AKI, KEIITI

(b. Yokohama, Japan, 3 March 1930; d. La Plaine des Cafres, La Réunion, France, 17 May 2005),

seismology.

Aki was a pioneer in almost all fields of seismology. He established scaling laws for a broad range of phenomena in seismology and seismotectonics. He initiated new seismological analyses of earthquake sources and the structure and dynamics of the Earth. Linking geodynamic models and nonlinear dynamics models, he greatly furthered predictive understanding of earthquakes. His leadership in developing new research programs in seismology and his vision for integrating seismological research has been felt around the world. Aki was the “dean of the world’s seismologists,” in the words of Frank Press given at a party honoring Keiiti Aki in 2004.

Keiiti Aki, known as Kei, was born on 3 March 1930 in Yokohama, Japan, to a family of engineers with a hundred-year tradition of education and openness to the West. When Aki was nineteen years old, he was among the twelve students admitted to the Geophysics Department of Tokyo University. There he was taught by world-class professors, including Chuji Tsuboi, Takeshi Nagata, Takeo Matuzawa, and Koji Hidaka, and obtained his BSc and PhD degrees in geophysics in 1952 and 1958, respectively.

From 1952 to 1966 Aki was mostly at Tokyo University, though he also visited the California Institute of Technology as a research fellow. In 1966 Frank Press recruited Aki to the United States to join the faculty of the Massachusetts Institute of Technology (MIT) as a professor of geophysics. Aki became a mentor to a large number of graduate and postdoctoral students. He also spent summers working with colleagues all over the world. Thinking that students should get their hands dirty with seismic data, Aki sent many of his students to the United States Geological Survey in Menlo Park in the summers, and Aki himself also visited frequently. To be close to California earthquakes, Aki in 1984 moved to the University of Southern California, where he became that university’s first W. M. Keck Foundation Professor of Geophysics. He was responsible for establishing the Southern California Earthquake Center, where his vision for integrated research on earthquakes has been practiced by scientists and engineers in many disciplines working together.

In 1995 Aki moved to La Réunion (a French island in the Indian Ocean) so that he could study its volcano firsthand. After making excellent progress in predicting volcanic eruptions, Aki returned to the problem of earthquake prediction and wrote a book-length manuscript on it in 2004. During the last five years of his life, Aki lectured annually in Japan as an advisor to the Japanese Association for the Development of Earthquake Prediction. His last project was promoting the Coda Club for collaborative research on using coda waves, which make up the late part of seismic signals, to predict earthquakes worldwide.

Aki died from a brain hemorrhage on 17 May 2005 at La Réunion, following an accidental fall. Aki had four children: sons Shota of Weare, New Hampshire, and Zenta of Redondo Beach, California, from his marriage to Haruko Uyeda; and daughters Kajika and Uka of La Réunion, with Valerie Ferrazzini.

Aki’s Own View of His Work. In 2004 Kei Aki was awarded the Bowie Medal, the highest honor bestowed annually by the American Geophysical Union. At the scientific symposium celebrating this honor, Aki, in a speech introducing the symposium, presented a brief summary of his work, a summary that started and ended with earthquake prediction. He said that his first paper in 1954 employed a statistical approach and was motivated by Norbert Wiener’s Cybernetics, published in 1948. After applying Wienerc’s prediction method to earthquake-catalog data (a list of origin time, hypocenter, and magnitude of earthquakes), Aki realized that the data then available were poor and that Wiener’s method for a stationary linear system was too simplistic to model the physics of earthquakes. Turning to a physical approach, Aki followed two paths: deterministic modeling and stochastic modeling. The deterministic approach required simple models of earth structures and earthquake processes and was only possible for long-period waves, which averaged the

complex details of structures and processes. This research started out as long-period seismology, producing useful concepts such as the seismic moment, and has grown to broad-band seismology, in which the upper limit of the applicable frequency range has been steadily extended. The stochastic-modeling approach accepts the existence of small-scale heterogeneities and tries to determine their statistical properties. While this approach cannot delimit heterogeneities in time and space, it can demonstrate their existence. Aki used this approach to study many aspects of short-period seismology.

After a career of fifty years in deterministic and stochastic modeling, Aki sought to encourage others to take a multipronged approach toward the goal of earthquake prediction. Aki took the general position that one’s success in predicting a phenomenon was a measure of how well one understands it. If one can successfully predict a natural phenomenon such as earthquakes, then mitigating its hazards and saving lives becomes effective and practical.

Contributions to Seismology. Aki said that his main contribution to seismology was to have “developed a variety of interpretation methods of seismological data for delineating earth structures and dynamic processes in tectonically active regions.” Realizing the inadequacy of earthquake-catalog data available in 1954 (consisting mostly of data from earthquakes with magnitude greater than 5), Aki proposed monitoring the more numerous micro-earthquakes (those with magnitude less than 3) as an important element in earthquake-prediction research. The frequency distribution of earthquakes occurring in a given area and time interval had been established by Beno Gutenberg and Charles Richter in the 1940s:

log N (M) = a –bM

where M is the earthquake magnitude, N(M) is the number of earthquakes with magnitude greater than or equal to M, and a and b are constants. Because the value of b is about 1, magnitude 2 earthquakes are about 1,000 times more frequent than magnitude 5 earthquakes. Aki’s idea was subsequently incorporated into the Japanese program for earthquake prediction in the early 1960s, and hundreds of micro-earthquake networks (consisting of many closely spaced and highly sensitive seismometers), which followed the Japanese program, were established around the world. The vast amounts of data from these micro-earthquake networks led to numerous advances in seismology, many of them pioneered by Aki and his students and colleagues.

Earthquake Sources . Aki’s contributions to seismology cover source, path, and site effects over the entire frequency range of seismic waves. In 1966 Aki introduced the concept of seismic moment, which quantifies earthquake size on a physical basis. This was the most significant advance since earthquake magnitude scales were introduced by Charles Richter and Beno Gutenberg in the 1930s as an empirical basis for the earthquake size. Aki realized that because a double-couple earthquake source is equivalent to a fault slip in an isotropic elastic body, the scalar value of its component is equal to the shear modulus times the fault slip integrated over the fault plane:

M₀ = shear modulus × average slip ×slipped area

The seismic moment can be estimated from the far-field seismic spectrum, and also from the average slip and the area of the slipped surface inferred from the near-field seismic, geologic, and geodetic data. Aki demonstrated the consistency of estimating seismic moments from two separate sets of data from the 1964 earthquake in Niigata, Japan.

In 1967 Aki discovered the fundamental scaling laws for seismic spectra of earthquakes and proceeded to interpret these laws in terms of physical models. He made the first calculation of the ground motion produced by an earthquake fault, independently from Norman Haskell, and he was able to infer the characteristics of slip on the fault.

In 1977 Aki introduced the barrier model of earthquakes and, with Shamita Das, made the first theoretical and numerical investigations of dynamic earthquake rupture on heterogeneous faults. In 1972 he and Yoshiaki Ida introduced the first seismological model of what later became known as slip weakening. In 1977 he and Michel Bouchon developed the discrete-wave-number method (which allowed the full calculation of strong ground motion for kinematic models of faulting). And in 1983 he and A. S. Papageorgiou proposed a specific barrier model for quantitatively describing inhomogeneous faulting and predicting strong ground motion.

Effects of Lateral Heterogeneities on Seismic Waves. In collaboration with some of his early students, Ken L. Larner and David M. Boore, in the late 1960s and early 1970s Aki developed powerful numerical methods for computing the response of realistic earth structures to seismic shaking. These methods were subsequently expanded on by others and applied to a number of important problems in engineering seismology. With these same students, in 1971 he published one of the first papers describing the effects of soft sedimentary basins on seismic waves, demonstrating that the basin response is dominated by surface waves scattered by wave conversion at the basin margins and showing that the motion in the center of a basin can be many times larger than that expected for flatlying layers.

Seismic Tomography from Travel Times. Realizing a dense seismic array recorded large amounts of data containing important information about the Earth, Aki pioneered travel-time tomography as a means of studying lithospheric structure beneath dense seismic arrays, and he and his collaborators published seminal papers almost a decade ahead of its widespread application to global seismology.

In the summer of 1974 Aki visited the Norwegian Seismic Array (NORSAR) at Kjeller, Norway. From his initial random-media studies, Aki expected that deterministic mapping of the Earth’s heterogeneities should be feasible. The NORSAR data were an inspiration in this regard: Changes in time and amplitude across the array were clearly visible in the records. Aki synthesized many diverse developments in inverse problems (see below) and array data to produce three-dimensional imaging through ray tracing of a block model of the lithosphere and asthenosphere. Anders Christoffersson and Eystein Husebye happily joined Aki in developing this concept of tomographic imaging into a research tool (the ACH method), and they used the P-travel-time residuals of the NORSAR data and the Large Aperture Seismic Array (LASA) data as a test.

At the fall meeting of the American Geophysical Union in San Francisco in 1974, Aki related the exciting work with the NORSAR data to William H. K. Lee. Aki and Lee realized that the inversion of arrival times of local earthquakes was unique (unlike the teleseismic inversion), because the studied volume of the Earth contained both the sources (earthquake hypocenters) and receivers (stations). Therefore, they could use arrival times of local earthquakes to calculate simultaneously both earthquake hypocenters and the velocity structure beneath the seismic network. Aki then spent the summer of 1975 with Lee at the U.S. Geological Survey in Menlo Park, and they completed the extension of the ACH method of teleseismic tomography to local earthquake tomography. Several of Aki’s students, notably Cliff Thurber, subsequently further advanced the ACH method. Since Aki and colleagues initiated its use in 1974–1975, seismic tomography has been further developed and/or applied by many seismologists all over the world. It has become the principal tool for mapping and understanding the structure of earth’s crust and mantle.

Coda and Scattering. Aki elucidated the scattering and attenuation processes that govern the propagation of high-frequency seismic waves. In his pioneering work in 1969, Aki interpreted coda waves of local earthquakes as waves scattered by randomly distributed heterogeneities in the lithosphere. In 1975 Aki and Bernard Chouet made the first attempt to predict the explicit form of the time-dependent power spectrum of coda waves for a mathematical model of earthquake source and earth medium. In 1980 Aki developed a method for normalizing coda on the basis of the uniform spatial distribution of coda energy.

Beginning in the 1980s, measurements of coda Q and scattering coefficients were made worldwide. Aki and his colleagues (Mike Fehler, Mitsuyuki Hoshiba, Haruo Sato, Ru-shan Wu, Yuehua Zeng) developed theoretical models for the synthesis of seismogram envelopes over short periods based on radiative transfer theory. Working principally with Anshu Jin, Aki also focused on spatiotemporal changes in coda Q. In his 2004 paper, Aki proposed using coda waves for monitoring temporal changes in parameters of the medium to predict earthquake occurrence and volcanic eruption.

Quantitative Seismology. In his original research Aki covered an extremely broad range of problems in seismology. His creativity in approaching topics at the forefront of seismology was based on his skill at devising new experiments and his superb mastery of the theoretical background. This creativity is best exemplified by his two-volume treatise Quantitative Seismology (1980), coauthored with Paul Richards. It has set the standard for teaching seismology and doing advanced research in the field since 1980 and has been the most frequently cited book in seismology since its publication. Even as of 2006 it is required reading for advanced classes in seismology and geophysics. A second edition appeared in 2002 and was translated into Japanese by Koji Uenishi, Nobuki Kame, and Hideo Aochi.

Fault-zone-guided Waves. In the 1990s Aki, with Yehuda Ben-Zion and Yong-gang Li, theoretically and observationally analyzed fault-zone-guided waves that result from constructive interference of critically reflected waves within low-velocity fault-zone layers. These waves can be used to obtain high-resolution information on the internal structure of fault zones, and have since been recorded and modeled in various fault zones around the world.

Volcanic Seismology. Aki also developed quantitative theory and methods for interpreting seismic signals originating from volcanoes. In 1977 Aki (with Mike Fehler and Shamita Das) proposed the first fluid-filled-crack model to explain the characteristics of volcanic tremors in Hawaii and introduced the seismic-moment rate to express the intensity of volcanic tremors at their source. In 1981 Aki and Bob Koyanagi applied this model to deep tremors at Kilauea Volcano and proposed that Kilauea receives a steady supply of magma from the mantle. Using a method of statistical analysis that Aki designed in 1957 for microseisms, Valerie Ferrazzini, Kei Aki, and Bernard Chouet in 1991 analyzed the wave field generated by the eruption of Pu‘u ‘O ‘o in Hawaii and showed that the shallow eruption tremors consist primarily of fundamet modes of Rayleigh and Love waves. Since then, this method has been used on numerous volcanoes. Aki and Valerie Ferrazzini in 2000 presented a model for predicting eruptions of the Piton de la Fournaise (La Réunion Island) by integrating geological, petrological, and seismic data (such as the occurrence, duration, and dominant frequency of long-period events).

Legacy. Aki published more than 200 papers (see “Publication List of Keiiti Aki,” compiled by Takashi Miyatake, in Ben-Zion and Lee, 2006), supervised more than fifty doctoral dissertations, and received many honors. Among those honors were election to the U.S. National Academy of Sciences (1979), the Medal of the Seismological Society of America (1986), the Thorarinsson Medal from the International Association of Volcanology and Chemistry of the Earth’s Interior (2000), the Bowie Medal of the American Geophysical Union (2004), and the Gutenberg Medal of the European Geosciences Union (2005).

Kei Aki will be remembered not only as a brilliant seismologist and teacher but also as a cheerful friend and colleague in collaborative research. Aki was optimistic and firmly believed that if people work together, any problem can be solved. Frank Press recognized that though Aki “could have been a leader of any scientific discipline he chose to engage in, Kei selected seismology for its humanitarian potential—or simply stated—for its promise (as yet only partially fulfilled) of saving lives and mitigating tragedy” (Tributes to Kei Aki, 2004).

BIBLIOGRAPHY

The 1964 Niigata Earthquake Archive at the IRIS Data Management Center (USA) was established in honor of Kei Aki in 2004 (available from http://www.iris.edu/seismo/quakes/1964niigata/). This archive serves as an online Web site for Aki, so that his many contributions and related materials can be posted for free access. The Web site includes a collection of personal tributes to Kei in 2004 and reveals aspects of Kei that are not captured in more formal publications. A list of these formal publications has been compiled by Takashi Miyatake, “Publication List of Keiiti Aki,” in Advances on Studies of Heterogeneities in the Earth’s Lithosphere, edited by Yehuda Ben-Zion and William H. K. Lee (Boston: Birkhäuser: 2006).

WORKS BY AKI

“Generation and Propagation of G Waves from the Niigata Earthquake of June 16, 1964, Part 2: Estimation of Earthquake Moment, Released Energy, and Stress-Strain Drop from the G Wave Spectrum.” Bulletin of Earthquake Research. Institute 44 (1966): 73–88.

“Scaling Law of Seismic Spectrum.” Journal of Geophysical Research 72 (1967): 1217–1231.

With David M. Boore and Ken L. Larner. “Comparison of Two Independent Methods for the Solution of Wave-Scattering Problems: Response of a Sedimentary Basin to Vertically Incident SH Waves.” Journal of Geophysical Research 76 (1971): 558–569.

With Yoshiaki Ida. “Seismic Source Time Function of Propagating Longitudinal Shear Cracks.” Journal of Geophysical Research77 (1972): 2034–2044.

With Bernard Chouet. “Origin of Coda Waves: Source,Attenuation, and Scattering Effects.” Journal of Geophysical Research80 (1975): 3322–3342.

With William H. K. Lee. “Determination of Three-Dimensional Velocity Anomalies under a Seismic Array using First P Arrival Times from Local Earthquakes, 1. A Homogeneous Initial Model.” Journal of Geophysical Research 81 (1976): 4381–4399.

With Michel Bouchon. “Near-Field of a Seismic Source in a Layered Medium with Irregular Interface.” Geophysical Journal of Royal Astronomical Society 50 (1977): 669–684.

With Anders Christoffersson and Eystein S. Husebye. “Determination of the Three-Dimensional Seismic Structure of the Lithosphere.” Journal of Geophysical Research 82 (1977): 277–296.

With Shamita Das. “Fault Plane with Barriers: A Versatile Earthquake Model.” Journal of Geophysical Research82 (1977): 565–570.

With Paul G. Richards. Quantitative Seismology: Theory and Methods. 2 vols. San Francisco: Freeman, 1980. 2nd ed., Sausalito: University of Science Books, 2002.

With Robert Koyanagi. “Deep Volcanic Tremor and Magma Ascent Mechanism under Kilauea, Hawaii.” Journal of Geophysical Research86 (1981): 7095–7109.

With Apostolos S. Papageorgiou. “A Specific Barrier Model for the Quantitative Description of Inhomogeneous Faulting and Prediction of Strong Ground Motion, Part I and II.” Bulletin, Seismological Society of America 73 (1983): 693–722, and 953–978.

With Valerie Ferrazzini and Bernard Chouet. “Characteristics of Seismic Waves Composing Hawaiian Volcanic Tremors and Gas-Piston Events Observed by a Near-Source Array.” Journal of Geophysical Research96 (1991): 6199–6214.

With Valerie Ferrazzini. “Seismic Monitoring and Modeling of an Active Volcano for Prediction.” Journal of Geophysical Research 105 (2000): 16,617–16,640.

“Synthesis of Earthquake Science Information and Its Public Transfer: A History of the Southern California Earthquake Center.” In International Handbook of Earthquake and Engineering Seismology, edited by William H. K. Lee, Hiroo Kanamori, Paul C. Jennings, and Carl Kisslinger, Part A. San Diego, CA: Academic Press, 2002.

“A New View of Earthquake and Volcano Precursors.” Earth Planetary Space 56, no. 8 (2004): 689–713.

OTHER SOURCES

Ben-Zion, Yehuda, ed. Seismic Motions, Lithospheric Structures, Earthquake and Volcanic Sources. Boston: Birkhäuser, 2003.

———,and William H. K. Lee, eds. Advances on Studies of Heterogeneities in the Earth’s Lithosphere. Boston: Birkhäuser, 2006.

Lee, William H. K., comp. “A Collection of Tributes to Kei Aki, December 16, 2004, San Francisco.” Available from http://www.iris.edu/seismo/quakes/1964niigata/ 2004.

Richards, Paul G. “In Memoriam—Keiiti Aki (1930–2005).”Seismological Research Letters 76 (2005): 551–553.

William H. K. Lee