Force How does momentum differ f
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24 Force the weights - that is, the
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26 Force Figure 2.6 Wall-sticking i
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3 Gravity Universal gravity When di
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30 Gravity are significant to geolo
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32 Gravity Figure 3.2 The tractive,
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34 Gravity Mean sea level It might
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36 Gravity The benefits of space fl
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38 Gravity Figure 3.6 Profile of th
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40 Gravity Figure 3.8 The siphon at
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4 Optics Light is an electromagneti
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44 Optics Figure 4.2 Refraction. (a
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46 Optics The coeficient of reflect
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48 Optics only the light oscillatin
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50 Optics called Iceland Spar. Two
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52 Optics Diffraction If you shine
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54 Optics Figure 4.7 Geometrical op
Page 73 and 74: 56 Optics Figure 4.9 The mirrors in
Page 75 and 76: 5 Atomic structure and age-dating P
Page 77 and 78: 60 Atomic structure and age-dating
Page 83 and 84: 66 Electromagnetic radiation radiat
Page 85 and 86: 68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91 and 92: 8 Electricity and magnetism Electri
Page 93 and 94: Electricity and magnetism 77 Figure
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99 and 100: Electricity and magnetism 83 is kno
Page 101 and 102: 9 Stress and strain Pressure, p, is
Page 103 and 104: Stress and strain 87 than some natu
Page 105 and 106: These three elastic constants are r
Page 107 and 108: Stress and strain 91 Figure 9.1 New
Page 109 and 110: Stress and strain 93 Figure 9.2 Com
Page 111 and 112: Stress and strain 95 Figure 9.3 Ide
Page 113 and 114: Fracture Stress and strain 97 We fo
Page 115 and 116: Stress and strain 99 from which we
Page 117 and 118: 10 Sea waves The nature of water wa
Page 119 and 120: Sea waves 103 Figure 10.1 Wave moti
Page 121 and 122: Sea waves 105 refraction by islands
Page 123: Acoustics: sound and other waves 10
Page 127 and 128: 12 Fluids and fluid flow Introducti
Page 129 and 130: Fluids and fluid flow 1 13 Figure 1
Page 131 and 132: Fluids and fluid flow 115 Figure 22
Page 133 and 134: Fluids and fluid flow 117 and the f
Page 135 and 136: water above a vertical thickness h
Page 137 and 138: Fluids and fluid flow 121 where V i
Page 139 and 140: Fluids and fluid flow 123 ardentes,
Page 141 and 142: Fluids and fluid flow 125 Figure 12
Page 143 and 144: - 14 $ 12 E 10 K .- 3 8 r cll + 6 0
Page 145 and 146: Fluids and fluid flow 129 the liqui
Page 147 and 148: Some dangers of mathematical statis
Page 155 and 156: Appendix 139 What would happen if y
Page 157 and 158: Notes 141 and since x is very large
Page 159 and 160: References Allum, J. A. E. (1966) P
Page 161 and 162: References 145 -(1950) 'Mechanism o
Page 163: Further reading 147 Trigg, G. L. an
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