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This book examines the reasons behind the resonant amplification of seismic and ocean waves that have the capacity to destroy cities and ocean-going vessels. Using Charles Darwin’s important geophysical research as a starting point, it provides insights into the interaction between earthquakes with volcanoes, seaquake, and tsunami formation.

In particular, the author details the observations that Darwin made on a powerful earthquake that occurred in Chile in 1835, noting how the famous naturalist and geologist used the concept of earthquake-induced vertical shock to explain the event's devastating impact. The book then goes on to show how Darwin's concept relates to the catastrophic results of the shallow quakes that recently destroyed Port-au-Prince (Haiti, 2010) and severely damaged Christchurch (New Zealand, 2011).

In addition, the author asks whether Darwin's ideas are endorsed by the discoveries of modern science and whether the results of destructive earthquakes can be modeled using strongly nonlinear wave equations. Coverage also proposes that similar equations can be used to simulate the dynamics of many objects on the surface of the Earth, and to model the origin of the Universe, dark matter, and dark energy as strongly nonlinear wave phenomena.

The book will appeal to students as well as researchers and engineers in geophysics, seismology, nonlinear wave studies, cosmology, physical oceanography, and ocean and coastal engineering. It will also be of use to those who are interested in the phenomena of natural catastrophes as well as those who want to learn more about the life and work of Charles Darwin.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Prologue: A Few Notes About Charles Darwin, His Researches and the Contents of the Book

Abstract
Charles Robert Darwin was the brilliant English naturalist whose theory of evolution became the foundation of modern science. Darwin at first shocked religious Victorian society by suggesting that animals and humans shared a common ancestry. Geological results of Darwin is also well-known. Here I attract an attention to geophysical researches of Darwin and emphasize the actuality them for modern science. I stress the Darwin’s interest to earthquake-induced processes during the voyage of the Beagle. I remind that global journeys of British naturalists (including Darwin) was associated with long-existing tradition of the British fleet. This tradition began with the voyage of Joseph Banks, who was the British explorer and long time president of the Royal Society, on H.M.S. Endeavour (1768–1771). In many ways Joseph Banks’ story starts out a lot like Darwin’s. He was born to a wealthy family and was formed as a scientist during his ocean voyage. Like Darwin he visited Brazil, Tahiti, New Zealand and Australia. After Banks the voyages of Robert Brown (1801–1803), Charles Darwin (1831–1836), Joseph Hooker (1839–1843), Tomas Huxley (1846–1850) and Henry Moseley (1872–1876) followed.
Sh. U. Galiev

Chapter 2. Introduction

Abstract
During the voyage of the Beagle, Darwin landed at Valdivia and Concepcion in Chile just before, during, and after the 20 February 1835 Chilean earthquake (Browne, Darwin’s “origin of species”. Atlantic Books, London, 2006). For several days his attention was devoted to results of the earthquake. He observed and described the ‘shivering’ of islands and ridges, fissured ground, volcanic eruptions, and a tsunami. In particular, Darwin wrote … Among the other most remarkable spectacles which we have beheld may be rankedan active volcano; and the overwhelming effects of a violent earthquake. These latter phenomena, perhaps, possess for me a particular interest, from their intimate connection with the geological structure of the world. The earthquake, however, must be to every one a most impressive event: the earth, considered from our earliest childhood as the type of solidity, has oscillated like a thin crust beneath our feet; and in seeing the laboured works of man in a moment overthrown, we feel the insignificance of his boasted power … (Darwin, The origin of species, 6th edn. John Murray, London, 1872, pp. 601–602).
Darwin suggested that the earthquake was a result of … the rending of strata, at a point not very deep below the surface of the earth … (Nature 456(7220), 2008, p. 70) and … From the intimate and complicated manner in which the elevatory and eruptive forces were shown to be connected during this train of phenomena, we may confidently come to the conclusion that the forces which slowly and by little starts uplift continents, and those which at successive periods pour forth volcanic matter from open orifices, are identical. From many reasons, I believe that the frequent quakings of the earth on this line of coast are caused by the rending of the strata, necessarily consequent on the tension of the land when upraised, and their injection by fluidified rock. This rending and injection would, if repeated often enough (and we know that earthquakes repeatedly affect the same areas in the same manner), form a chain of hills; and the linear island of S. Mary, which was upraised thrice the height of the neighbouring country, … (Darwin, The origin of species, 6th edn. John Murray, London, 1872, pp. 376–377).
Thus, Darwin wrote about crust tension and we emphasize that he connected the earthquake and the eruptions with the crust rupture. Darwin thought that the earthquake-induced vertical motion of the land surface could explain his observations. Perhaps that is true if the accelerations of the land are large enough. However, usually the earthquake-induced acceleration of the land surface is not large (smaller than g). And the vertical ground motion is usually much smaller than the horizontal motion. Therefore, earthquake-hazard assessment studies have usually been focussed on the horizontal shocks, and the effects of strong vertical shocks were practically never discussed. The margins of safety against gravity-induced static vertical forces in constructing buildings usually provide adequate resistance to dynamic forces induced by the vertical acceleration during an earthquake.
But what does modern science know about the amplitude of strong wave motions of the Earth’s surface? Can the strong vertical motion of the land be responsible for the results of the 20 February 1835 Chilean earthquake? Can modern experimental and theoretical data explain Darwin’s observations? We try to reply to these questions here and later in this book.
Sh. U. Galiev

Chapter 3. Extracts from Darwin’s Publications, and His Basic Geophysical Ideas

Abstract
The 3-volume Narrative of the Surveying Voyages of His Majesty’s ships Adventure and Beagle was published in London by Henry Colburn in 1839. Volume 1 contains FitzRoy’s Proceedings of the first expedition, Volume 2 contains FitzRoy’s Proceedings of the second expedition and Volume 3 contains Darwin’s Journal and Remarks. Darwin’s Volume 3 was reprinted a few weeks later as a separate book Journal of Researches into the Geology and Natural History of the various countries visited by H. M. S. Beagle under the command of Captain FitzRoy, R.N. from 1832 to 1836, which got published in German translation. Darwin revised that book significantly for the second edition published in 1845 by John Murray, and that 2nd edition has been reprinted very many times (with many variations in the title) and translated into many languages. The texts of the 1839 and 1845 editions of Journal of Researches can conveniently be compared at the website http://​www.​rockvillepress.​com/​tierra/​texts/​Journal-2.​PHP. FitzRoy’s Volumes 1 and 2 have twice been reprinted: in the facsimile edition of the 3 volumes (including Darwin’s Journal and Remarks) by AMS Press, New York 1966; and in a 4-volume version (edited by Katharine Anderson), Pickering & Chatto, London 2012.
On February 20, 1835 Darwin experienced a great earthquake at Valdivia. The devastation was horrifying – nearly every building in the area was destroyed. Then the Beagle went to the city of Concepcion, and while the Beagle tried to make anchorage there, Darwin landed on the island of Quiriquina. There he found areas of the land that had risen a few feet due to the earthquake, and he was very excited by that discovery. It was direct evidence that the Andes Mountains, and indeed all of the South America, were very slowly rising above the ocean. That confirmed Charles Lyell’s theory that land masses were rising in tiny increments during an extremely long period of time. Charles Lyell (1797–1875) was a great geologist, and the first edition of his famous Principles of Geology was Charles Darwin’s ‘vade mecum’ during the voyage of the Beagle (Sibson Seismological Res Lett 77(3):358–363, 2006). Lyell argued that the face of the Earth had changed gradually over long periods of time through continuing, cumulative effects of local disturbances, such as eruptions, earthquakes, erosion and deposition. The planet was changing locally, eroding here, erupting there, in a state of perpetual directional flux during an unimaginable span of time. Darwin was greatly impressed by Lyell’s ideas, and he considered them to be an important influence on his theory of natural selection. Given this fact of uplift, Darwin accepted the idea that the Earth must be extremely old. The next day he sailed to the town of Talcahuano and from there he rode a horse to Concepcion to meet up with the Beagle.
Darwin concentrated on one of the most important geological problems: elevation and subsidence of the Earth crust. This enhanced his interest in the effects of the great earthquake which he witnessed in Chile. He observed the earthquake-induced uplift of the ground surface, and that observation supported his opinion that the high Andes have been formed as a result of the ceaseless vertical movement of the crust. The modern theory explains this formation by movement of the tectonic plates.
In this Chapter we present some pages from the accounts by Darwin of that great earthquake. And there are some of Darwin’s memories of the voyage of the Beagle, and of that period when he thought of himself as a geologist. At the end of the Chapter we shortly discuss Darwin’s thoughts about the earthquake-induced catastrophic phenomena (Keynes, The Beagle record. Cambridge University Press, Cambridge, 1979; Darwin, Journal of researches into the geology and natural history of the various countries visited by H.M.S. Beagle, under the command of Captain FitzRoy, R.N. from 1832 to 1836, 1st edn. Henry Colburn, London, 1839; FitzRoy, Narrative of the surveying voyages of His Majesty’s Ships Adventure and Beagle, between the years 1826 and 1836, describing their examination of the southern shores of South America, and the Beagle’s circumnavigation of the globe, vol 2. Henry Colburn, London. Proceedings of the second expedition, 1831–1836, under the command of Captain Robert Fitz-Roy, R N, 1839; Darwin, On the connexion of certain volcanic phenomena in South America; and on the formation of mountain chains and volcanoes, as the effect of the same power by which continents are elevated. (Read March 7, 1838). In: Barrett PH (ed) (1977) The Collected Papers of Charles Darwin. The University of Chicago Press, Chicago, 1840), the Earth’s dynamics and extreme waves.
Sh. U. Galiev

Chapter 4. Darwin’s Reports on Catastrophic Natural Phenomena and Modern Science: Topographic Effect and Local Circumstances

Abstract
Earthquakes, eruptions of volcanoes, connection of seismic and volcanic processes – all these phenomena stand among Darwin’s most strong impressions during the round-world voyage of the Beagle. He saw the powerful forces which had been, for a long time, changing the surface of the Earth. Darwin thought over these processes and their connections, and that led to his reflection in the books (Darwin, Journal of researches into the geology and natural history of the various countries visited by H.M.S. Beagle, under the command of Captain FitzRoy, R.N. from 1832 to 1836. Henry Colburn, London, 1839; Darwin, Journal of researches into the natural history and geology of the countries visited during the voyage of H.M.S. Beagle around the world, under the command of Captain Fitz Roy, R N. T Nelson and Sons, London, 1890; Narrative of the surveying voyages of His Majesty’s Ships Adventure and Beagle, between the years 1826 and 1836, describing their examination of the southern shores of South America, and the Beagle’s circumnavigation of the globe. Henry Colburn, London, 1839. Vol 2. Proceedings of the second expedition, 1831–1836, under the command of Captain Robert Fitz-Roy, R N) and his large article (Darwin, On the connexion of certain volcanic phenomena in South America; and on the formation of mountain chains and volcanoes, as the effect of the same power by which continents are elevated. (Read March 7, 1838) In: Barrett PH (ed) (1977) The Collected Papers of Charles Darwin. The University of Chicago Press, Chicago; 1840).
Local effects of great earthquakes can be determined by three main factors: distance from the earthquake source, travel path of seismic waves from the source to a particular location, and local site conditions (Darwin, On the connexion of certain volcanic phenomena in South America; and on the formation of mountain chains and volcanoes, as the effect of the same power by which continents are elevated. (Read March 7, 1838) In: Barrett PH (ed) (1977) The Collected Papers of Charles Darwin. The University of Chicago Press, Chicago; 1840; Reiter, Earthquake hazard analysis. Columbia University Press, New York, 1990; Robinson, Earth shock. Thames and Hudson, London, 1993). Darwin saw personally only some results of the strong earthquake. Apparently, Darwin observed results of local amplification of the earthquake-induced ground motion.
Sh. U. Galiev

Chapter 5. Darwin’s Reports on Catastrophic Natural Phenomena and Modern Science: Seaquake-Induced Waves, Atomization and Cavitation

Abstract
Darwin reported that … From the great wave not immediately following the earthquake, but sometimes after the interval of even half-an-hour, …it appears that the wave first rises in the offing; and as this is of general occurrence, the cause must be general. I suspect we must look to the line where the less disturbed waters of the deep ocean join the water nearer the coast, which has partaken of the movements of the land, as the place where the great wave is first generated. It would also appear that the wave is larger or smaller, according to the extent of shoal water which has been agitated together with the bottom on which it rested…(Darwin, Journal of researches into the natural history and geology of the countries visited during the voyage of H.M.S. Beagle around the world, under the command of Captain Fitz Roy, R.N. T. Nelson and Sons, London, 1890, p. 374). These words, and also the material given in the Chap. 3 show that Darwin had described the formation and the coastal dynamics of ocean waves caused by the earthquake. Obviously, he was the first who had given a qualitative, but scientific, analysis of this phenomenon, and had emphasized the complex character of the coastal development of tsunamis. Describing results of the earthquake Darwin wrote also … two explosions, one like a column of smoke, and another like the blowing of a great whale, were seen in the bay of Concepcion. The water also appeared every where to be boiling; and it ‘became black, and exhaled a most disagreeable sulphureous smell’.The two great explosions in the first case must no doubt be connected with deep-seated changes; but the bubbling water, its black colour and fetid smell, the usual concomitants of a severe earthquake, may, I think, be attributed to the disturbance of mud containing organic matter in decay … (Darwin, Journal of researches into the geology and natural history of the various countries visited by H.M.S. Beagle, under the command of Captain FitzRoy, R.N. from 1832 to 1836. Henry Colburn, London, 1839, р. 374). Thus, Darwin had described the behaviour of the shallow sea and the bottom mud during a seaquake. The explosions are results of the passing up of large cavitation zones (bubbles) through the sea/atmosphere surface. These zones were formed because of vertical oscillations of the sea bed. Surface waves and the boiling may be also explained by the seaquake. Apparently, bubbles and surface waves may also appear in the mud because of the underwater earthquake.
Darwin drew very complex pictures of the behaviour of the sea during severe seaquakes, when different kinds of extreme waves may form in the water, with some of them evolving into vortices. Generally speaking, extreme waves similar to those in the ocean might exist in different media and physical fields. In the last sections of the Chap. 7 we consider waves and vortices in scalar fields which resemble excited by seaquakes.
Sh. U. Galiev

Chapter 6. Extreme Wave/Ship Interaction

Abstract
Catastrophic (extreme) ocean waves differ from tsunamis. Tsunamis become dangerous only when they come to the coastal zone. On the contrary, catastrophic ocean waves most often arise far from the coast. The Beagle met an extreme wave near Cape Horn. Darwin wrote … On the 13th the storm raged with its full fury; our horizon was narrowly limited by the sheets of spray borne by the windAt noon a great sea broke over us, and filled one of the whale-boats,The poor Beagle trembled at the shock, and for a few minutes would not obey her helm; but soon, like a good ship that she was, she righted and came up to the wind again. Had another sea followed the first, our fate would have been decided soon and for ever … (Darwin, Journal of Researches into the Natural History and Geology of the Countries Visited during the Voyage of H.M.S. Beagle Around the World, under the Command of Captain Fitz Roy, R N T Nelson and Sons, London, 1890, pp. 264–265).
This description indicates that the Beagle met a storm transforming into a hurricane. According to the standard scale of Sir Francis Beaufort, during a storm there are extremely high waves whose crests are blown off in foam. The maximum height of these waves is up to 16 m, an average height is 11.5, the wind is 28.5–32.6 m/s. During a hurricane the wind speed may be larger, the air is filled with foam and splashes, and the visibility is very bad. The situation is extremely dangerous for small vessels, such as the Beagle. Thus, according to the scale, the storm described by Darwin was a hurricane, for which the ocean around Cape Horn is famous. Huge waves reaching 16 m kept the crew under extreme pressure. However, during such an event which the crew had probably got used to, the vessel was shaken by a single huge wave. From Darwin’s description, it appears that this wave may be described as catastrophic. Only during recent years have these waves drawn the attention of the public and of scientists (Kurkin and Pelinovsky, Волны-убийцы: Факты, Теория и Моделирование (Freak waves: facts, theory and modelling). NNSTU, Nizhny Novgorod, 2004; Liu and MacHutchon, Are there different kinds of rogue waves? OMAE2006-92619, 2006; Liu et al. Exploring rogue waves from observations in South Indian Ocean. http://www.ifremer.fr/web-com/stw2008/rw/fullpapers/liu.pdf, 2006; Fochesato et al. Wave Motion 44(5):395–416, 2007; Dysthe et al. Annu Rev Fluid Mech 40:287–310, 2008; Olagnon and Prevosto, Rogue waves 2008. Ifremer http://www.ifremer.fr/web-com/stw2008/rw/, 2009; Kharif et al. Rogue waves in the ocean. Springer, Berlin, 2009; Denchfield et al. A deep-water beach laboratory generation of abnormal waves. In: Olagnon M, Prevosto M (eds) Rogue waves. Ifremer, 2009; Akhmediev et al. Phys Lett A 373:675–678, 2009; Akhmediev et al. Phys Lett A 373:2137–2145, 2009; Zakharov et al. Eur Phys J-Spec Top 185(1):113–124, 2010; Kibler et al. Nat Phys 6:790–795, 2010; Vennell, J Fluid Mech 650:427–442, 2010; Nikolkina and Didenkulova, Nat Hazards Earth Syst Sci 11:2913–2924, 2011; Latifah and van Groesen, Nonlinear Process Geophys 19:199–213, 2012; Chabchoub et al. Phys Rev X 2:011015, 2012; Galiev and Mace, Lagrangian description of extreme ocean waves. Известия Уфимского Научного Центра Российской Академии Наук (Herald of Ufa Scientific Center, Russian Academy of Sciences (RAS)) 4:6–13, 2014). Indeed, over the last 20 years more than 200 super-carrier-cargo ships over 200 m long have been lost at sea. Eyewitness reports suggest that many were sunk by high and violent walls of water that rose up out of calm seas (Kurkin and Pelinovsky, Волны-убийцы: Факты, Теория и Моделирование (Freak waves: facts, theory and modelling). NNSTU, Nizhny Novgorod, 2004; Kharif et al. Rogue waves in the ocean. Springer, Berlin, 2009) (see also the Sect. 3.​3.​6).
Sh. U. Galiev

Chapter 7. Modelling of Extreme Waves in Natural Resonators: From Gravity Waves to the Origin of the Universe

Abstract
Many objects in Nature may be considered as natural resonators. When an object is stimulated at its resonant frequency, the amplitude of the vibrations is greatly increased. We connected above the appearance of extreme waves with this phenomenon. In particular, there natural resonators exist including sediment layers, ocean, hills, volcanoes, the ocean shelf and so on. Their resonant effects can cause rapid and very large amplitude growth of seismic waves. For example, our model of a natural resonator explained particularities of the tsunami evolution described by Darwin (cf. the Chap. 5) and the behaviour of Tarzana hill during an earthquake (cf. the Sect. 4.​1.​4).
In this Chapter we will give further remarks about experimental observations of this catastrophic amplification, and our theoretical research about it. On the other hand, it is our purpose to emphasize the common character of some results presented in the book. We considered above extreme seismic and ocean waves. We have shown that there are similarities of highly-nonlinear wave phenomena in many areas of wave dynamics. However, up to now highly-nonlinear wave phe-nomena have been poorly understood. Is there a universal, generic theory that can describe all these wave phenomena? We believe that such a theory has been created for 1-dimensional waves which are sufficiently long. We think that many extreme waves are the result of resonant nonlinear amplification of initially small-amplitude waves. We also believe that this theory, when applied to the nonlinear Klein-Gordon equation might shed light on the emergence and initial evolution of the Universe.
For example, Darwin described the local amplification of the seismic waves which ruptured the small island Quiriquina. I suggested that this island could be regarded as a natural resonator Galiev (J Phys A Math Gen 32:6963–7000, 1999). Darwin wrote about…the parallel and steep sides of the narrow island… (Darwin, Journal of researches into the geology and natural history of the various countries visited by H.M.S. Beagle, under the command of Captain FitzRoy, R.N. from 1832 to 1836, 1st edn. Henry Colburn, London, 18392, p. 370). Very long seismic waves excited the shelf and vibrated the base of the island. Qualitative scheme of waves which might be excited on the island surface are shown in Fig. 7.1. Generally speaking, shock-like waves might have been excited in the island material during of the 20 February 1835 Chilean earthquake (Galiev J Phys A Math Gen 32:6963–7000, 1999; Galiev Geophys J Int 154:300–354, 2003). Analogously, the earthquake-induced motion of ground surface can force surface waves in sediment valleys (basins) and lakes (Fig. 7.1).
In this Chapter we outline briefly an approximate, but universal, generic theory of extreme waves, which can appear in different processes from earthquakes till the origin of the Universe (Galiev J Phys A Math Gen 32:6963–7000, 1999; Galiev Geophys J Int 154:300–354, 2003; Galiev, Нелинейные волны в ограниченных средах (Nonlinear waves in bounded continua). Naukova Dumka, Kiev (in Russian), 1988; Galiev, Resonant oscillations governed by the Boussinesq equation with damping. In: Proceedings of 5th international congress on sound and vibration, Adelaide, pp 1785–1796, 1997; Galiev Adv Hydrosci Eng 3:179–182, 1998; Galiev and Galiyev Phys Lett A 246:299–305, 1998; Galiev and Galiyev Chaos 11:686–704, 2001; Galiev Phys Lett A 311:192–199, 2003; Galiev Phys D 208:147–171, 2005; Galiev, Strongly-nonlinear wave phenomena in restricted liquids and their mathematical description. In: Perlidze T (ed) New nonlinear phenomena research. Nova, New York, 2008; Galiev, Modelling of Charles Darwin’s earthquake reports as catastrophic wave phenomena. https://researchspace.auckland.ac.nz/handle/2292/4474, 2009; Galiev, Геофизические Cообщения Чарльза Дарвина как Mодели Теории Катастрофических Волн (Charles Darwin’s geophysical reports as models of the theory of catastrophic waves). Centre of Modern Education, Moscow (in Russian), 2011; Galiev and Galiyev, Scalar field as a model describing the birth of the Universe. InterNet. Galiev – Galiyev, Dec 18 2013, 2013; Galiev ShU, Galiyev TSh (2014) Nonlinear scalar field as a model describing the birth of the Universe. Известия Уфимского Научного Центра Российской Академии Наук (Herald of Ufa Scientific Center, Russian Academy of Sciences (RAS)) 2:7–33). We use well-documented experiments and observations so to check the theory.
Sh. U. Galiev

Chapter 8. Last Comments on Charles Darwin’s Geophysical Observations

Abstract
We tried to show in the book that Charles Darwin’s geophysical observations continue to arouse great interest up to this moment.
Sh. U. Galiev

Backmatter

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