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Bulletin of the Seismological Society of America, Vol. 85, No. 4, pp. 1202-1225, August 1995

Review A Concise History of Mainstream : Origins, Legacy, and Perspectives

by Ari Ben-Menahem

Abstract The history of seismology has been traced since man first reacted lit- erarily to the phenomena of and volcanoes, some 4000 yr ago. Twenty- six centuries ago man began the quest for natural causes of earthquakes. The dawn of modern seismology broke immediately after the Lisbon of 1755 with the pioneering studies of John Bevis (1757) and John Miehell (1761). It reached its pinnacle with the sobering discourses of Robert Mallet (1862). The science of seismology was born about 100 yr ago (1889) when the first te- leseismic record was identified by Ernst yon Rebeur-Pasebwitz at , and the prototype of the modern seismograph was developed by and his associates in . Rapid progress was achieved during the following years by the early pioneers: Lamb, Love, Oldham, Wieehert, Omori, Golitzin, Volterra, Mohorovi~ie, Reid, Z~ppritz, Herglotz, and Shida. A further leap forward was gained by the next generation of seismologists, both experimentalists and theoreticians: Gutenberg, Richter, Jeffreys, Bullen, Lehmann, Nakano, Wadati, Sezawa, Stoneley, Pekeris, and Benioff. The advent of long-period seismographs and computers (1934 to 1962) finally put seismology in a position where it could exploit the rich information inherent in seismic signals, on both global and local scales. Indeed, during the last 30 yr, our knowledge of the infrastructure of the 's interior and the of seismic sources has significantly grown. Yet, an ultimate goal of seismology, namely, the prediction of earthquakes, is not forthcoming. In spite of vast deployment of instru- ments and manpower, especially in the United States and Japan, no substantial pro- gress has been made in this direction. The nonlinear dynamic processes at the sources of earthquakes are not yet understood, and with the lack of proper mathematical tools and physical theory, breakthrough is not apt to come through computers and seis- mographs. The conclusion of the present historical study can be succinctly phrased as follows: seismology has reached a where its lofty goals cannot be pursued by seismol- ogists alone. Unless we launch a concentrated interdisciplinary research effort, we shall always be surprised by the next major earthquake.

Introduction "Everything is a matter of chronology" made by applied mathematicians (Wiener, 1930; Lighthill, Marcel Proust, Remembrance of Things Past 1960), physicists (Jeans, 1923; Born, 1925; Foek, 1946), and engineers (La Coste, 1934), continued to play central Seismology is an interdisciplinary science: most of the the- roles in seismology. ory needed to interpret seismograms, prior to 1922, had been Thus, the history of seismology is inseparable from the made available through the efforts of physicists and math- history of the great achievements in continuum mechanics, ematicians of the seventeenth, eighteenth, nineteenth, and applied mathematics, and general wave theory. Moreover, it early twentieth centuries. Even after 1922, contributions is not possible to isolate theoretical seismology from the rest

1202 A Concise History of Mainstream Seismology: Origins, Legacy, and Perspectives 1203 of the science, since phenomenology, experiment, and the- 7. Earth's internal structure (E), ory are strongly linked throughout. 8. anelasticity (AE), and The history of seismology did not really begin in 1889; 9. anisotropy (AI). if we may compare this science to a plant, then 1889 was the year that the seed broke the surface. Its true origin may Each "event" describes some step, or landmark, in the evo- be placed on 1 November 1755, during the Lisbon earth- lution of seismology; it is associated with a date (mostly a quake--an event that changed dramatically man's outlook year), a short specification of the nature of the discovery or on the phenomenon of earthquakes. Since then, major earth- invention, associated persons, and finally a category (one of quakes continued to serve as milestones on the road of pro- the above nine initials). gress. [E.g., Mino-Owari, central Japan, 28 October 1891: The choice of the items and of the individual first documentation of surface faulting. India, 12 June 1897: in these lists is unavoidably based on my own judgement, Oldham's first observation of P, S, and R waves. California, taste, and knowledge. There will always be arguments about 18 April 1906: Reid's elastic rebound theory. Long-Beach, omissions and commissions in such lists, and no two re- 10 March 1933: advent of . Chile, 22 viewers will emerge with identical choices. I must therefore May 1960: experimental verification of the propagating rup- define here the scope and intent of the writing, together with ture of faults and the Earth's free oscillations.] my criteria for exclusion of researchers. The year 1889 is nevertheless a remarkable year in the Let us first address the problem of the role of the indi- history of our science the birth year of the teleseismic seis- vidual in the history of science. As long as one is mogram; seismology became at once a global science! interested in scientific results only, one may ignore the man Earthquakes ceased to be the local affairs of cities. A grand behind the discovery, and then time becomes amorphous, communication line has been opened, which goes across while science is anonymous. But as soon as one studies the countries, continents, oceans--all geographical barriers evolution of ideas, the mask is unveiled and one is con- were suddenly broken. fronted with people, flesh and blood, and people have names, This was indeed the first revolution in seismology. The territories, and destinies. Like any other group of humans, second revolution occurred during 1950 to 1955 when dig- they have their heroes, villains, and saints. Thus, their lives ital computers were first introduced in seismology. The abil- become an integral part of science, as well as their scientific ity to perform fast calculations increased the dimensionality achievements. of seismology both in space and time: huge amounts of data The scope of the present essay is limited to a succinct could suddenly be processed in a relatively short time; in- description of the landmarks (alias signposts; alias mile- tegrals and sums could be evaluated quickly, and equations stones) in the evolution of earthquake lore. The choice of of all sorts could be solved most efficiently. these events was based on the following three rules: As one delves into the history of seismology, one be- 1. Every item of the list could not have evolved without the comes gradually more and more fascinated with the internal "pre-knowledge" of some or all of its predecessors, i.e., logic of its heritage, with the people behind the discoveries, no item is redundant; every link in the chain is essential, and with the intricate subtle interrelations between seismol- although not of equal importance. ogy, , astronomy, meteorology, and physics. How- 2. Each item is referenced in a leading encyclopedia (e.g., ever, unfolding this story before an audience is a totally dif- Britannica) and/or an authoritative history book. I did not ferent matter, for then the science historian must answer to include information that had not been cross-referenced in himself and to others certain important questions: in what at least two such sources (see References). way does this history manifest itself? Does it abide by a 3. All results in theoretical seismology and seismometry are chronological sequential order of events? Is it a linear pro- essential to the understanding and quantification of pres- cess, does it swing back and forth, are there gaps, is it ran- ent-day phenomena and data analyses. dom or is it deterministic? There are many ways of displaying the answers to these Credit by name was given to 150 men, the majority of whom fundamental questions. Given the limits of our knowledge are not alive today. The References, which cover the period and the limited scope of the present article, I have decided up to 1964, includes the works of some additional 200 men to open with a short historical overview, followed by a more of science. detailed list of "events." The "events" cover nine disciplines: Historical Overview 1. phenomenology (P), 2. seismometry and experimental seismology (S), Early historical records contain references to earth- 3. theory of seismic fields in the earth (rays, waves, modes, quakes as far back as 2000 B.C.E. These accounts are, for beams) (T), the most part, of little value to the seismologist. There is a 4. surface waves (SW), natural tendency to exaggeration in describing such phenom- 5. free oscillations of the Earth (F), ena, sometimes indeed to the extent of importing a super- 6. seismic sources (SS), natural element into the description. Nevertheless, attempts 1204 A. Ben-Menahem

were made by some ancient writers on natural philosophy In 1857, the first true seismologist (as we would now to offer rational explanations of earthquake phenomena. recognize the term in hindsight), appeared on the scene: These views (although based upon hypotheses which, as a Robert Mallet (1810 to 1881, Ireland), the engineer who rule, are too fanciful to be worth dwelling upon in great laid the foundation of instrumental seismology. He was born detail), as summarized in the writings of such historians and in Dublin, and after taking his degree at Trinity College in philosophers as Thucydides, , Strabo, Seneca, Livy that city, he went into his father' s small engineering factory. and Pliny, indicate very clearly that the early Greek philos- After building a lighthouse and a number of bridges, he be- ophers had already abandoned the mythological explana- came interested in global and earthquake engi- tions in favor of natural causes of earthquakes inside the neering problems. His detailed study of the damage caused earth. by the Napolitan earthquake of 1857 led him to suggest the Aristotle (ca. 340 B.C.E.) gave a classification of earth- setting up of a network of observatories over the Earth's quakes into six types, according to the nature of the earth surface. He published the first world seismicity map and movement observed; for example, those which caused an made the first systematic attempt to apply physical principles upward earth movement, those which shook the ground from to earthquake effects (1862). Mallet made estimates of the side to side, etc. The earliest instrument known to us that epicentral depth and also carded out a number of experi- was made to respond to earthquake ground motion is the ments to determine the velocity of earth waves by setting off seismoscope, invented in 132 A.D. by the Chinese scholar charges of explosives in different soils and by measuring the Chang Heng. It revealed the direction of ground motion. results on bowls of mercury set at varying distances up to Later seismoscopes were designed to also give the time of 800 m away. occurrence of a shock. This instrument is reputed to have The first , deserving its name, was designed detected some earthquakes not felt locally. in 1841 by the physicist James David Forbes (1809 to Not much was gleaned from the pages of medieval and 1868, ). The name was coined by David Milne later writers on earthquakes. In England, the earliest work Home in 1841. A few years later, the name seismograph worthy of mention is Robert Hooke's Discourse on Earth- was given to an instrument built by Luigi Palmieri (1855) quakes (1667 to 1697). This publication, though containing in the observatory on Vesuvius. It consisted of an inverted many passages of considerable merit, tended but little to a pendulum, hinged below by a cylindrical steel wire. A pencil correct interpretation of the phenomena in question. Equally attached to the top of the pendulum rod recorded the motion unsatisfactory were the attempts of Joseph Priestley and on paper. The first useful seismograph system, recording some other scientific writers of the eighteenth century to ground displacements, was constructed in Japan in 1880 by connect the cause of earthquakes with electrical phenomena. John Milne and his assistants James and Moreover, some scientists were not sure anymore of the nat- Thomas Gray. However, this instrument had insufficient ural origin of earthquakes, as we learn from a writer in the magnification and could record only local earthquakes. Philosophic Transactions of the Royal Society of London, as In 1889, Ernst von Rebeur-Paschwitz (1861 to 1895, late as 1750 A.D., who deemed it expedient to apologize to ) was experimenting in Potsdam with a modified "those who are apt to be offended at any attempts to give a form of Z611ner's horizontal pendulum (V0 = 50, To = 18 natural account of earthquakes." Notwithstanding, stubborn sec, no damping) when an earthquake from Japan was re- facts of earthquake effects continued to accumulate, espe- corded. This event marks the birth of instrumental seismol- cially in the wake of the disastrous Lisbon earthquake of ogy in its worldwide sense. Stimulated by these observa- 1755. Finally, it was firmly established by the Rev. John tions, by 1894 Milne was able to design, construct, and test Michell (1761), professor of geology at Cambridge, that the now famous seismograph that bears his name. It was earthquakes originate within the Earth. He declared that capable of detecting earthquake waves that had traveled "earthquakes were waves set up by the shifting masses of many thousands of kilometers from their origin. Moreover, miles below the surface.., the motion of the earth in it was sufficiently compact and simple in operation to enable earthquakes is partly tremulous and partly propagated by it to be installed and used in many parts of the world. It waves which succeed each another," and he estimated that could record all three components of the ground displace- the earthquake waves after the Lisbon earthquake had trav- ments (up-down, east-west, north-south). From this time eled outward at 530 m/sec. onward, precise instrumental data on earthquakes began to Another person to suggest that the influence of earth- accumulate, and seismology has developed from the quali- quakes propagate in the earth in the form of waves with finite tative toward the quantitative side. The seismograph is to the velocity was Thomas Young (1807). earth scientist what the telescope is to the astronomer--a Most of the work on earthquakes during 1760 to 1840 tool for peering into inaccessible regions. For that reason was concerned with appraisals of geological effects, and ef- one may consider the year of the deployment of the Milne fects on buildings. Early in the nineteenth century, earth- seismographs as an important milestone in the history of quakes lists were being regularly published, and in 1840 seismology. Indeed, since 1894, the number of instrumen- there appeared the first earthquake catalog for the whole tally recorded earthquakes steady increased; the earliest world. known list of earthquakes with computed origin times and A Concise History of Mainstream Seismology: Origins, Legacy, and Perspectives 1205 is that for the period 1899 to 1903. Further im- of the Earth's . This discovery demonstrated that the provement in the design of seismographs was due to Fusak- structure of the Earth's outer layers could be deduced from ichi Omori (1868 to 1923, Japan) and (1861 travel times of reflected and refracted seismic signals. This to 1928, Germany), who gave a detailed account of his me- was known to John Milne already in or prior to 1906! chanical seismograph (1900), Boris Borisovieh Golitzin (Milne, 1906, pp. 365-376.) (1862 to 1916, Russia), designed the first electromagnetic In 1914, (1889 to 1960, Germany and seismograph with photographic recording (1906). Wiechert U.S.A.) published his accurate determination of the depth of designed a seismograph in which the pendulum is vertical the boundary of the Earth's core at 2900 km below the sur- and inverted, being maintained by small springs pressing face. (In 1926 he discovered a global low-velocity zone at a against supports rigidly attached to the ground. The mass of depth of 70 to 250 km in the Earth's , known as the the pendulum is large (up to several tons), and the seismo- .) In 1936, Inge Lchmann (1888 to 1993, graph records both horizontal components at once. A car- Denmark) produced the first evidence of the existence of the dinal development took place when Golitzin introduced the Earth's solid inner core with a radius of ca. 1400 km. idea of recording ground motion by means of a ray of light The advent of elastodynamics began with the discovery reflected from the moving mirror of a galvanometer: the mo- of longitudinal and transverse waves by Poisson in 1828, tion of the mirror is excited by an electric current generated and their physical interpretation by Stokes in 1845. In 1885, by electromagnetic induction when the pendulum of the seis- Lord Rayleigh discovered, ahead of observations, another mometer moves. The next development came in 1935, when type of elastic waves (to be known later as the Rayleigh Hugo Benioff (1899 to 1968, U.S.A.) designed and con- wave) that is associated with material discontinuities such as structed an instrument to measure a component of ground a free surface of a body. In 1897, Oldham identified on strain. earthquake recordings (seismograms) the three main types The strain seismometer measures the variation in the of waves predicted by Poisson and Rayleigh, thus confirm- distance between two points, some 30 m apart, caused by ing that, at least for short-period wave motion (dominating the passage of seismic waves. Benioff's recording was elec- periods: 0.1 to 1 sec), the Earth indeed behaves like an elastic tromagnetic, the original galvanometer period being 40 sec, body for which Hooke's law may apply. In 1899, Cargill subsequently increased to 480 sec. His strain seismograph Gilston Knott (1856 to 1922, Scotland and Japan) derived was the first to record earth motions with periods up to the the general equations for and refraction of plane order of 1 hr, such as the gravest mode of the free oscilla- elastic waves at plane boundaries. This was needed to relate tions of the Earth (1952). the amplitudes of the waves activating the seismometer to The science of seismology aims simultaneously to ob- the corresponding seismogram traces, modified by the pres- tain the infrastructure of the Earth's interior with the aid of ence of the free surface of the Earth. In 1904, Horace Lamb phenomena, and to study the nature of earth- (1849 to 1934, England) came forth with the first mathe- quake sources with the ultimate goal of mitigating and even- matical theory of a point-source earthquake in a half-space tually controlling the phenomenon. This double feature is Earth model. He thus layed the theoretical foundation for the apparent from the early days of this science. propagation of seismic waves in layered media. The first The achievements toward the first goal began in 1799, inverse problem in was formulated and solved when Cavendish employed Newton's law of universal grav- in 1907 by Gustav (Ferdinand Joseph) Herglotz (1881 to itation to estimate the Earth's mean density [(p) = 3/(4riG) 1953, Germany), enabling the intrinsic compressional and g(R)/R ~-- 5.5 g/cm3]. As this density exceeded the density shear velocities to be determined from travel-time data. By of surface rocks, the conclusion was that the density must 1909, E. Wiechert, K. Zoeppritz, and L. Geiger exploited increase with depth in the Earth. By means of observations this method and obtained for the first time a profile of com- of the tidal effect on the solid Earth, Lord Kelvin claimed pressional wave velocity in the Earth's mantle. A significant in 1863 that the Earth as a whole is more rigid than glass. contribution to theoretical seismology was made in 1911 by (This opinion has been confirmed later, when it was found Augustus Edward Hough Love (1863 to 1940, England) that steel offers a better comparison, where the gravest mode with his discovery of a horizontally polarized of the Earth's free oscillation is concerned.) In 1897, Wiech- (now known as the ), from the analysis of which eft conjectured from theoretical calculations that the Earth's seismologists could derive estimates of the thickness of the interior consists of a mantle of silicates, surrounding a core Earth's crust and its rigidity. of iron. The existence of the Earth's core was established by A further advance during 1915 to 1936 was made by Richard Dixon Oldham (1858 to 1936, India and England) (1891 to 1989, England), who brought to in 1906, from observations of earthquake waves. bear mathematical and statistical methods and a great knowl- In 1909, Andrija Mohorovifiie (1857 to 1936, Zagreb) edge of wider geodynamical problems. His attention to sci- discovered a sharp material discontinuity at some level be- entific method and statistical detail has been one of the main low the Earth's surface (known today as the Moho), which forces through which pre-World War II seismology has at- could explain the travel times of seismic rays from a local tained its level of precision. earthquake. It was subsequently found to demarcate the base Significant progress in seismology has been made 1206 A. Ben-Menahem

through the first four decades of the twentieth century: in Since 1556, about 6 to 7 million persons have been 1901, the first Geophysical Institute was founded in G6ttin- killed by earthquakes. gen (Germany), and the number of seismic observatories capable of teleseismic recording reached 25 (compared to Calendar of Progress eight in 1894). By 1940, there were about 10 major seismic research centers and 250 seismic stations around the globe. ca. 2100 to 600 B.C.E. Biblical allusions to major earth- An international Association of Seismology was quakes on the Dead system occurring since ca. founded in 1905 at a meeting in Berlin of representatives 2100 B.C.E. (P) from 23 countries, which met again in Rome in 1906 where ca. 1560 B.C.E. and 759 B.C.E. Although the primary it was decided to establish an international center at Stras- causes of these events were attributed by prophets and the bourg. The year 1919 saw the appearance of a bulletin of scribes of the Bible to a single supreme power, the descrip- global recordings of earthquakes, published at Oxford, under tions of the phenomena itself are rather accurate, and must the name International Seismological Summary (I.S.S.). have originated with keen observers of nature. These were Following the catastrophic San Francisco earthquake of among the first documented literary reactions of men to nat- 18 April 1906, (1859 to 1944, U.S.A.) ural phenomena. (P) advanced his elastic rebound theory (1911): that earthquakes ca. 585 B.C.E. Thales of Miletos (624 to 546 B.C.E.) are associated with large fractures, or faults, in the Earth's was the first to expound the theory of a natural cause for crust and . As the rock is strained, elastic energy earthquakes; he proposed that they were caused by water. is stored in the same way that it is stored in a wound-up (P) watch spring. The strain builds up until the frictional bond ca. 550 B.C.E. Anaximenes of Miletos (585 to 525 that locks the fault can no longer hold at some point on the B.C.E.), pupil of Anaximander, went further than his fault, and it breaks. Consequently, the blocks suddenly slip teacher in completely ignoring the mythical elements in the at this point, which is the focus of the earthquake. (It was natural laws. He taught that, with age, the Earth broke down discovered in 1960 that once the rupture is initiated, it will under its own weight, thus causing the motion of earth- travel at a speed of about 3.5 km/sec, continuing as much as quakes. (P) 1000 km.) In great earthquakes, the slip, or offset, of the two ca. 340 B.C.E. Aristotle (384 to 322 B.C.E.) speculated blocks can be as large as 15 m. Once the frictional bond is that earthquakes are caused by air in motion: air trapped broken, the elastic strain energy, which had been slowly inside the Earth shakes the Earth as it is trying to escape. stored over tens or hundreds of years, is suddenly released This theory influenced European thought till the seventeenth in the form of intense seismic vibrations--which constitute century. (P) the earthquake. The process through which the frictional ca. 45 A.D. Lucius Annaeus Seneca gave the best sum- bond is "lubricated" to enable to commencement of the slip mary of the views on earthquakes in the Greco-Roman tra- is yet not understood. About 109 erg of strain energy is re- dition: earthquakes are caused by natural causes such as leased from each cubic meter of the earthquake source vol- water, air, or fire, located inside the Earth. (P) ume. The greatest earthquakes each release energy from a ca. 1260 Albertus Magnus (1206 to 1280) recognized strained volume of 1000 by 100 by 100 km = 1016 m 3, which the vibratory character of the motion of earthquakes. (P) yields a total energy of 1025 erg. This is about the equivalent 1638 Galileo Galilei considered for the first time the of 1000 nuclear explosions, each with strength of 1 megaton resistance of solids to rupture. His enquiries gave the direc- (1 million tons) of TNT. It is of interest to note that the few tion that was subsequently followed by many investigators. large earthquakes each year release more energy than hun- 1660 Robert Hooke stated the one-dimensional linear dreds of thousands of small shocks combined. About 1026 stress-strain relationship, thus laying the foundation for the erg of seismic energy are released each year. This is about theory of elasticity (published in 1678). (T) 1% of the yearly amount of heat energy reaching the Earth's 1664 Athanasius Kircher (1601 to 1680) proposed a surface from the interior. system of channels of fire inside the Earth that end in the The time between great earthquakes is about 50 to 100 surface at the volcanoes; earthquakes are related to the mo- yr in California and somewhat less in more active seismic tion of the fire inside these tunnels working against the rocks regions, such as Japan or the Aleutians. Thus, the time re- that block this motion. (P) quired to build up the elastic strain energy in the rocks ad- 1696 Johann Zhan added to the Aristotelian theory that jacent to a fault is enormous compared with the time that the air trapped inside the Earth is mixed with flammable elapses during the release of stored energy. material. (P) The present state of knowledge of earthquake phenom- 1703 Martin Lister (1638 to 1712) and Nicolas Lem- ena precludes the reliable prediction of the time of occur- cry (1645 to 1715) broke away from the Aristotelian theory rence of the next major earthquake in any given location. of earthquakes and conjectured that the internal fire that pro- Perhaps the most apt remark in this regard was given long duces earthquakes and volcanoes was produced by chemical ago by Mark Twain: "I was gratified to be able to answer means through a mixture of iron, sulfure, and salt with water. promptly, and I did. I said I did not know." The important aspect of this theory, which became very pop- A Concise History of Mainstream Seismology: Origins, Legacy, and Perspectives 1207 ular in the eighteenth century, was that the source of an They found that, in general, wave surfaces have three sheets. earthquake was an explosion produced by the mixing inside Cauchy established the stress-strain relations for general an- the Earth of the same chemicals used for explosives. Isaac isotropic crystals in terms of 21 coefficients. (AI) Newton, in his Opticks (1704), refers to this theory in Book 1828 S. D. Poisson established the existence of com- III, Part I, Query 31. He stated that when these minerals are pressional and shear waves in elastic solids (observed by accumulated in a subterranean cave they explode with a Oldham, 1897). His finding created at the time a new dif- great shaking of the Earth. (P) ficulty in the wave theory of light: if the ether behaved like 1749 Comte de Buffon (1707 to 1788) proposed that an elastic solid, two types of light waves should be visible. an explosion of inflammable materials, such as the fermen- Maxwell circumvented the difficulty by ascribing the ether tation of pyrites, produces a quantity of heated air in sub- a Poisson ratio a = 1/2 (infinite longitudinal velocity). (T) terranean chambers that could escape horizontally for a great 1829 to 1896 First theoretical studies on the vibrations distance through underground tunnels and caves. This would of elastic spheres and plates: S. D. Poisson (sphere, 1829), explain why earthquakes are felt through a long distance. (P) Lord Kelvin (sphere, 1863), P. Jaerish (isotropic sphere, 1755 1 November. Lisbon earthquake. Some effects are 1880), H. Lamb (sphere, 1882), C. Chree (sphere, 1889, scientifically described. (P) 1896), H. Lamb (plate, 1889), and Volterra (1894). (F) 1757 John Bevis (or Bevans; 1693 to 1771) published 1840 Von Hoff published an earthquake catalog of the in London a remarkable volume on The History and Philos- whole world. (P) ophy of Earthquakes in which he collected accounts of the 1841 Reports on earthquake investigations began to ap- Lisbon earthquake from diverse authentic sources. His sur- pear intermittently in the General Reports of the British As- vey, the first of its kind, was subsequently used by John sociation for the Advancement of Science (prepared regu- Michell (1761). larly by John Milne from 1881). (P) 1761 Following the Lisbon earthquake, First mechanical seismometer designed by James Da- demonstrated that earthquakes originate within the Earth and vid Forbes. (S) that waves spread out from the source throughout the Earth's 1845 G. G. Stokes defined the moduli of elastic com- interior (his velocity = 530 m/sec) (incidentally, he origi- pressibility and rigidity. (E) nated the concept of a black hole). Nevertheless, Michell 1848 Lord Kelvin integrated the equation of elasto- still held to the explosive theory of earthquakes. (P) statics. (T) 1783 5 February and following. Earthquakes in Cala- 1849 G. G. Stokes formulated the fundamental equation bria, Italy. Investigated by scientific commissions. (P) for viscous fluids. (T) 1798 Henry Caveudish determined the mean density 1852 to 1859 G. Lain6 defined the elastic parameters of the Earth, invoking Newton' s law of universal gravitation of homogeneous media and the concept of stress ellipsoid. [(p) = 3g(R)/(4nGR) ~ 5.448 g/cm3]. (E) (T) 1807 Thomas Young defined the modulus of elasticity 1855 Luigl Palmieri built a seismometer for use in the (Y = rll/e11) and was the first to recognize shear as an elastic Vesuvius observatory. (S) 1857 16 December. Earthquake east of Naples, Italy. strain. Field investigations by Robert Mallet; first systematic at- 1819 16 June. Earthquake in Cutch, India. Earliest well- tempt to apply physical principles to earthquake effects in documented observations of faulting accompanying the detail. According to him, earthquakes are caused "either by earthquake. (P) the sudden flexure and constraint of the elastic materials 1821 to 1831 C. L. M. H. Navier, A. L. Cauchy, and forming a portion of the earth's crust, or by their giving way S. D. Poisson discovered the fundamental equations of linear and becoming fractures." Mallet published the first world elastodynamics. Navier (1821), a disciple of Fourier and seismicity map (1860) and made first attempts to measure professor of analytical mechanics at the t~cole Polytechnique velocities of seismic waves. He was indeed the first true in Paris, was first to derive the elastodynamic displacement seismologist. (P) equation, and the equation of motion of a viscous fluid. He 1863 Lord Kelvin used tidal observations to show that laid the foundation to the mathematical theory of elasticity the mean rigidity of the Earth exceeds that of ordinary steel (definition of stress and strain tensors, 3D stress-strain re- [(/a) ~ 1.45 X 1012 cgs]. (E) lation for a general anisotropic solid), and correctly estab- 1869 F. Zrllner constructed a horizontal seismograph. lished the number of elastic constants for isotropic and non- (s) isotropic media. His equation of motion (in modem notation) 1872 E. Betti discovered the reciprocity relation and reads: div I" + p~7 = p[c32~/Ot2]. (T) the "Betti relation" leading later to the representation theo- 1826 to 1839 A. J. Fresnel (1826), S. D. Poisson rem of elastodynamics. (1828), A. L. Cauchy (1830), and G. Green (1839) dis- 1874 De Rossi sets the first earthquake intensity scale. cussed the propagation of plane waves through crystalline J. F. J. Sehmidt coined the names: , principal media, and obtained equations for the velocity of propaga- shock. (P) tion in terms of the direction of the normal to the wave front. 1874 to 1892 Earliest linear theories of internal friction 1208 A. Ben-Menahem

and attenuation losses in elastic solids by O. E. Meyer types of waves predicted by Poisson (1828) and Rayleigh (1874), L. Boltzmann (1876), J. C. Maxwell (1876), Lord (1885). (T) Kelvin (1878), and W. Voigt (1892). (AE) Emil Wiechert worked out numerical details of an 1877 to 1904 E. B. Christoffei (1877) derived the cubic Earth model consisting of a core of uniform density p~ = equation for the three plane-wave phase velocities in general 8.21 g/cm3 and radius a~ = 5000 km surrounded by a rock anisotropic elastic media, for any given direction of the nor- shell of uniform density P2 = 3.2 g/cm3. A model of this mal to the plane (Christoffel's equation). His work was fol- type was contemplated earlier by Kelvin and P. G, Tait lowed up by Lord Kelvin (1904), who described the nature (1879), and R. R. Radau (1885). Wiechert conjectured that of the displacement vectors () and defined a the central core is metallic. (E) twelfth degree wave surface in velocity space. (AI) 1898 T. J. I'A Bromwieh studied the influence of grav- 1878 R. Hoernes' classification of earthquakes (vol- ity on elastic waves, and in particular on the vibrations of canic, tectonic, etc.). (P) an elastic globe. (F) 1880 John Milne, James Alfred Ewing, and Thomas 1899 C. G. Knott derived the reflection and refraction Gray constructed in Japan the first useful seismograph sys- coefficients of plane seismic waves at planar discontinuities. tem for the recording of local earthquakes. (On 22 February (T) 1880 they were able to obtain satisfactory records of a local 1899 to 1903 The earliest known list of instrumentally tremor.) (S) recorded earthquakes with computed origin times and epi- 1881 Lord Rayleigh's principle of eigenvalue pertur- centers. (P) bation. (Rayleigh's variational principle.) 1900 World seismicity maps prepared by John Milne 1882 R. Canaval coined the names: , after- and Ferdinand Montessus de Ballore. (P) shock. Emil Wiechert constructed a three-component mechan- 1883 to 1884 Rossi-Forel scale for earthquake effects published (based on observations in Italy and ). ical seismograph system. (S) (P) 1901 Geophysical Institute founded at Gtttingen, Ger- 1885 In a theoretical study, Lord Rayleigh discovered many, by Emil Wiechert. (P) that, in addition to the known dilatational and shear body 1902 Improved intensity scale published by G. Mercalli waves (Poisson, 1828), a homogeneous elastic substance can in Italy. (P) accommodate a third wave at its boundary. This is subse- 1904 A. E. H. Love gave an exact singular analytic quently known as the . (Rayleigh considered solution to the inhomogeneous Navier equation in an infinite

free waves in a sourceless medium.) (SW) solid: (2 + /z) grad div fi +/zV2fi + p~ = p[(Oz~l)/(Ot2)]. 1888 A. Sehmidt argued that since in general wave ve- He then proceeded to construct Green's functions for a va- locity must increase with depth in the Earth, wave paths will riety of derived point sources such as dipoles, couples, center be curved and concave upward toward the Earth's surface. of compression, and center of rotation. Love based his work (W) on previous results of G. G. Stokes (who in 1849 modelled 1889 Milne began the production of the "Shide Ciru- a light origin as a point source of SH waves in the luminif- lars," which dealt with earthquakes. (P) erous elastic ether), and L. M. Lorenz (1861) who showed 17 April, 17 hr 21 min. The birthday of instrumental how to solve the above equations in terms of potentials. seismology in its worldwide sense: the first teleseismic event In the same article, Love derived for the first time the (a Japanese earthquake), recorded by Ernst yon Rebeur- three-dimensional elastodynamic integral representation Pasehwitz in Potsdam, Germany, with a modified form of theorem, which is essentially an extension of Kirchhoff's Ztillner's horizontal pendulum (Vo = 50, To = 18 sec, no theorem for elastic isotropic media. Love's integral, how- damping A = 8221 km; origin time ca. 17 hr 10.3 rain ever, was not written in compact tensor notation. Moreover, GMT). (S) the fundamental singular solution of elastodynamics 1891 28 October. Mino-Owari earthquake, Japan. Large (Green's tensor) does not appear explicitly in his analysis. fault displacements; great damage. Imperial Earthquake In- vestigation Committee set up in consequence. (P) A closely related representation theorem was given in- 1892 to 1894 Milne and his associates develop in Japan dependently by C. Somigliana (1905 to 1906). (SS) a compact seismograph system for worldwide use. Useful H. Lamb presented the first mathematical model of an instrumental data began to accumulate in a number of sta- earthquake in a half-space configuration. The generation of tions in Japan, Europe, and the United States, and seismol- elastic waves by the application of time-dependent surface ogy emerged as a quantitative science. (S) tractions on the boundary of a half-space or in it, is known 1895 F. Omori established a law for time as Lamb's problem. Lamb represented a point force in a series. (P) semi-infinite homogeneous isotropic elastic medium as a di- 1897 12 June. Great Indian earthquake. Investigated by vergent Fourier-Bessel integral. In lack of computational R. D. Oldham. (P) means, he could only sketch the displacement transients at R. D. Oldham identified on seismograms the three the far field for a vertical surface traction and certain im- A Concise History of Mainstream Seismology: Origins, Legacy, and Perspectives 1209 pulsive source time functions. His results confirmed the ex- coefficients of surface waves in the period range 20 to 25 istence of Rayleigh waves. (SW) sec (7 ~ 2.8 x 10 -4 km-h Q ~ 180). This was the first use He thus generated the first far-field synthetic seismo- of observed wave amplitudes for the estimate of attenuation. gram. Moreover, he anticipated the later Cagniard method Similar results followed by Meissner (1913), Wegener (1939), but did not recognize its generality. (SS) (1912), Golitzin (1913), and Gutenberg (1924). (AE) 1904 to 1905 F. T. Trouton, A. O. Rankine (1904), M. R. Freehet: functional calculus (the "Frechet deriv- and P. Phillips (1905) discovered a logarithmic creep law ative"). [th(t) = q log(1 + t/to)], which gives a fair description of 1906 to 1911 Following the San Francisco earthquake, the strain in specimens under long continued stress. [Applied seismologists realized that crustal earthquakes are associated to rocks in 1956 by C. Lomnitz and generalized by H. Jef- with finite faulting, fracture, and slip. H. F. Reid studied the freys (1958) to the Earth as a whole.] (AE) geodetic measurements along the San Andreas Fault before 1905 R. Beeker developed the theory of the standard and after its rupture (18 April 1906) and consequently ex- linear solid with continuous relaxation, as a physical model pounded (1911) his elastic rebound theory, which drew at- of anelasticity. The model yields a bandlimited constant Q tention to the significance of elastic strain energy in con- by a continuous superposition of single relaxation mecha- nection with earthquakes: a tectonic earthquake occurred nisms. Applied to seismic wave propagation in the Earth in when the stresses in some region inside the Earth have ac- 1976. (AE) cumulated to the point of exceeding the strength of the ma- 1905 to 1912 Establishment of elementary ray theory terial, leading rapidly to fracture. This information was not for seismic signal propagation in a spherically symmetric conveyed to the level of models, and con- Earth model by H. Benndorf (p = dT/dA, 1905), K. Ziip- sequently the natural development of seismic source theory pritz, and E. Wieehert. (T) was arrested for the next 50 yr. (SS) 1906 18 April. California earthquake. Observed faulting 1907 Vito Volterra presented his theory of disloca- and slip. (P) tions, incorporating previous results of E. Betti (Betti's re- Boris Borisovich Golitzin designed and built the first lation, Betti reciprocity theorem, 1872), and C. Somigllana electromagnetic seismograph with photographic recording. (Somigliana's relation, 1885 to 1889). Previously (1894) (s) Volterra derived a two-dimensional integral representation 22 March. John Milne delivered the Bakerian Lecture theory. (SS) in which he announced the discovery of the "Moho discon- 1907 to 1910 K. Ziippritz evolved the first travel-time tinuity"! In his own words: "Preceding the large waves of a tables for a few seismic phases (1907). G. Iterglotz (1907) teleseismic disturbance we find preliminary tremors.., for and, independently, H. Bateman (1910), gave an exact an- (ray paths) which lie within a depth of 30 miles, the recorded alytical solution to an Abel-type integral equation, the so- speeds do not exceed those which we would expectfor waves lutions of which determine the intrinsic velocity as a func- of compression in rocky material This therefore, is the max- tion of the radial distance from the Earth's center, This imum depth at which we should look for materials having enabled seismologists to invert the ray travel-time data (T, similar physical properties to those we see on the earth's A) in terms of the intrinsic velocity at the turning point of surface. Beneath this limit, the materials of the outer part of the ray. Through 1909 to 1910 E. Wieehert, Ziippritz, and this planet appear rapidly to merge into a fairly homoge- L. Geiger used this method to calculate velocities of lon- neous nucleus with high rigidity." In the same lecture Milne gitudinal waves in the mantle. (E) was also the first to observe (1906) that breaks in the trajec- 1909 Andrija Mohorovifiic found evidence in Croatia of tory of the secular motion of the Earth's North Pole (relative a sharp increase in the P-wave velocity at depth, which he to its mean position) could be correlated with the occurrence placed at 54 km below the Earth' s surface. Later work by oth- of major earthquakes during 1892 to 1904. A quantitative ers showed such an increase to be worldwide, and the bound- theory of this effect was given only in 1970. (E) ary where it occurs came to be called the Mohorovi?ic discon- R. D. Oldham supplied positive seismological evidence tinuity (the depth of this discontinuity is in general about 35 for the presence of a central core of an approximate radius km below the surface in continental shield areas, reaches 70 of 1600 km. (He found a substantial delay in the arrival of km under some mountain ranges, and can be as little as 5 km P waves at angular distances beyond 120 ° from an earth- or so below the floors of deep oceans. The region of the Earth quake focus, and inferred that the Earth contains a central above the Moho is now called the crust. (E) region characterized by an average P velocity appreciably 1911 A. E. H. Love explained the occurrence of a trans- less than that in the surrounding shell, later to be called the versely polarized surface waves not included in the theories mantle.) It was found that the mantle everywhere transmits of Rayleigh and Lamb. It was subsequently known as the P and S waves and is thus solid for stresses with periods not Love wave in layered elastic media, and its existence on greatly exceeding tidal periods. No S waves were observed seismograms was diagnostic of the Earth's crust. Love's below the mantle, and it was surmised that most of the core work gave rise to a large number of mathematical investi- is molten. (E) gations and yielded much information on the structure of G. Angenheister obtained first values for absorption continents and oceans. (SW) 1210 A. Ben-Menahem

He presented the theory of oscillations of a uniform tables of 1935, and from 1937 onward, the JB tables of 1940. gravitating compressible sphere and obtained a period of 60 (P) min for the gravest mode of his steel-like earth model. (F) J. H. Jeans developed the basic asymptotic theory of 1912 H. Lamb suggested that group velocity may be the Earth's normal modes (Jean's formula), relating the applicable to the theory of seismic surface waves and the phase velocity at a given eigenfrequency to the colatitudinal interpretation of seismograms. (SW) mode number associated with that frequency. (F) 1914 Beno Gutenberg studied records of earthquakes Hirosbi Nakano showed that the observed patterns of that had epicentral distances of over 80° from Gfttingen. He initial motions are explainable in terms of certain combina- had found that at a depth of 2900 km, the velocity of lon- tions of point forces of the classical Stokes--Love solution. gitudinal waves decreased from 13,25 to 8.5 km/sec and that One of the models, known as a double couple, is a combi- the radius of the core is about 3500 km, a value little dif- nation of two orthogonal couples with zero moment. It was ferent from modem determinations. (E) shown to be equivalent to a pressure and tension acting si- 1914 to 1919 A. A. Miehelson and H. G. Gale used an multaneously at right angles. (SS) interferometer to measure body in the solid Earth by E. D. Williamson and L. H. Adams coupled values of the disturbance of the water level in two vertical tubes with d) =k/p = a z - 4/3fl 2 from seismological data with the a long horizontal connection underground. With this gear equation dp/dr = - GMp/r249, to obtain estimates of density they were able to measure the Earth's mean rigidity, (S) gradients in the Earth. Using the available seismological data 1915 to 1936 Harold Jeffreys introduced advanced and taking p as continuous, they constructed an Earth model mathematical and statistical methods into seismic data anal- consistent with the values of the Earth's mass and moment ysis. (T) of inertia. Their value for the density just below the crust is 1917 J. Radon: "Radon transform." 3.3 g/cm3 (ultrabasic rock), proposing an -like com- 1917 to 1925 J. Shida (1917) first noticed certain reg- position for the mantle. Their work also supplied the first ularities in the distribution of polarities of the initial P-wave direct evidence that there is substantial change of chemical motion as observed on seismograms in an area within a ra- composition in the Earth's deep interior. (E) dius of a few hundred kilometers around the source. Shida Wenzel, Kramers, Brillouin, and Jeffreys (WKBJ) de- found that the epicentral region is divided into four parts by veloped independently an approximate explicit solution to two perpendicular lines intersecting at the epicenter. Obser- some differential equations that govern the transition region vations by Nakamura (1922), Gherzi (1923), and Somville from wave to geometrical optics. (1925) followed. (SS) 1923 to 1937 Using travel times of near-field headwaves 1918 First year covered by the International Seismolog- (Pg, P*, P,, Sg, S*, S,) from European earthquakes, V. Con- ical Summary, collating readings from most of the seismo- rad (1923 to 1927) and H. Jeffreys (1926 to 1937) obtained logical stations of the world. (P) a three-layer crustal model (sediments, granite, basalt). (E) 1919 H. Weyl presented the spherical wave function as 1924 to 1928 R. Stoneley proved the existence of an a Fourier integral over all complex values of spherical angles interface wave propagating at solid-solid or solid-fluid dis- in wavenumber space, continuities, subsequently known as the Stoneley wave 1920 L. M. Hoskins studied the free oscillations of a gravitating radially inhomogeneous sphere. (F) (waves generated by the diffraction of curved fronts of body waves at a plane boundary). This was important to explo- 1921 E. Meissner used observations of group-velocity dispersion of Rayleigh waves to model the Earth's crest. ration geophysicists since it modeled sediment-rock inter- About the same time, E. Tams and G. Angenheister noticed face in shallow . Stoneley also emphasized (1925) the already that seismic surface waves over paths in the Pacific importance of surface-wave group-velocity dispersion for region travel faster than and are differently dispersed from modeling the Earth's crust. In 1926, Stoneley was able to those in continental regions, and suggested that there are show (from observations of group-velocity dispersion of significant differences in the crustal structures. (SW) Rayleigh and Love waves) that the Euroasian crust is twice 1922 Existence of deep earthquakes established by H. as thick as that of the Pacific region (H = 10 km), and H. Turner. (P) therefore that the crustal structures of the two regions differ 1923 1 September. Earthquake, destructive at and significantly. (SW) Yokohama. Detailed investigation; many published reports. 1925 J. A. Anderson and H. O. Wood developed the Earthquake Research Institute established at Tokyo. (P) torsion seismometer. (S) Jun Sbida discussed the possibility Appearance of the first ISS (International Seismological of observing the free oscillations of the Earth. (He designed Summary) for earthquakes of 1918. From 1923 to 1963, the an electromagnetic seismograph with pendulum period of ISS was the most comprehensive publication on earthquake 180 sec and galvanometer period of 1200 sec!) (F) occurrence. Origin times and epicenters for all sufficiently 1926 First use of observed absolute wave amplitudes well-read earthquakes were reported. For earthquakes 1918 from seismograms in the estimation of earthquake energy to 1929, the Zfppritz-Tumer travel-time tables were used release by H. Jeffreys. These were used by him to demon- in preparing the ISS; for 1930 to 1936, the preliminary JB strate the existence of a liquid core in the Earth. (P) A Concise History of Mainstream Seismology: Origins, Legacy, and Perspectives 1211

K. Uller formulated the general Navier equations in in- Neumann following the Long Beach earthquake of 10 homogeneous media. (T) March 1933. (P) E. Meissner invoked the Rayleigh principle to deter- 1934 L. J. B. La Caste invented the zero-length-spring mine group velocities for Love waves without resorting to long-period vertical seismograph. (S) numerical differentiation (Meissner's formula). H. Jeffreys 1934 to 1944 Measurements of seismic velocities in ex- (1961) extended this work to Rayleigh waves. (SW) ploration geophysics from travel times of P, SV, and SH Beua Gutenberg proposed a low-velocity layer in the waves disclosed that many rocks in sedimentary basins ex- outermost 100 to 200 km of the mantle, arguing from evi- hibit significant degree of anisotropy. (AI) dence on bodily wave amplitude. Later work substantiated 1935 Charles F. Richter introduced an instrumental this claim. The main seismological evidence appeared to be earthquake magnitude scale. This was based on an earlier sufficiently met by assuming a negative rigidity gradient in- attempt by Wadati in Japan (1931). (P) side part of the outermost 200 km, a condition that is feasible Hugo V. Beuiaff designed and built the linear strain in the light of evidence on temperature gradients. Gutenberg seismograph. (S) produced new evidence for his conjecture in 1939. (E) F. B. Blanehard uses a well-gauge as a seismometer. M. Born: "Born approximation." Narman A. Haskell determined the mean viscosity of 1926 to 1960 Perry Byerly developed a graphical the asthenosphere from the rate of uplift of the Earth's crust method of displaying the initial motion distributions on a after the melting of the last Pleistocene ice sheets. He found plane, and determining therefrom the fault-plane solutions. a kinematic viscosity of the order of 3 × 102~ cgs units. (E), Thousands of earthquakes were solved in this way by his (AE) students, disciples, and colleagues. The method had two 1936 Inge Lehmann postulated the existence of an in- drawbacks: first, the initial motion is characteristic only of ner core to account for the amplitudes of P waves between the first fraction of a second of the complex rupture process, angular distances of 105 ° and 142° previously thought to be which may last hundreds of seconds in major seismic events. diffracted waves. The radius of the inner core was found by Second, the initial P-wave motion is not sufficient to deter- B. Gutenberg (1938) and by H. Jeffreys (1939) to be about mine which of the two fault-plane solutions is the real fault. 1200 to 1250 km. (E) It is indeed disheartening that as far as realistic source mod- 1939 tt. Jeffreys applied the Airy theory of diffraction els were concerned, seismologists were sidetracked for 56 near a caustic to the seismological case of wave diffraction yr (since Reid!) on studies of initial motion alone. Yet, fault- by the Earth's core (A = 142°). (T) plane solutions were a key to later work on tectonic plate 1939 to 1958 The Jeffreys-Bullen Seismological Ta- motions. (SS) bles. 1927 T. Terada and C. Tsuboi conducted experimental H. Jeffreys (1939) and B. Gutenberg (1951 to 1958) model studies of seismic waves. (S) produced each statistically well-based spherically symmet- V. V/iis/il/i measured ground displacements by means rical and laterally averaged distribution of compressional of interference of light waves. (S) and shear-velocity profiles in the Earth, based on large quan- 1927 to 1928 K. Sezawa formulated scattering of elastic tities of data. The differences between their respective curves waves by spheres, cylinders, and apertures. (T) are small except in the outer part of the mantle and in the 1927 to 1940 K. Sezawa (1927), H. Jeffreys (1931), between the outer and inner core. Both mod- and N. Rieker (1940) studied the damping of pulses in vis- els ignore the Earth's anelasticity, anisotropy, lateral inho- coelastic media and applied the theory to propagation of mogeneity, and asphericity. K. E. Bullen was able to clas- seismic waves in the Earth. This was needed for magnitude sify the Earth's interior (1940 to 1942) into a number of and energy determinations, as well as for the physical state shells occupying ranges of depth from the surface to the of the crust and upper mantle. (AE) center. He also contributed to the inverse problem of density 1927 to 1950 K. Sezawa, H. Jeffreys, and R. Staneley distribution. (E) worked out the dispersion theory of surface-wave propaga- 1939 to 1960 Transition period; end of the classical age tion in crustal models with two layers. (SW) of the Oxford-Cambridge analytical school. Final attack on 1928 K. Wadati demonstrated the existence of deep- the Lamb problem with the aid of the transform calculus. It focus earthquakes in Japan. (P) resulted in a better understanding of the nature of the various 1930 A. Sieberg published a comprehensive treatise on seismic and acoustic signals transmitted through half-space the geography of earthquakes. (P) models of the Earth. For half a century after Lamb's seminal N. Wiener developed generalized harmonic analysis, paper of 1904, the main thrust of theoretical seismology was forging the tools for future computerized signal analysis. aimed at an exact analytical solution of the "problem" and 1932 L. B. Slichter extended the Herglotz-Bateman the numerical evaluation of the ensuing displacement tran- travel-time inversion method to multi-layered horizontal sients. Of the many publications on the subject, three studies structures. (T) stand out: L. Cagniard (1939) addressed the problem of an 1933 Quantitative instrumental study on the effects of explosion (cylindrical symmetry, unit-step time dependence) earthquakes on man made structures by N. H. Heek and F. buried in a half-space or in a configuration of two welded 1212 A. Ben-Menahem

half-spaces. He used the Laplace transform method with his Stokes-Love solution the fundamental singular solution of own ingenious way of inversion, in which the integrand of elastodynamics, otherwise known as the elastic Green's ten- the Bromwich inversion integral is forced into a form of a sor Gij. The elastodynamic integral representation theorem Laplace transform of a calculable integral. was then compactly expressed in terms of this tensor [Go C. L. Pekeris presented in 1955 the first computer-gen- and T~(Gu)], both in the time and frequency domains. (SS) erated synthetic seismogram for a point force in a Poisson 1953 to 1965 Observation and interpretation of seismic solid (2 = /t). In the precomputer era, many methods of interface phases and guided waves came with the increasing approximation were used to extract useful information out frequency and dynamic ranges of seismograph systems on of the Lamb integral representation. Most efficient was the one hand, and computational capabilities on the other; saddle-point method, through which initial motions at the crustal guided waves (since 1953), pseudo Rayleigh waves far field could be obtained at relative ease. (T,SS) (1959), leaking interface modes, and PL phase (1960 to Lapwood (1949) was able to develop further the results 1961). (T) of Lamb; using the saddle-point method of approximation, 1954 With the advent of their new long-period seis- his line-source field integrals yielded several subsidiary mograph system, M. Ewing and F. Press extended the re- phases (besides the classical P, S, and Rayleigh waves), cording and analyses of Rayleigh and Love waves up to which arise due to diffraction of the source's cylindrical periods of the order of 100 sec. (SW) wavefronts at the planar free surface. 1955 Quantitative studies on the effects of strong 1942 to 1956 First empirical relations between earth- ground-motion earthquakes on man-made structures. (S) quake magnitude, intensity, energy, acceleration, and fre- 1955 to 1960 Y. Sato introduced Fourier-transform quency of occurrence established by B. Gutenberg and C. methods into the analysis of surface-wave dispersion and F. Richter. (P) attenuation. (SW) 1946 Nuclear testing began. The use of underground 1956 F. Press developed the method of determination nuclear explosions as point sources, each with accurately of crustal structure from phase-velocity dispersion of crustal known location and time of origin, greatly enhanced the ca- and mantle surface waves. (SW) pabilities of seismic studies of the Earth's interior. The first Nelly Jobert calculated the free-oscillations periods of event of this type for which data became available to seis- a heterogeneous Earth model, using the Rayleigh principle. mologists was the underwater explosion near Bikini Atoll (F) on 24 July 1946. Since then, data from over 1000 nuclear V. A. Vvedenskaya was first to obtain the double-cou- explosions have been analyzed and studied in research cen- ple equivalence for an effective point source of slip. ters around the world. (P) 1958 F. Press, M. Ewing, and F. Lehner completed 1949 R. Stoneley examined the effect of anisotropy on the development of a stable long-period seismograph system elastic surface waves and established their existence for cer- for worldwide use. (S) tain symmetry regimes. Under anisotropy conditions pre- Hugo Benioff drew attention to ultralong waves with a vailing in the Earth's crust and upper mantle, dispersion period of ca. 57 rain, which he noticed on his strain seis- curves are little affected by anisotropy. (AI) mograms of the Kamchatka earthquake of 4 November 1952 1950 to 1969 Dawn of the computer era: the first com- (recording was made in an old mine tunnel at Isabella, Cal- puter algorithm for the calculation of dispersion in multi- ifornia). (F) layered media is set by W, Thomson (1950) and N. A. Has- A rigorous derivation of the 3D time-domain integral kell (1953). The solution of the Lamb problem is calculated representation theorem in terms of the Green' s tensor, valid and computer-generated seismograms are produced (Pek- for unbounded regions was provided (1958). (SS) eris, 1955). Numerical integration of the equations of motion J. A. Steketee proved the equivalence theorem, stating of the whole Earth (free oscillations) (1959), epicentral lo- that the displacement field produced by a dislocation on a cation ISS, USCGS (1960), acoustic-gravity waves in the at- plane element in an elastic body equals that produced by a mosphere (1962), radiation patterns of surface waves in re- double couple on that plane. This lead to the definition of a alistic Earth models (1964), inversion of Q data (1965), and source moment equal to tt US, where/t is the rigidity over fast algorithms for the calculations of Fourier amplitude and the fault of area S and dislocation U. Steketee derived the power spectra (FFT, 1965, 1969). (T) equivalence by comparing the Stokes-Love (1903) solution 1952 Perry Byerly developed the general theory of the for a double couple with Volterra's (1907) solution for a hinged seismometer with support, in general motion. (S) corresponding dislocation. (SS) B. Gutenberg and C. Richter defined the surface-wave 1958 to 1965 Seismic data on attenuation of seismic magnitude, Ms, for shallow-focus earthquakes in terms of rays, waves, and modes in the Earth pointed to a quasi con- the maximum amplitude of the ground motion for crustal stancy of Q over the period band 10 -5 to 10 a sec. Various surface waves having a 20-sec period. (SW) physically realizable mechanisms of attenuation were sug- 1953 Integral formulation of Huygens' principle for gested. Perturbative inversion schemes were set up to derive steady-state vector elastic waves: W. D. Kupradse, P. M. the intrinsic anelastic parameters of the mantle from the ob- Morse, and H. Feshbaeh independently extracted from the served surface attenuation data (1965). (AE) A Concise History of Mainstream Seismology: Origins, Legacy, and Perspectives 1213

1959 The effect of azimuthal isotropy on the wave ysis and processing digital filtering, multi-dimensional Fou- fronts and rays from a localized point force was derived rier analysis, F-K transforms, time-varying spectra, and fast through an integral representations of the field in terms of Fourier transforms. Increase of dynamic ranges of seismo- Fourier integrals. These were estimated asymptotically graph systems and computer capabilities. (T) through stationary phase approximation. (AI) 1963 Francis Birch noticed that the relation between a F. C. Karal and J. B. Keller formulated the theory of = x/~pp and density in a wide range of elements and com- ray propagation in inhomogeneous elastic media based on pounds depends systematically on their mean atomic weight. Uller's equation (1926). On this basis, the seismological Earth models suggest that 1960 22 May. Chile. The first major earthquake in his- the inner core is almost pure iron. (E) tory to be studied comprehensively both macroseismically 1963 to 1967 Deployment of 120 WWNSS in 60 coun- and instrumentally. (P) tries. Advent of broadband three-component analog record- Existence of the free oscillations of the Earth firmly ings on magnetic tape. (S) established by various groups of observers in Europe, Japan, 1964 The ISS was replaced by the ISC (International and the United States from analyses of records of the great Seismological Center, Newbury, England). It received about Chilean earthquake of 22 May 1960. Observations yielded 80,000 readings each month from about 1200 stations, also the expected splitting of the degenerated eigenfrequen- worldwide. (P) cies due to the Earth's diurnal rotation (1961). The matching 1964 to 1965 Unraveling the latent interrelations and of the observed spectral lines with theoretical calculations dualities between rays, waves, and modes of the Earth's equipped seismologists with a new tool to sample the gross global seismic field. Asymptotic theory of the normal mode structure of the Earth's interior (C. L. Pekeris, G. Backus, solution are applied. (Jean's formula, Watson's transfor- F. Gilbert). (F) mation, etc.) (T) Analyses of seismograms revealed that energy release 1964 to 1969 Large-aperture seismometer arrays come in tectonic earthquakes takes place through a propagating into vogue. Construction of feedback-controlled seismome- rupture over the causative fault. The theory provides for a ters. (S) simple way to recover the fault length and the average rup- 1965 Seismologists in the United States proposed a 10- ture velocity from the spectral directivity of body waves and yr program of research for . (P) surface waves. It was thus found that the source of the Chi- Benioff's strainmeter equipped with continuous inter- lean earthquake of 22 May 1960 released its energy along a ferometric calibration. (S) fault 1000-km long, with an average rupture velocity of 3.5 1966 Advent of the optical maser strainmeter. (S) km/sec. (SS) 1966 to 1980 Additional evidence on the distributions Linear system theory was applied to show that surface- of the density, incompressibility, and rigidity in the interior wave signals can be sent back to the source by a spectral- of the Earth arose from recordings of the free oscillations of phase "bookkeeping" of far-field data. The "initial-phases" the Earth excited by the Chilean earthquake of 1960. Inver- of the far field could then serve as a diagnostic signature for sion schemes show the capability of observations of long- the temporal and spatial character of the source. (SS) period oscillations of the Earth to discriminate between dif- 1960 to 1964 Far-field phase and amplitude spectra of ferent Earth models. (E) long-period surface waves were used for the study of source 1967 to 1969 The conjecture of continental drift, pro- mechanisms of earthquakes and upper-mantle structure. pounded in 1912 by Alfred L. Wegener (1880 to 1930), (sw) verified in the framework of earthquake seismology; global 1961 to 1966 The moving-source discovery led to the seismicity patterns linked to plate motions. (P) formation of the kinematic dislocation model with the fol- Development of the dynamical model of plate , lowing source parameters: fault length, rupture velocity, rise which rendered global theoretical explanation to seismicity time, fault width, and slip. The model is characterized by patterns. In this context, the kinematic source model was three basic features: instrumental in estimating long-term accumulation of slip along major fault systems. • The far displacement field is determined by the slip veloc- Plate-tectonic theory holds that the Earth's upper shell ity on the fault. The radiation pattern is diagnostic of the (lithosphere) consists of several (about eight) large and source and depends on the source parameters. quasi-stable slabs called plates. The thickness of each plate • The short-period components of the radiation are coherent extends to a depth of about 80 km; the plates move horizon- only over distances considerably smaller than the total tally relative to neighboring plates, on a layer of softer rock. fault length. The rate of movement ranges from 1 to 10 cm a year over • The energy budget of major earthquakes requires the as- a lower strength shell, called the asthenosphere. At the plate sumption of a superimposed irregular component of mo- edges where there is contact with adjoining plates, boundary tion on the fault during rupture. (SS) tectonic forces operate on the rocks, causing physical and chemical changes in them. New lithosphere is created at 1962 to 1969 Advances in numerical techniques of data anal- mid-oceanic ridges by the upwelling and cooling of magma 1214 A. Ben-Menahem

from the Earth's mantle. In order to conserve mass, the hor- used in conjunction with Green's theorem for slowly izontally moving plates are absorbed at the ocean trenches varying elastic media (ray-Kirchhoff forward method). where a subduction process carries the lithosphere down- (c) Migration of stacked reflection data (Kirchhoff migra- ward into the Earth's interior. The is consistent tion) through which discontinuity surfaces are imaged with high seismicity along the edges of the interacting plates. in exploration seismology (1973 to 1988). The above Interplate earthquakes must be explained by other mecha- Kirchhoff method is also used for data migration in in- nisms. (SS) homogeneous media (inverse scattering problem). Ge- 1968 to 1985 Asymptotic wave theories in vertically in- ometrical migration was developed by J. G. Itagedroon homogeneous media: generalized rays for a layered Earth (1954) and A. W. Musgrave (1961). During 1971 to model with application to core phases diffraction, and tun- 1978, the following migration schemes were developed: neling. First-order decoupled equations of motion. The wave-equation migration, Fourier-transform migration, acoustic approximation in exploration seismology. WKBJ Kirchhoff migration, frequency-wavenumber (FK) mi- approximations, and extended WKBJ methods. (T) gration, and Born-WKBJ inversion migration. Parabolic wave equation, Gaussian beams, and the par- axial approximate solution of the wave equation (Leonto- • Seismic wave tomographic inversion (1984 to 1992). The rich and Foek, 1946). (T) application of the Radon transform began in 1967 in as- Seismologists obtained (1972) numerical solutions of trophysics (Bracewell). It reached seismology in 1981, and the vector Navier equation in isotropic inhomogeneous me- emerged in 1984 as an imaging method for determining dia with boundaries, showing coupling, mode conversion, subsurface structure. Its uses are as follows: scattering, and diffraction. Parabolic theory used to solve forward-scattering problems in inhomogeneous media. (T) (a) Mapping the upper mantle from inversion of seismic 1969 The Apollo passive seismic experiment. (S) data (normal modes, body-wave travel times, and sur- Development of high-gain broadband long-period elec- face-wave dispersion and attenuation): teleseismic body- tromagnetic seismograph system, with digital recording. (S) wave travel times on arrays yield lateral velocity varia- 1969 to 1977 Analyses of travel times and polarization tions, both regionally and globally. Travel-time delays of seismic waves furnished evidence for anisotropy in the are backprojected along ray paths, against a reference Earth's crust and mantle (e.g., polarization of higher mode velocity model. surface waves). Development of methods for calculating ray (b) Diffraction tomography in seismic exploration from amplitudes in anisotropic media. (AI) cross-borehole measurements. (T) 1970 NASA (U.S.A.) put a seismograph on the . (s) 1971 A global network of observing seismic stations Earth strain measurements with laser interferometer. (S) (WWNSS) established by the U.S. Coast and Geodetic Sur- 1970 to 1985 Asymptotic ray theory: 3D two-point ray- vey. (S) tracing of both travel times and amplitudes in general media A mercury tiltmeter developed at the Massachusetts In- (inhomogeneous and anisotropic), ray-series expansion, and stitute of Technology. (S) dynamic raytracing in ray-centered coordinates. Modifica- 1972 to 1987 Theoretical and numerical calculations of tions of expansions around turning points, caustic, shadow the free oscillations of the Earth take into account pertur- zones, etc. (Complemented by modal expansions, finite-dif- bations due to asphericity, anisotropy, anelasticity, and lat- ference methods, or finite-element methods for short-time or eral inhomogeneity. (F) near-field behavior.) (T) 1972 to 1992 After the consolidation of the theory of 1970 to 1988 New trends in 3D seismic modeling: solv- the kinematic source model and its verification through the ing forward and inverse problems of scattering and diffrac- analyses of hundreds of earthquake seismograms, the theory tion in inhomogeneous elastic media (both deterministic and developed further in the direction of more complex media stochastic), and across irregular boundaries: to account for the effects of anisotropy and lateral hetero- geneity. The availability of fast electronic computers enabled • Theory of inversion and resolution of gross Earth data theoreticians to calculate the fields of earthquake sources in (1970 to 1972). more realistic media subjected to the Navier equation: div T(fi) - p[(02 ~)/(0t2)] = - F'(P,t) - div ~/(?,t), where ~" is • Kirchhoff-Helmholtz integral formula (Huygens' princi- 4 ple) is used in various problems: the source's force density and ~1 = niu)cij,pq ~ fi~t:C is the source's moment tensor density [for isotropic media ~/ = (a) Scattering by smooth obstacles: an algorithm is estab- 2(~ • fi)l +/z(~fi + fi~)]. Calculations of the moment den- lished for numerical calculation of the scattering of vec- sity of earthquakes became routine during the past decade. tor elastic waves by smooth obstacles of arbitrary shape The above formulation is also suitable for problems of scat- (T-matrix method for forward scattering). tering of elastic waves by inhomogeneities where the (b) Calculations of body-wave amplitudes in the Earth sources are generated virtually by the scatterers. (SS) (1981 to 1983). In this scheme, ray theory (eikonal) is 1974 to 1992 Development of computational perturba- A Concise History of Mainstream Seismology: Origins, Legacy, and Perspectives 1215 tive schemes for the quantification of surface-wave fields in tic properties at all depths in the planet. This is the tomo- Earth models that account for lateral heterogeneity, anisot- graphic mapping stage: high-precision measurement and ropy, anelasticity, and scattering. Ray and Gaussian-beam images are required since lateral fluctuation in velocity are theory of surface-wave propagation on a sphere. (SW) at most a few percent of the average velocity at a given 1976 Causal dispersion due to attenuation of waves and depth. normal modes is observed. (AE) Interpreting the 3D seismic velocities and density varia- 1977 to 1992 Improved y and Q measurements from tions as manifestations of the dynamic thermally driven global networks enable seismologists to invert attenuation convective process of the mantle-core flow regime. Since of free-oscillation data and study the effects of mantle une- shear stresses involved in flow can induce recrystallization lasticity on nutations, Earth tides, and tidal variations in ro- and preferred orientation of the anisotropic minerals, the tation rate. They study the effect of a shallow low-viscosity mantle may acquire a bulk anisotropy. If this anisotropy zone on the mantle flow, and the geoid anomalies. affects seismic wave propagation in the Earth to an ob- Seismologists try to separate attenuation of surface servable level, it can eventually be inverted to yield further waves due to scattering from the overall observed attenua- information on the flow regime. (E) tion. Seismology enters a stage where seismic imaging of the interior uses all available data. (AE) Establishment of 1981 Two-dimensional surface digital strong-motion array the theory of seismic fields generated by point sources in of aperture 2 km used in Taiwan to record near-field accel- multi-layered anisotropic media. Topics of research include eration vectors. (S) the following: shear-wave splitting, scattering by anisotropic 1982 Over 100 digital seismic stations operate world- inclusions, dynamic in anisotropic media, free wide. About 30 of these constitute the GDSN network oscillations in a slightly anisotropic Earth, and ray-centered (Global Digital Seismograph Network). (S) coordinates in anisotropic media. (AI) 1986 to 1992 Research is mostly computer oriented. 1978 Ocean-bottom seismographs (OBS) placed on the The main topics are as follows: seafloor off the Pacific coast of central Honshu, Japan. (S) 1980 to 1992 With the ever-increasing quantity and • Inversion of seismic data for lateral heterogeneity and an- quality of seismic data, deviations from isotropy, spherical isotropy. Global images of the Earth's interior. symmetry, and pure elasticity could be observed with greater • Wave propagation from realistic earthquake sources in precision. multi-layered anisotropic media. On the other hand, the mounting capabilities of digital • Nonlinear inversion problems. electronic computers enabled seismologists to use more so- • Scattering from rough interfaces and randomly distributed phisticated forward and inverse computational schemes. scatterers. In the past decade or so, we witnessed the first 3D im- • Wave propagation in finely layered media. ages of seismic velocities and anisotropy in the mantle and • Ray perturbation theory and the Born approximation. inner core, along with refinement of the detailed velocity • Wave theory in complex media. structure near major internal boundaries such as the inner • Core dynamics. core-outer core, core-mantle, and upper mantle-lower man- • Application of GPS (Global Positioning System) to crustal tle transition zones. Through , seismol- deformation measurements. ogists have exploited the accumulated P- and S-wave data • Higher order Gaussian beams. (T) base of millions of travel times and thousands of waveforms as well as new, digitally recorded data sets of surface waves 1988 to 1992 Morphological fault studies: a study of offset and their standing-wave counterparts, free oscillations. The or deformations of large crustal earthquakes that occur sources for seismic waves are primarily earthquakes, distrib- within continental interiors. Systematic quantitative study of uted globally in mid-ocean ridges, subduction zones, and the surface morphology around faults, in lieu of analyses of along strike-slip faults. This computational process of 3D historical seismicity. (Long recurrence times indicate that global tomographic imaging of the deep interior is divisible historical seismicity is not sufficient to give adequate esti- into three distinct stages: mation of the in regions of moderate seis- micity. The morphological approach is less time consuming • Amassing a wide-frequency-range data base (fraction of a and cheaper than the technique of trenching, upon which second to 1 hr) of compressional and shear body waves, most of the paleoseismological studies of the last decade long-period surface waves, and free-oscillations time se- have been based.) The three-dimensional geometry of active ties. Given the quasi-elastic behavior of the Earth for fault systems, including segmentation and bifurcation, are short-time-scale transient loads, these elastic waves spread determined by careful combined use of satellite images, air through the interior from their respective sources, reflect- photos, and topographic and geological maps. Once that ge- ing, refracting, and converting between wave types when- ometry is defined, quantities like slip rates, slip vectors, and ever they encounter changes in material properties. recurrence times of large events may be retrieved by meas- • Inversion of the above data to determine density and elas- urements of the morphological record using a digital the- 1216 A. Ben-Menahern

odolite distansometer, complemented by state-of-the-art sur- It can thus be said that we belong to a generation that bridged face-dating techniques. (SS) between the precomputer era and the age of the electronic 1989 to 1992 Detailed study of the geometry of rupture revolution. of recently active faults: the source model is based on a A number of important observations and conclusions diversified set of data: surface ruptures, aftershock spatial can be readily drawn from our historical enquiry: our first distribution, and . The aftershock sequence concern is with the factors that have accelerated or impeded is recorded by a dense portable network deployed around the the growth of ideas in seismology, especially throughout the source region and then analyzed in order to obtain a precise twentieth century. The obvious stimuli of rapid growth were description of the mechanics of rupture. In the near field, as follows: geometry, segmentation, and stress regime are determined from the analyses of sequence. In the far field, • Occurrence of major devastating earthquakes in cultural high-quality recordings on broadband long-period channels centers, and global singular geophysical events (e.g., Lis- at teleseismic distances are used. This multi-disciplinary ap- bon, 1755; Mino-Owari, 1891; Chile, 1960). proach, through which seismology and tectonics are inte- • Economic stimulators (e.g., exploration for oil). grated, permits a detailed and accurate picture of the rupture • Advances in mathematics and in theoretical physics (e.g., and the involved mechanics. quantum mechanics). Results obtained so far point to the complexity of seis- • Technological breakthroughs (solid-state physics, lasers, mic sources. Their complexity is evidenced in the geometry holography, communication, computers, satellites, etc.). of aftershocks, the variation of focal mechanism throughout • Exploration of the moon and the solar system. the source's volume, and its temporal evolution. Seismic • Nuclear explosion tests and Test Ban Treaties verification studies are supplemented with trenching across faults and (1963 to 1976). C 14 dating to discover past tectonic activity and recurrence times of previous events. (SS) Impediments are harder to pinpoint, but they are probably mainly due to wars, economic recessions, and lack of vision 1991 Global Positioning System (GPS) applied to and perspective of scientific leaders. A striking example is crustal deformation measurements. (S) 1992 14 April. Unpredicted earthquake of magnitude 6 furnished by the inadequacy of the seismological community in the heart of Europe, amidst hundreds of seismographs, during 1912 to 1950 to exploit the theoretical know-how that computers, and professors of seismology. (Epicenter near the had been accumulated until the eve of . The following list summarizes what seismologists knew in the common border of Germany, Holland, and Belgium). The strongest shock in central Europe since 1755. Damages es- year 1912: timated at 1 billion Marks. (P) • Dislocation theory (Volterra, 1907). Just another reminder that even with all the accumulated • Representation theorem (Love, 1904). seismological lore since the Lisbon earthquake, we are still • Logarithmic creep law (Trouton and Rankine, 1904). as surprised by earthquakes now as we were then. (P) • Cagniard's method (Lamb, 1904). Numerical calculations of modes of oscillations of the • Continental drift theory (Wegener, 1912). Earth's core. (F) • Slip and fracture on long faults (Reid, 1906). • oS2 - 57m (Love, 1911). Perspectives • 7R (20s) = 2.8 × 10 -4 km -1 (Angenheister, 1906). • Group-velocity dispersion for crustal structure (Lamb, The present manuscript does not pretend to be a fun- 1912). damental analysis of the history of the subject. This task • Standard linear solid with continuous relaxation (Becker, must be left to professional historians. It may be likened, 1905). instead, to an aerial photo of a multi-lane highway on which • Breaks in secular pole motion (Milne, 1906). a set of discrete signposts are distributed, presenting an im- age of discoveries and inventions along a number of parallel The next question that concerns us is the rate of growth routes on the time axis. of knowledge in seismology. There is certainly no unique During 1959 to 1965, at the Caltech Seismological Lab- way to quantify the concept of "knowledge." One may, how- oratory, I was privileged to watch, with my schoolmates, the ever, estimate certain parameters that are related to growth. "change of the guard." The founding fathers slowly receded For example, by into the background while new ideas and technologies took over. This "happening" made us rather perceptive and ap- • Counting the yearly number of printed pages in four lead- preciative of the grand heritage of the nineteenth-century ing journals during this century [BSSA, JGR, Geophysics, applied mathematicians and the turn-of-the-century seis- GJRAS (now GJI)]. Assuming exponential growth n = mologists. At the same time it amplified in us the awareness No2~u~, it is found that 2 ~ 15 yr, i.e., printed pages dou- of the impact that electronic computers and modem seis- bled every 15 yr. mograph systems made on the growing field of seismology. • Assembling bibliography lists of some 50 textbooks pub- A Concise History of Mainstream Seismology: Origins, Legacy, and Perspectives 1217

lished during the twentieth century. This renders a chrono- known to Henry Fielding Reid in 1906. Seismologists are logical list of some 1000 papers, which was taken as the handicaped; meteorologists can put their sensors in the eye kernel of knowledge. Assuming, again, the above growth of a hurricane, we cannot put a sensor in the focal region. law, there resulted a doubling-up period of 25 yr. It means So far, most of our knowledge of the source came from that the yearly number of papers with significant novelty measurements at the far field. We do not have yet a physical increased by a factor of 16 since 1892. theory regarding the processes that take place at and near • The number of seismic stations increased exponentially the earthquake source, neither prior to the event nor even at since 1900, with 2 ~ 15 yr [N(1900) ~- 25; N (1992) the time of its occurrence. 2000]. It was stated in the introduction that seismology has • The population of seismologists increased exponentially always been an interdisciplinary science. In this respect it is since 1892 with 2 ~- 15 yr [N (1892) -- 50; N(1992) similar to medicine: The knowledge of anatomy alone is not 5000]. sufficient to cure a patient: you need the chemistry of drugs, the physics of lasers, and the mathematics of tomography Thus, four independent processes indicate a doubling-up pe- for diagnosis treatment and surgery. riod of 15 to 25 yr. Therefore, prediction must be first and foremost rec- It is tempting to make assumptions about the future, ognized as a problem at the junction of the sciences of en- based on the past record. Do we see today visible trends in gineering, geology, physics of condensed matter, and non- the evolution of seismology? First, there is clear transition linear mathematics. to computer-oriented research. During my recent visits to Prediction is not a matter of wave propagation at all, leading research centers in Europe and the United States, I and the conventional seismometer is not the adequate tool noticed that most of the Ph.D. students in seismology were to accomplish this goal. engaged in one form or another of "computer simulation games" or seismic-data reduction schemes, with insufficient So, just sprinkling the face of the Earth with seismo- efforts to construct new theoretical physical models. There graphs, and hooking up these instruments to computers and was too much reliance on finite-difference and finite-element satellites is not the answer either. algorithms, and only modest endeavors to come up with new What then, must be done to advance the cause of pre- ideas. Who then will forge the new mathematical weapons, diction? A major interdisciplinary effort is needed to develop so badly needed today in nonlinear source dynamics? a prediction scheme based on multi-premonitory phenom- Nevertheless, there is no escape from the fact that the ena: it means that the nearfield of a future focal zone must role of the computer will increase, as its speed and capacity first be identified, and then monitored for electrical, mag- will rise as a result of new technological innovations. netic, acoustic, seismic, and thermal precursors simultane- As the number of seismic sensors will continue to ously and continually. mount, so will the data recorded by these systems. We shall The young science of seismology has now reached a certainly witness data acquisition by networks via interna- critical point in its evolutionary trail. In a relatively short tional telemetry. time it has gained valuable knowledge on the structure of The role of satellites in geodetic strain measurements the Earth's interior and on the nature of seismic sources. will become more central. All told, seismology will move Like a traveler who reaches a crossroad, we must halt toward, what I call, the holistic stage: imaging the Earth's our forward rush, look back, and take stock. Let us meditate interior and seismic sources with all available data. for a moment on our achievements and weigh them against Will all this lead eventually to ? the shortcomings: did we exploit all our opportunities, were Clearly, the ultimate test of every scientific theory worthy the signals properly read and understood, or were some of its name, is its ability to predict the behavior of a system missed or misinterpreted... ? The history of seismology governed by the laws stated by the said discipline. Apart teaches us that the standards set by our predecessors are from the obvious goal of imaging the Earth's interior, which high; the spirits of the founders, Navier, Poisson, Stokes, is now proceeding with great vigor, the prediction of earth- Rayleigh, Milne, Love, Lamb, Volterra, Wiechert, Golitzin, quakes is the most important target of contemporary seis- Mohorovi~ic, Omori, Shida, Lehmann, Gutenberg, Richter, mology. How do we stand now on this issue? Jeffreys, Bullen, Pekeris, and Benioff breathe constantly on During 1935 to 1960, the study of an earthquake meant our necks. We must not fall. two things: assignment of magnitude and plotting the pattern It is perhaps adequate to end our essay with the words of initial motions. Thousands of earthquakes were analyzed of T. S. Eliot in his "Four Quartets" (1942): in this way. Another 30 yr passed by, and instead of magnitude, we talk about moment, and instead of initial motions, we plot "We shall not cease from exploration radiation patterns, and computers spit out fault lengths, stress And the end of all our exploring drops, etc. The terminology changed, the semantics changed, Will be to arrive where we started but the source dynamics are essentially the same as those And know the place for the first time." 1218 A. Ben-Menahem

Acknowledgments Barber, N. F. (1958). Optimum arrays for direction finding, New Zealand J. Sci. 1, 35-37. The prototype of this paper was presented at the International Symposium Bateman, H. (1910). The solution of the integral equation which connects on Frontiers in Fundamental Seismology, EOPG, Strasbourg, 23-25 Sep- the velocity of propagation of an earthquake wave in the interior of tember 1992. the earth with which the disturbance takes to travel to dif- Professor A. Udias of the University of Madrid, kindly sent me important ferent stations on the earth's surface, Phil. Mag. (Ser. 6) 19, 576-587. data on the history of seismology before 1755, and with his permission I Bath, M. (1954). The elastic waves Lg and Rg along Eurasian paths, Arkiv have incorporated the material in the second section. Geophys. 2, 295-342. Sarah Fliegelmann spared no effort to transform the handwritten manu- Bath, M. (t954). The density ratio at the boundary of the earth's core, Tellus script into its present form. I also extend my thanks to the librarians of the 6, 408-413. Wix Library of the Weizmann Institute of Science, Libeta Chernobrov, and Bath, M. (1958). The energies of seismic body waves and surface waves. Miriam Gordon, for assisting me in the location of biographical data. In: H. Benioff, M. Ewing, B. F. Howell, Jr., and F. Press (Editors), In retrospect, this study has been inspired through the affect of a lifelong Contributions in Geophysics: In honor of Beno Gutenberg. Pergamon, chain of teachers, among them: Gulio Racah, Menahem Schiffer, Arthur New York pp. 1-16. Erdtlyi, Harold Jeffreys, Chaim L. Pekeris, Markus Bath, , B~tth, M. and A. Arroyo (1962). Attenuation and dispersion of G waves, J. Charles H. Dix, Hugo Benioff, and Richard P. Feynman. I owe much to Geophys. Res. 67, 1933-1942. my schoolmates during our formative Caltech heydays: D. G. Harkrider, Becker, R. (1925). Elastiscbe Nachwirkung und Plastizit~t, Zeit. Phys. 33, M. N. Tokstz, S. S. Alexander, J. H. Healy, R. A. Phinney, S. W. Smith, 185-213. C. B. Archambeau, A. Cisternas, and R. L. Kovach. Beer, A. and J. M. Stag (1946). Seismic sea wave of November 27, 1945, In the years that followed, I had the benefit of creative interaction with Nature 158, 63. [Also: (1945). Nature 156, 712-713.] my colleagues: R. Lapwood, V. Keilis-Borok, F. Gilbert, J. GiUis, S. J. Benioff, H. (1935). A linear strain seismograph, Bull. Seism. Soc. Am. 25, Singh, A. Weglein, E. Wolf, P. Tapponier, D. H. Eckhardt, and A. Taran- 283-309. tola. Benioff, H. (1951). Earthquakes and rock creep, Bull. Seism. Soc. Am. 41, I agree wholeheartedly with the ancient maxim of Rabi Hannina (ca. 200 31-62. A.D.): "! have learned much from my teachers, more from my colleagues Benioff, H. (1958). Long waves observed in the Kamchatka earthquake of and mostfrom my students." Among these last I count Moshe Israel, Marcel Nov. 4, 1952, J. Geophys. Res. 63, 589-593. Weinstein, Mosbe Vered, Shahar Ben-Menahem, Wafik Beydoun, Arcan- Benioff, H. (1962). Movements on major transcurrent faults, in: Continental gelo Sena, Richard Gibson, and Oleg Mikhailov. Drift S. K. Runcorn (Editor), Academic Press, New York, 103-134. All of them helped me throughout the years, in one way or another, to Ben-Menahem, A. (1961). Radiation of seismic surface waves from finite shape the perspectives of our science, and for that I am grateful. moving sources, Bull. Seism. Soc. Am. 51, 401-435. Ben-Menahem, A. (1962). Radiation of seismic body waves from a finite moving source in the earth, Z Geophys. Res. 67, 345-350. Ben-Menahem, A. (1964). Mode-ray duality, Bull. Seism. Soc. Am. 54, References (up to 1964) 1315-1321. Ben-Menahem, A. and D. G. Harkrider (1964). Radiation patterns of seis- Airy, G. B. (1838). On the intensity of light in the neighborhood of a mic surface waves from buried dipolar point sources in a flat stratified caustic, Camb. Phil. Trans. 6, 379-401. earth, J. Geophys. Res. 69, 2605-2620. All, K. (1960). The use of Love waves for the study of earthquake mech- Ben-Manehem, A. and M. N. Tokstz, (1963). Source mechanism from arfism, J. Geophys. Res. 65, 322-331. spectra of long-period seismic surface waves, 2. The Kamchatka All, K. (1960). Study of earthquake mechanism by a method of phase earthquake of Nov. 4, 1952, J. Geophys. Res. 68, 5207-5222. equalization applied to Rayleigh and Love waves, Z Geophys. Res. Benndorf, H. (1905). Uber die Art der Fortpflanzung der Erdbebenwellen 65, 729-740. in Erdinnem, Mitt. Erdbeben-Komm. Akad. Wien 29, 1407. Alsop, E. (1964). Spheroidal free periods of the earth at eight stations Bedage, H. P. (1932). Seismometer, Handbuch der Geophysik, Band 4, 20- around the world, Bull. Seism. Soc. 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