BULLEN, KEITH EDWARD

(b. Auckland, New Zealand, 29 June 1906; d. Auckland, 23 September 1976)

seismology, applied mathematics, geophysics.

Bullen’s parents were George Sherrar Bullen, a journalist, and Maud Hannah Burfoot. Both his parents were burn in 1875 and lived to be ninety-nine. His father was born in New Zealand and his mother came from England. Bullen’s sister, Jean Maud Bullen, twelve years younger, became a member of the research staff of the Ionosphere Section of the Department of Scientific Research, Christchurch, New Zealand. In 1935 Bullen married Florence Mary Pressley; they had a son and a daughter.

Bullen gained an international reputation as a pioneer in modern seismology. He was a superb applied mathematician, particularly adept at constructing mathematical models of the earth’s interior that enabled him to draw inferences about the numerical values for its various properties, especially density. Bullen’s reputation was secured with the publication in 1940 of the Jeffreys-Bullen Seismological Tables. His work on these tables initiated his lifelong concern with density determinations of various layers of the earth’s interior, which, in turn, led to his construction of Earth Model A (1940–1942) and Model B (1950), his compressibility-pressure hypothesis (1946), his hypothesis of a solid inner core (1946), and his various models for the interior of the moon and of other planets.

Bullen became a fellow of the Royal Society in 1949, a foreign associate of the United States National Academy of Sciences in 1961, and a fellow of the Pontifical Academy of Science in 1968. He was also a fellow of the Australian Academy of Science, and an (honorary) fellow of the Royal Society of New Zealand and the Royal Society of New South Wales. He received numerous scientific prizes, including the William Bowie Medal of the American Geophysical Union (1961). The Day Medal of the Geological Society of America (1963), the Research Medal of the Royal Society of Victoria (1965), and the gold medal of the Royal Astronomical Society (1974).

Bullen devoted considerable time to scientific organizations. With the advent of the International Geophysical Year he became, in 1955, chairman of its Australian National Committee; was later appointed convener of the Australian National Committee for Antarctic Research (1958–1962); and, in 1959, became vice president of the International Special Committee for Antarctic Research. From 1955 to 1957 he was president of the International Association of Seismology and Physics of the Earth’s Interior and was vice president of the International Union of Geodesy and Geophysics from 1963 to 1967. He also served on the governing council of the International Seismological Summary during the 1960’s.

Bullen’s other interests included numismatics, cricket, and tennis. He was wont to visit coin shops when traveling abroad and served as president of the Auckland University Cricket Club during the 1939–1940 academic year. History of science was also one of his interests, and he contributed to the Dictionary of Scientific Biography. Among his articles are those on such early workers in seismology as Cargill Knott, Horace Lamb, Augustus Love, John Milne, Andrija Mohorovičić, Richard Oldham, Herbert Turner, and Emil Wiechert. He also wrote the entry on Alfred Wegener.

Bullen’s early schooling was typical for a New Zealander. His primary education was at Bayfield School, Herne Bay, Auckland (1912–1918), and his secondary education was at Auckland Grammar School (1919–1922). His brilliance in mathematics expressed itself at an early age; he used to work out his mathematics homework while cycling five miles home. According to his sister, he was an extremely active boy, participating in tennis, swimming, surfing, rock climbing, and hiking with survey parties. She attributed his later increasing deafness, which he began to experience in his late twenties, to his diving. Bullen also took boat trips to White Island, the site of an active volcano; and he later suspected that these trips, along with the famous Hawke’s Bay earthquake of 2 February 1931, kindled his interest in seismology and geophysics.

In 1922 Bullen earned an entrance scholarship to Auckland University College. In 1925 he became senior university scholar in pure and applied mathematics at the University of New Zealand, and he obtained a B.A. degree in 1926. He also took courses in Latin. French, philosophy, and education. He received an M.A. degree from the University of New Zealand in 1928 with a first class in mathematics, and took a B.Sc. in physics in 1930 with chemistry as a minor. During much of this time he worked at various teaching posts and was employed as a parttime lecturer at Auckland University College. In 1928 he became a full-time senior lecturer and, except for the period 1931 to late 1934, spent in England and continental Europe, he remained at this post until 1940, when he became senior lecturer in mathematics at the University of Melbourne. He stayed at Melbourne for five years, then left to become professor of mathematics at the University of Sydney. In 1946 he was awarded the Sc.D. from Cambridge.

Bullen entered St. Johns College, Cambridge, in 1931 as an advanced student, intending to take the mathematical tripos in two years. He decided, however, to become a research student and “had the outstanding good fortune” to be taken in hand by Sir Harold Jeffreys, who, in Bullen’s words, “literally brought me down to earth and rescued me from a pure mathematical fate.” Indeed, Bullen’s career as a research scientist began on 12 January 1932, during his first meeting with Jeffreys, who asked him to collaborate with him on the enormous task of constructing earthquake travel-time tables of greater accuracy than those then available. Bullen, who saw all the previous issues of the International Seismological Summary—the quarterly journal of the International Seismological Association, containing masses of seismological data collected throughout the world—spread upon the floor before him, accepted the offer, even though he later confessed that “on that first day, my impression of the I.S.S. was of a very dull-looking collection of numerical entries and strange place-names that conveyed to me little more than would, say, a collection of horse-racing booklets or the financial columns of a foreign newspaper.”

Revision of the travel-time tables was not completed until 1940. Bullen and Jeffreys worked together at Cambridge until near the end of 1934. Around this time they decided it would be best for Bullen to return to Auckland to work alone since, as far as Jeffreys knew, there was no precedent for the whole of the work of a Ph.D. candidate being done jointly with a supervisor. After several months visiting a number of countries in continental Europe, Bullen returned home and began mailing his own contributions to the tables.

Earthquake travel-time tables give the length of time, T, it takes bodily seismic waves, P (longitudinal) and S (transverse) waves and various multiphased P and S waves, to travel from the focus of an earthquake through the earth’s interior to a point on the surface in terms of Δ, the angular distance subtended at the center of the earth by the are from the earthquake’s epicenter to the designated point on the surface. The first travel-time tables were constructed by Karl Zöppritz. Jr., of Göttingen in 1907. They were amended and extrapolated to the antipodes by Herbert H. Turner of Oxford. Theresulting Zöppritz-Turner Tables were adopted by the International Seismological Association in 1918 and used in preparing the International Seismological Summary.

Beginning around 1922, a number of seismologists, including Turner, Perry Byerly, and James B. Macelwane, came to the realization that the Zöppritz-Turner Tables were in need of revision. Although these researchers made considerable improvements, their work was not consistent; and about 1930 Jeffreys decided that a total revision of the tables was required. Jeffreys and Bullen published their preliminary set of tables in 1935. These tables were used by the International Seismological Association from December 1936 until near the end of 1939, when it began using a more refined set of Jeffreys and Bullen tables that were published in 1940. In 1947 these became the official tables of the International Seismological Association. Beno Gutenberg and Charles F. Richter constructed their own set of tables while Jeffreys and Bullen were busy with theirs. Although both teams used a tremendous amount of data, Jeffreys and Bullen used more. The two sets of tables compared quite well with each other: the greatest differences were less than onetenth of the greatest correction that had to be made to the Zöppritz-Turner tables.

The Jeffreys-Bullen travel-time tables treat Earth as spherically symmetrical. Consequently the calculated travel time, T, for any given phase of a P or S wave is the same for any pair of points on the surface of the earth with the same Δ, regardless of the longitude and latitude of the epicenter and seismological recording station. In 1933 Leslie J. Comrie, a New Zealander, and Gutenberg and Richter independently suggested that further improvements in travel times would be possible if the effect of the earth’s ellipticity upon earthquake travel times were taken into consideration. They pointed out that the use of geocentric instead of geographic latitudes, which had been used previously, would further reduce such errors. (A geocentric latitude of a point on the earth’s surface is the angle between the radius vector from the earth’s center to the point of the surface and the plane of the equator; therefore its use in seismological tables eliminates the need for making any corrections in travel time due to the ellipticity of the earth’s outer surface.)

Jeffreys showed, however, that although this eliminated errors in the travel time of earthquakes that were due to the ellipticity of the earth’s surface, it failed to eliminate all the effects of the earth’s ellipticity, since it did not take into account errors due to the ellipticity of different layers. The travel times of seismic rays are affected not only by the surface ellipticity bulges at the end of rays but also by the ellipticity of each internal surface of constant seismic velocity encountered by the ray. Bullen took on the task of making these internal ellipticity corrections. He soon realized that in order to solve the problem, he needed to determine the density distribution at the different layers transversed by seismic rays.

At the time Bullen began working on the density problem, earth scientists generally agreed there were two major discontinuities in the earth’s interior: one corresponding to the crust-mantle boundary, the other to the mantle-core boundary. In 1909 Andrija Mohorovičié of Zagreb, Yugoslavia, argued in favor of a seismological discontinuity corresponding to the crust-mantle boundary. Three years earlier Richard D. Oldham suggested a mantle-core boundary on the basis of seismological evidence. He overestimated its depth, however, placing it at 3, 800 kilometers. In 1912 Gutenberg, again on seismological grounds, placed the boundary at 2, 900 kilometers, extremely close to the current estimate.

There also was general agreement as to the fluidity of the earth’s core. In 1926 Jeffreys was able to show, contrary to what most had believed, that the average rigidity of the earth deduced from tidal motion and Chandler wobble could be made consistent with the seismic velocities of P and S waves in the mantle only by assuming the existence of a core of very low rigidity. (The discovery of the fluidity of the earth’s core, contrary to popular accounts, was not based simply upon the “fact” that seismologists had not observed the propagation of S waves through the core. In general, negative existential claims are problematical, and in this case, at least one seismologist, J. B. Macelwane, thought that he had detected the transmission of an S wave through the core. Rather, the fluidity of the earth’s core depended upon Jeffreys’ demonstration that an acceptable average rigidity of the earth required a liquid core)

Despite the discovery of these two basic discontinuities, Bullen did not have too much to draw upon when he turned to the density problem, and he quickly realized that he would have to determine the answer himself. The most recent work (1923) had been done by two American earth scientists. E. D. Williamson and Leason H. Adams. Bullen began by applying their method, which contains equation (I) as its key formula, where r is the distance of a point from the earth’s center, p is the density at r, λ is the universal gravitational constant, m is the mass of the matter within the sphere of radius r, and a and B are the velocities of P and S waves at level r:

Equation (l) is applicable only to regions where constitution is essentially uniform, provided the deviation from adiabatic conditions is minimal.

Beginning with a density of 3.32 at a depth of 35 kilometers for the density and depth of the outside of the mantle, and taking the velocities of P and S waves from Gutenberg and Richter (none of this being very controversial), Bullen used equation (1) to calculate the density of the mantle at 100-kilometer intervals. This also gave him the mass of the earths mantle, winch allowed him to determine the mass of the core. At this point Bullen decided to check his results by combining them with the known moment of inertia of the core. The check proved to be effective, but not in a manner that gave him cause for immediate happiness, for it showed that his results implied the implausible hypothesis that the core was much denser near the outside than at its center. Bullen escaped the impasse by making a major discovery: that the density of the mantle does not vary continuously and, therefore, that the Williamson-Adams formula cannot be applied to the mantle as a whole.

Bullen first published his results in 1936, the same year that Inge Lehmann, a Danish seismologist, published her paper on the existence of an inner core. In his paper Bullen tentatively placed the jump in density at a depth between 300 and 400 kilometers, since he and Jeffreys, and Lehmann, independently had reported a jump in the rate increase of the velocity of P and S waves that they took to indicate a first-order discontinuity. This discontinuity came to be called the 20° discontinuity, since it shows up as a rapid change in the gradient of the P and S travel-time curves around epicentral distances of 20°. Bullen also pointed out that his calculation of the density of the earth’s core, which was lower than previous estimates, was consistent with the idea of a core composed entirely of molten iron. This was important because previous estimates required the supposition that the core contained a proportion of heavier elements.

Bullen continued to work on his “density-jump” hypothesis during the next two years. In 1937 he placed the discontinuity at 481 kilometers ± 21 kilometers in light of more refined seismological estimates of the velocity of S and P waves, the boundary of the 20° discontinuity, and the depth of the mantle-core boundary. In 1939 he argued that his hypothesis gained support from findings in terrestrial magnetism and petrology. The suggestion had been made by Sydney Chapman and Albert T. Price that certain aspects of the secular variation of the geomagnetic field suggested a significant increase in the electrical conductivity of the mantle beginning at around 150 kilometers and becoming more pronounced at about 700 kilometers. Bullen noticed a report by Price and B. N. Lahiri that offered some confirmation of the idea. He proposed that if the 20° discontinuity is gradual, it might extend to a depth of 700 kilometers. This, he added, coincided with the depth of the deepest earthquakes. He then referred to Jeffreys’ recent suggestion, expanded by John D. Bernal that his “density discontinuity” might correspond to a change in the crystal structure of olivine due to tremendous pressure that could also account for increasing electrical conductivity.

While Bullen was developing his analysis of Earth’s density distribution, he found time to construct earthquake time-travel tables for Earth’s ellipticity, the reason he had begun working on the density problem; published a number of articles analyzing New Zealand earthquakes; and offered an estimate of twenty-six kilometers for the thickness of the upper layer of the oceanic crust in the Pacific through analysis of the Rayleigh waves from an earthquake in the Bering Sea. Moreover, he pursued the work on planetary density problems begun in 1937. In 1940 Bullen published a lengthy article on density distribution in which he summarized his previous work and introduced part of his nomenclature for layers of the earth’s interior: A for the crustal layer; B. C. and D. for the mantle, with C being the inhomogeneous layer containing the jump in density; E for the outer core; G for the inner core; and F for a transitional layer between E and G. He did not, however, use his nomenclature for the core because he thought it premature to offer density estimates for the inner and outer portions of the core.

In 1942 Bullen published an expanded version of his 1940 treatment of density to the layers E. F. and G. In essence this was his first presentation of a complete version of his Earth Model A. He didn’t refer to it by such a designation until 1950, when he needed to contrast such models with B-type models.

Although Francis Birch, a geophysicist from Harvard, was the first to suggest (1940) a solid or “frozen” inner core, Bullen was the first to offer extensive arguments for its solidity and to propose a seismological test for its existence. He first advanced the hypothesis in 1946. The idea grew out of his work on the density problem and his construction of Earth Model A. He realized that the results of Model A suggested (1) that even though the density ρ and rigidity μ greatly change at the mantle-core boundary, there was only a 5 percent change in the incompressibility k; and (2) that when values of k were plotted against values of pressure p, there was no significant change in dk/dp on either side of the mantle-core boundary.

In 1950 Bullen began referring to (2) as the compressibility-pressure hypothesis. It is tantamount to the claim that the compressibility of a substance, at least at high pressure and temperature, is largely independent of chemical composition. With (2) Bullen was able to infer the existence of a solid inner core. Beginning with the observed jump in the velocity of P waves, vp, from the outer to the inner core, and the formula for vp,

He reasoned that the jump in velocity could be explained by a drop in density, a jump in incompressibility, or a jump in rigidity across the outerinner core boundary. A sharp increase in k was ruled out by his compressibility-pressure hypothesis, while a decrease in ρ approached the impossible. Therefore he concluded that the jump in the velocity of P waves is the result of a tremendous jump in μ from an outer core of little rigidity (a fluid outer core) to an inner core of sizable rigidity (a solid inner core). He then proceeded to relate his hypothesis to Birch’s solution to the origin of Earth’s magnetic field and suggested that one way to test the idea was to find a PKJKP seismic wave. This is a wave that passes through the mantle and outer core as a P type, is transformed into an S type in the inner core, and then back into a P type through the outer core and mantle.

Although Bullen continued working on a number of other problems—for example, the problem of planetary densities—much of his later research was devoted to confirmation of a solid inner core. In 1961 he told a reporter from the New York Times that “if I can see part of the Earth proved solid before I die. I’ll die happy.” In 1949, starting with the compressibility-pressure hypothesis and knowing Jeffreys’ values for the velocities of P waves in the inner core, he estimated that the velocity of S waves through a solid inner core should fall somewhere between 4.9 and 6.0 kilometers/second. The following year he began presenting his Earth Model B. which, unlike Model A, directly incorporates into its formalization (1), (2), and the hypothesis of a solid inner core. He also derived a set of theoretical travel-time tables for PKJKP waves, hoping that seismologists would put the tables to use and thereby confirm his hypothesis of a solid inner core. He suggested that PKJKP waves would most likely be detected over an epicentral distance Δ ranging from 130° to 155°.

In 1951 Bullen pointed out that it would be extremely difficult to observe PKJKP waves, “that they would be on the border of observability” because their amplitude would be extremely low— 0.04 to 0.2 of the amplitude of their companion PKIKP waves, in which I represents the passage of a P wave through the inner core. He also hinted that matters might be even worse because the amplitude might be even less than the above estimates if the transition layer, whose character was unknown, absorbed some of the energy used in the conversion of a P wave into an S wave at the outer-inner core boundary.

In 1952 a colleague of Bullen’s. T. N. BurkeGaffney of Riverview College Observatory in Sydney, examined the observatory’s seismological records back to 1909 in an attempt to identify PKJKP waves. He and Bullen concluded that although a few of the recorded impulses were found to agree with the predicted travel times of PKJKP waves, the readings were too ambiguous to warrant positive identification, and that a prerequisite for identification of PKJKP waves was that the accompanying PKIKP wave have an amplitude of at least 20μ. They also further restricted the epicentral range for observing PKJKP waves to 130° ≤ Δ ≤ 142° and 145° ≤ Δ ≤ 155° because it was difficult to estimate the amplitude of PKIKP waves from 142° to 145°.

Bullen suggested in 1953 that perhaps he had overestimated the rigidity of the inner core—not that it was not solid but that its rigidity might not be as great as he had previously supposed. He had used Jeffreys’ estimate of the increase in the velocity gradient of P waves passing into the inner core in his former estimate of its rigidity. Gutenberg’s later and somewhat lower estimate of the jump in the velocity of P waves implied a less rigid inner core. In addition, if Gutenberg’s estimate were correct, it was quite likely that PKJKP waves would have insufficient amplitude for detection, since his estimate implied the use of even more energy in the P-S wave conversion at the inner core boundary.

Observation of PKJKP waves continued to be unsuccessful, and in 1955 R. O. Hutchinson argued that because he failed to observe them on two “ideal” occasions, the likelihood of their existence was quite remote. Bullen promptly replied that the “ideal” cases were not ideal. Fairly strong seismological confirmation of the existence of a solid inner core came in 1960, albeit in an unsuspected form: free oscillations of the earth brought about by a major earthquake in Chile on 22 May. In 1962 Bullen eagerly reported an analysis of the free oscillations put forth by Chaim L. Pekeris, an Israeli mathematician, showing that, among the available models, only Bullen’s Earth Model B, distinguished from the other models by its postulations of a solid inner core, could explain some of the periods of the free oscillations. Additional evidence was provided by an analysis of the March 1964 earthquake in Alaska, and by the 1970’s the existence of a solid inner core was well established.

To this day observation of PKJKP waves remains a matter of dispute. In 1972 Bruce Julian, David Davies, and Robert Sheppard claimed that they had identified such a wave, but it had a velocity of only about half the value predicted by Bullen. Since its velocity, even by today’s standards, is too low, others have suggested that these researchers probably had observed a SKJKP wave, whose predicted velocity is much closer to what was observed. However, because both interpretations contain a J phase, either of them provides additional evidence for the solidity of the inner core, but one of less rigidity than originally predicted by Bullen. To the end of his life he believed that additional confirmation of the solidity of the inner core was needed.

Bullen was involved in an extrascientific controversy of some interest. In 1954 he was able to determine the precise time when the United States exploded a number of hydrogen bombs, and he quickly realized the scientific value that could be gained by planned nuclear explosions: that they could be used by seismologists to learn more about Earth’s interior. This led him to propose their detonation for scientific purposes during his presidential address at the 1955 annual meeting of the International Association of Seismology and Physics of the Earth’s Interior. Needless to say, his suggestion failed to gain universal applause.

Bullen died in 1976 of a heart attack.

BIBLIOGRAPHY

I. Original Works. Bullen published five books and more than 280 articles and papers. The most complete listing of his publications is in Sir Harold Jeffreys. Biographical Memoirs of Fellows of the Royal Society, 23 (1977), 19–39. Among his books are An Introduction to the Theory of Seismology (Cambridge, 1947; 2nd ed., Cambridge. 1953: 3rd ed., Cambridge, 1963): An Introduction to the Theory of Dynamics (Sydney, 1948); An Introduction to the Theory of Mechanics (Sydney. 1949; 8th ed., Cambridge. 1971): and that The Earth’s Density (London, 1975).

Some of the key articles, particularly relevant to his work on the density distribution problem and the solidity of the earth’s inner core, are “The Variation of Density and the Ellipticities of Strata of Equal Density Within the Earth,” in Monthly Notices of the Royal Astronomical Society, and Geophysical Supplement, 3 (1936), 395–401; “Note on the Density and Pressure Inside the Earth,” in Transactions and Proceedings of the Royal Society of New Zealand, 67 (1937), 122–124; “Composition of the Earth at a Depth of 500–700 km.,” in Nature, 142 (1938), 671–672; “The Problem of the Earth’s Density Variation,” in Bulletin of the Seismological Society of America, 30 (1940), 235–250: “Density Variation of the Earth’s Central core,” ibid., 32 (1942), 19–29; “A Hypothesis on Compressibility at Pressures of the Order of a Million Atmospheres,” in Nature, 157 (1946), 405: “Compressibility-Pressure Hypothesis and the Earth’s Interior,” in Monthly Notices of the Royal Astronomical Society, Geophysical Supplement, 5 (1949), 355–368: “An Earth Model Based on a Compressibility-Pressure Hypothesis,” ibid., 6 (1950), 50–59; “The oretical Travel-Times of S Waves in the Earth’s Inner Core,” ibid., 112–118: “Note on the Phase PKJKP ,” in Bulletin of the Seismological Society of America, 46 (1956), 333–334: “Oscillations of the Earth and the Earth’s Deep Internal Structure,” in Australian Journal of Science, 24 (1962), 303–307; and “Free Earth Oscillations and the Internal Structure of the Earth,” in New Zealand Mathematical Chronicle, 5 (1976), 17–45.

Several of the best notes and articles by Bullen on his own work include his 1969 Matthew Flinders lecture, “Researches on the Internal Structure of the Earth,” in Records of the Australian Academy of Sciences, I (1969), 39–58; and “Some International Seismological Summary Reminiscences,” in Geophysical Journal of the Royal Astronomical Society, 20 (1970), 359–365.

II. Secondary Literature. Besides that by Jeffreys, a commemorative article is Bruce A. Bolt. Bulletin of the Seismological Society of America, 67 (1977), 553–557. The best historical treatment of the discovery of Earth’s core that includes a section on Bullen’s hypothesis of a solid inner core and its eventual confirmation is Stephen G. Brush, “Discovery of the Earth’s Core,” in American Journal of Physics, 48 (1980). 705–724.

Henry Frankel