In the early 1960s, the United States and Soviet Union signed treaties not to conduct atmospheric, outer space, or oceanic nuclear tests. But no treaty was signed for underground tests. So, there was a need to monitor what unfriendly countries were doing. The program
to identify and detect underground nuclear events was established and funded by the Air Force, and it provided money for the development of geophysics in many universities. Knopoff was well placed to get involved, given his background in seismology. With the help of Frank Press, in 1960 he installed four high quality long-period seismic stations around the European Alps for one year, and then the next year the stations were moved to the western Mediterranean. These instruments, designed by Frank Press and Maurice Ewing, could measure surface waves of periods of up to a hundred seconds with great sensitivity. Shortly after these experiments, in 1964, the Air force began to install the World Wide Standard Seismic Network, WWSSN, which included both short-period and long-period seismographs of this design installed at stations in friendly countries across the globe. The Air force made the data available to university researchers. Funding for university seismological research was ensured when Press and colleagues, based on their analysis of global seismic data, presented to the military precise times and locations of supposedly secret United States nuclear tests in the Pacific.
The fieldwork in Europe was coupled with a rather remarkable sabbatical leave in 1960 and 1961 at the University of Cambridge, in England. There he developed analysis procedures to invert the seismic recordings for Earth's structure. The analysis revealed for the first time a low velocity channel under the Alps. Most seismic investigations found that velocity increases with depth in the Earth, attributed mainly to the increasing pressure. That the trend reverses suggested that between the competing effects of pressure and temperature, the latter had begun to dominate. As early as 1932, Gutenberg had used the variation of amplitudes from P body waves to deduce the presence of a low velocity zone in the upper mantle, but the response to his approach was great skepticism. Knopoff provided the first surface wave confirmation.
In addition, in 1960, while on sabbatical in Cambridge, Knopoff gave a lecture on thermoluminescence at Oxford University. This lecture was the basis for the formation of a famous thermoluminescence lab at oxford. He was then invited to join an archaeological expedition to the Dead Sea. He combined this with a gravity survey across the Jordan River, just north of the Dead Sea (Knopoff and Belshé 1966). Among the stations visited, which included Jacob's Well, Jerusalem (Qalandaiya) Airport, Bethlehem, and Jericho, he obtained permission to make a gravity reading at Amman (Marka) Airport in Jordan. But, in case the gravimeter was a bomb and not a scientific instrument, he was supervised by a guard who pointed a gun at his head while he took the reading. The published profiles show that the Amman reading was consistent with the others, and that even though his mind may not have been calm, his fingers apparently were, in spite of this adversity.
He caught infectious hepatitis in Jordan that became severe on return to Cambridge. His fiancée, Joanne Van Cleef, had to be telephoned in the United States to say that the groom was in a hospital in Cambridge, England, and that he could not make the wedding. The wedding took place two months later, and both of them returned to Cambridge to complete the sabbatical. So began a fifty-year relationship of mutual support that helped him throughout the remainder of his life, both in triumph and adversity.
With a well-funded lab and a burgeoning reputation in the mid-sixties, Knopoff began to attract students and post-docs with an impressive array of quantitative skills. The WWSSN provided a rich source of data. Knopoff's group began to develop the theories and analysis techniques for these data in earnest, adapting them to then newly developed mainframe computers.
Plate tectonics was in its infancy. The seminal Vine-Matthews paper on magnetic stripes associated with sea floor spreading was published in 1963, but details on plate thickness and motions relative to the mantle were unknown. Knopoff provided the vertical dimension of plate tectonics by initiating a search for low-velocity channels across the globe. for example, under the Pacific he discovered the low-velocity channel that extended from 100 to 200 km depth. It soon became recognized as defining the base of the Pacific plate and the zone-decoupling moving plate from the underlying mantle. Similar low-velocity zones were found beneath all the oceans and tectonically active regions on continents. In contrast, continental shields developed no such low-velocity zones. This explained why the continental plates move much slower (centimeters per year) through the mantle than the oceanic plates, rather as if they have a deep keel. The Pacific plate travels fastest (10 centimeters per year). Thus, the work of these early days showed that the Pacific plate was one of the major drivers of the global convective circulation of plate tectonics.
Much of the globe was covered by WWSSN long-period stations in the mid-1960s, but the geopolitically neutral Antarctic continent still had none. Knopoff was awarded a grant from the National Science Foundation to establish a seismograph at a Russian station, Novolazarevskaya, on the coast of Antarctica, and a matched station at the South Pole itself. By analyzing seismic waves along the path between the two stations, he showed that indeed Antarctica had a continental structure with a deep keel.
Slichter had been running tidal gravimeters both at UCLA and the South Pole that also served as long-period seismometers. With Slichter's passing in 1978, Knopoff took over the South Pole project.
The South Pole was a special location for tidal and earthquake studies. The response of the solid Earth to diurnal and semi-diurnal tides was known to be elastic, whereas the response to loadings such as the removal of the ice sheets over 10,000 years or so was more fluidic. So, there was interest is measuring the response at longer periods such as the 14-day, monthly, and 18.6-year lunar tides. South Pole was ideal to search for these periods because the diurnal and semi-diurnal tides were absent there. However, for Knopoff it had other desirable features.
It was well known at the time that when a large earthquake occurs, the Earth vibrates with a series of normal-mode frequencies that depend on its internal structure. Slichter, along with groups at Caltech and Lamont Observatory, was the first to unambiguously measure the Earth's modes in 1960 when the largest ever-recorded earthquake (magnitude 9.5) struck in Chile. As this new field of "terrestrial spectroscopy" became a subject in its own right, it became recognized that the asymmetry caused by rotation and ellipticity of the Earth causes the frequencies of the modes to be split from values that they would have if the Earth were spherical and stationary, rather like the Zeeman effect. Modes measured by a long-period station at South Pole, because of its symmetric location, were free from such splitting, and so other effects, such as those from lateral heterogeneity or hitherto undiscovered modes, might be observable.
One such mode, the Slichter mode, involves displacement of the earth's inner core by a large earthquake and subsequent oscillations. In 1961, Slichter predicted that it should have a frequency of several hours dependent on the density contrast between inner and outer core. (The analytic expression in his paper was left as an exercise for the student.) In spite of a thorough and systematic search, including removal of all residual tidal effects, the Slichter mode proved elusive, not helped by the fact that no event as large as the 1960 Chile earthquake has ever occurred since. (Observation of the Slichter mode was reported in data from superconducting gravimeters in Europe by Spiros Pagiatakis and colleagues in 2007, but multiple confirmations are still needed.)
Knopoff's international collaborations were legendary. He worked with Edgar Kausel (Chile),
Stephan Mueller (Germany), Giuliano Panza (Italy), Keilis-Borok (Russia), Chen Yuntai (China), and Teruo Yamashita (Japan). The list is too extensive to complete here, and at all of these institutions he was appointed visiting professor. Knopoff, who had been limited to streetcar rides near Boyle Heights in his youth, became an academic traveler of some virtuosity, thanks to exposures at international meetings such as the 1957 International Union of Geodesy and Geophysics meeting in Toronto. Knopoff's interaction with Soviet scientists began at this meeting, where he met long-term collaborator Vladimir Keilis-Borok of the Soviet Academy of Sciences.
Beginning in the early 1960s, Knopoff traveled to Moscow to collaborate with Keilis-Borok. Thus began a long-term relationship of exchange visits that persisted through the Cold War, culminating with an invitation to keilis-Borok to join Knopoff permanently at UCLA in the late 1990s. Keilis-Borok was instrumental in reuniting the Soviet and American branches of the Knopoff family when he located Knopoff's uncle in Leningrad.
Keilis-Borok's group was applying pattern recognition and statistical methods developed by Russian mathematicians, such as Gelfand and Kolmogorov, to the problem of earthquake prediction and other geophysical phenomena. A joint USA/USSR Working Group on Earthquake Prediction was formed to pool expertise in the two countries.
The Russian school was also strong in inverse theory. In the inverse problem, one wishes to determine the properties of an inaccessible region from measurements at selected locations, usually on the surface. Knopoff had shown that the geophysical inverse is non-unique – that is, one can never determine the properties of the inaccessible region with precision – and hence, it is incumbent upon geophysicists to indicate the range of uncertainties in their interpretations. Keilis-Borok, Knopoff, and a number of students developed the hedgehog method of inversion, which directly specified the class of solutions consistent with the
data. Like a hedgehog eating out the interior of a bush, the method explores the volume of solutions compatible with the data. The method is still occasionally used in the problems of geophysical inversion. Knopoff and Jackson constructed a solution to the problem of over-parameterization of structure – that is, how to fit the detailed structure of the Earth with insufficient data.
At the 1960 IUGG meeting in Helsinki, incoming president of the union, Vladimir Beloussov, proposed the Upper Mantle project, an international program for study of the structure of the Earth's crust and the shell beneath it. Beloussov was elected chairman of the project and Knopoff its general secretary. The United States' participation had to be approved at the Presidential level. Knopoff and colleagues testified before the President's Scientific Advisory Committee. The approval took the form of a telegram from then-president lyndon Johnson, which Knopoff communicated to the IUGG, and which had the effect of both increasing United States funding for geophysics and advancing global collaboration. One of the more active working groups of the Upper Mantle Project, focused on geophysical theory and computers, was led by Keilis-Borok. When the project wound down, Knopoff used the working group as a basis for founding the Committee on Mathematical Geophysics, which continues to hold biennial meetings even to this day.
Knopoff's most famous paper is one he published with Robert Burridge, in 1967, on "Model and Theoretical Seismicity." They constructed one-dimensional models of earthquakes using masses, attached to springs, that slid on a frictional substrate, the so-called "slider model," to serve as a basis for earthquake simulations. These devices, operated physically or simulated with a computer, reproduced the earthquake statistics known at the time.
For example, it was known that the plot of the logarithm of the number of shocks above a given magnitude versus magnitude fell on a straight line of negative slope b=1, which is known as the Gutenberg-Richter relation. Also, the frequency of aftershocks decayed in time as 1/time, which is known as the Omori Law. Knopoff and Burridge showed that aftershocks relied on processes involving time delays, which they synthesized using viscous elements. They found that the unloaded system generated small shocks while being loaded to a critical energy, above which large shocks were generated. After reaching the critical point, the resulting shocks were clustered in time, with aftershocks generating aftershocks, rather than following a random Poisson process. The shocks obeyed the Gutenberg-Richter and Omori relations. They showed that radiated seismic energy was a small fraction (12 percent) of the change in potential energy of an event – that is, seismic efficiency is low. All these effects, seen in modern catalogs, were generated by the simplest model, which captured the essential physics. The paper was later regarded as one of the most important models in condensed-matter physics, a subject that was not developed until more than a decade later.
Following this paper, Knopoff continued his concerted effort to understand statistical seismology, which earned him the title, "the father of statistical seismology."
Earthquake prediction has had mixed success. Early results, usually based on precursors recognized in hindsight, seemed very promising, but with time it has become apparent that prediction in a narrow four-dimensional box of space and time (kilometers and days) remains elusive. However, statistically-based forecasting in broad regions (hundreds of kilometers and years) has had more success, at least in a statistical sense.
Knopoff and his collaborators established how rigorous statistical testing of prediction claims could put them in perspective. He collaborated on the project first with Robert Burridge, then with John Gardner, Yan Kagan, and later with Didier Sornette. One of his 1974 papers with Gardner on earthquake catalog declustering is still widely cited. In the mid-1970s he collaborated with Yan Kagan on statistical analysis of earthquake catalogs and stochastic models of earthquake occurrence. They worked on the development of a comprehensive theory of earthquakes, including sudden increases in precursory seismicity, aftershocks, and foreshocks. He and Kagan established the statistical validity of the inverse 1/t Omori law for foreshocks. Among problems investigated were earthquake size distribution; dependence of earthquake inter-relationship on size, depth range, and temporal intervals; fractal features of earthquake spatial and temporal distribution; and quantitative studies of earthquake focal mechanisms.
Knopoff and Kagan were the first to employ the results of statistical analysis to numerically forecast the probability of earthquake occurrence in time and space, and to evaluate quantitatively the forecast skill. They developed the first clustering models of earthquakes based on first principles, including stochastic branching, clustering, irregularity, triggering, and scale invariance (Kagan and Knopoff, 1981) predating the highly successful Epidemic Type Aftershock Sequence model, published by Ogata in 1988, that is being used today in operational forecasting of aftershocks.
As his career developed, Knopoff became interested in applications of complexity theory to different disciplines:
How does one assemble small building blocks into large structures that have pattern ... Earthquakes are an example as small earthquakes organize into a large one. Music is another. Notes are organized into a symphony, and different composers, Beethoven and Mozart for example, can be recognized from indefinable patterns that allow us to distinguish jazz from classical or oriental music. In the same way, letters or words are organized into language whose patterns distinguish French from English, Spanish from Russian. It is not quantitative. The brain does not analyze letters individually, or consonants and syllables. It makes an abstraction, and even if you do not know the meaning of the French or Russian, you can recognize it as French by the music. (KOH)
As well as elucidating the phenomena of self-organization and chaotic behavior in seismic systems, he pioneered pattern recognition in musicology and literature. For example, he characterized authors or composers by repeatable patterns. He recognized the following: "In all phenomena long-range correlation plays a vital role in its self-organization, and hence nearest-neighbor structural analysis, such as through Markov process analysis, is not justified. In the area of musical structure, these problems are even more intricate because several sensory detectors (of tonal duration, pitch and loudness) are all in interactive play simultaneously." (KOH)
At the time Knopoff recorded these thoughts, the new field of condensed matter physics was being developed. Per Bak had coined the term "self-organized criticality" (SOC) to describe an unstable sand pile, and Benoit Mandelbrot coined the terms "fractal" and "fractal dimension" to describe rough structures that appear in nature, such as coastlines, clouds, and It was recognized that because the laws of physics and chemistry have no intrinsic scale, these dynamics and structures exhibited scale invariance. For physicists who had been approximating nature with simple geometries such as cylinders, spheres, and blocks, these were new and exciting developments.
Knopoff knew Mandelbrot from their days as students at Caltech. The Burridge-Knopoff model of a decade earlier became the case-example of condensed matter physics applied to earthquakes. The b value of Gutenberg and Richter was interpreted as the fractal dimension, resulting from the non-linearity of friction effects and the scale invariance of the fracture process; while the attainment of critical energy for large events was interpreted as a self-organized critical state. In the early 1980s, Mandelbrot became aware of the work of Burridge and Knopoff, as well as the work of Kagan and Knopoff that was being extended by Jean Carlson and Jim Langer at the Institute of Theoretical Physics at the University of California, Santa Barbara. exchange visits took place. As a result, in the second edition of his book,
The Fractal Geometry of Nature, Mandelbrot included a section on earthquakes.
At first, Knopoff enjoyed these developments in modern physics and the recasting of his approach into the modern vernacular. The statistical analysis of earthquakes was interpreted to imply that fault zones were in a state of self-organized criticality. But this concept led to
the conclusion, by some, that earthquakes were intrinsically unpredictable. If a seismic zone was always on the point of criticality, long- and short-range interactions were equally probable. There was no chance of seeing precursors associated with a subcritical-to-critical transition, nor of identifying localized changes in geophysical measurements.
Knopoff found this view too pessimistic and based on an idea that may, or may not, apply. In the latter part of his career he became disenchanted with the SOC description, feeling the model had been pushed too far and had removed the incentive to look for precursors.
First of all, he argued, catalogs are dominated by aftershocks, which are small and not affected by boundaries, and so the scale invariance and SOC may be more apparent than real. The Earth is not an infinite system for which self-organized criticality applies at all scales. The Earth is scale-limited, in which finite dimensions, such as the depth of the seismogenic zone or the damage zone about faults, break the scale. He contended that catalogs, with aftershocks removed, do not exhibit scale invariance. He had established that earthquakes were not random events, but occurred in clusters, and that, were we to understand the physics better, earthquake forecasting should be possible, if not prediction itself. The work was left unfinished, but the structures Knopoff set in place leave room to hope for future success in this critical area.
INVOLVEMENT WITH MUSIC
By the time Knopoff returned to UCLA from Miami, he was already interested in music as the organization of sound into language according to patterns. This interest was formalized when he became part of the Institute of Ethnomusicology, created at UCLA in 1961, with Mantle Hood as its director and senior faculty who included Charles Seeger and William Hutchinson of the Music Department.
Knopoff and Hutchinson taught a course called "Seminar in the Acoustics of Music."
Knopoff said that he thought of acoustics in an unusual way; in the course, he and the students looked into the psychological perception of music and how a culture organizes the available sound into language. This was also the focus of papers he wrote with Hutchinson.
A Caltech friend of Knopoff's later became a part-time music critic for a Pasadena newspaper. On occasion, from the mid to late 1950s, he would ask Knopoff, who was then at UCLA, to substitute for him at a concert. Knopoff's concert reviews displayed deep knowledge of music and performance. At UCLA, after meeting physics professor David Saxon (a lifelong friend and later University of California president), he started going to the Saxon home for evening gatherings of a group that played baroque chamber music. Saxon played recorder while Knopoff played Saxon's harpsichord.
During the year that Knopoff spent at Caltech (1962–1963), he met a technician at the Seismological laboratory whose hobby was making harpsichords and other baroque-style instruments, and Knopoff bought a harpsichord from him. After that, for many years Knopoff hosted chamber music evenings at his home for a group that varied in size from a half dozen to a dozen musicians, who played violin, cello, flute or recorder, and occasionally viola or oboe. They met once or twice a month, occasionally at the home of one of the violinists, where Knopoff played piano (there being no harpsichord), and they met the rest of the time at his house, where he played his harpsichord. In later years, when the larger group no longer met, Knopoff continued for years to play every couple of weeks with two of the violinists, usually on the piano, alternating between his home and the home of one of the violinists.
Knopoff also played four-hand piano music regularly for many years with William Hutchinson. Knopoff had an extensive collection of four-hand piano music, much of which had belonged to Beno Gutenberg – a Caltech seismologist and colleague – and was given to him by Gutenberg's widow, Hertha, after Gutenberg's death. While traveling, Knopoff took the opportunity, when he could, to play the piano, for example with a chamber music group of academics in Washington, DC, or four-hand piano with Bertha Swirles, Lady Jeffreys (Sir Harold Jeffreys' wife), in Cambridge, England.
TEACHING AND HIS PERSONALITY
Knopoff was a gifted teacher, extremely generous with his time, with an infectious excitement in describing science. He won the UCLA Physics teaching award four times for teaching undergraduates. He graduated thirty-eight graduate students. Visitors traveled from all over the world to study in his laboratory, including thirty-nine post-doctoral scholars, as well as other senior scientists. Students and visitors alike benefited from his extraordinary ability to teach complexity in the simplest of terms, with animation but patience to impart understanding.
He often used his sense of humor to emphasize a point. His famous paper, which has the briefest of titles, "Q," describes in detail the attenuation of elastic waves in the laboratory and in the earth, and then provides thorough theoretical analysis of several mechanisms that might explain such attenuation. Published in 1964, "Q" continues to be widely quoted. In contrast, he published with John Gardner a paper that has the remarkably long title, "Is the sequence of earthquakes in Southern California, with aftershocks removed, Poissonian?" followed by the shortest abstract, "Yes."
In avant-garde musical composition, during 1974 he copyrighted his own version of Mahler's "Das Lied von der Erde" in two (earth) movements, composed with a computer. The first movement was based on seismicity from the 1952 Kern County earthquake, while the second was an accelerated digital recording of the normal modes of the Earth.
Extremely dedicated to his academic institution, Knopoff and his wife, Joanne, created in 2001 an important endowment in UCLA's College of letters and Science. The Leon and Joanne VC Knopoff Chair in Physics and Geophysics was the first chair in the basic sciences to be endowed by a faculty member during the Campaign UCLA fundraising effort. This endowed chair supports the research of a promising young scientist in solid-Earth geophysics, encouraging research that will help us better understand patterns in complex systems and solid-earth geophysics.
A story from Knopoff's remote travels in the seventies illustrates his generosity of spirit. He was hiking in the mountains of Tajikistan with a Russian colleague when he came across a group of shepherds, and through an interpreter he engaged them in conversation. Having established he was an American, he asked if he could take their picture. They agreed and asked, when he returned to America, if he would send them a print. When it came time to write down an address, he found that the lead of his pencil was broken, and so he pulled out his pocketknife to sharpen it. They expressed amazement, having never seen a folding knife before. So, he gave it to them as a gift.
After much consultation, as was their custom, they insisted on giving him a return gift and asked, "How about a sheep?" Knopoff recounted that he was, at this point, ten miles up a trail from the automobile, a small plane ride from Dushanbe, a further plane ride from Moscow, and that a sheep would be more trouble than its worth. So, they compromised: the shepherds started a fire and they all had a meal of mutton soup and bread. This example typifies the warm and generous man Knopoff was, someone who gave more than he got, whether it be while instructing students, interacting with shepherds or visitors, or imparting his generosity to his family who, with him, endowed the university with their personal wealth. His friends and colleagues knew him as a man of integrity, brilliance, humor, generosity, kindness, and modesty. ever ready with a broad smile and a hearty laugh, he possessed an enormous sense of fun and adventure.
Knopoff was an extraordinary human being and a gift to all who knew him. He is survived by his wife Joanne and his children Katie, Rachel, and Michael, as well as a grandson.
The authors gratefully acknowledge comments by Joanne Knopoff and the UClA Center for Oral History Research for use of material from a forthcoming oral history interview of Leon Knopoff coducted by William Van Benschoten in August and September 2003.
L E O N K N O P O F F ____________________________________________________________________________________________________________
