IntroductionDuring the December 2004 annual meeting of the American Geophysical Union(AGU), Professor Keitii (Kei) Aki was awarded the Bowie Medal, which is thehighest honor bestowed annually by the AGU. To celebrate this occasion, a scientificsymposium in honor of Kei was organized by Yehuda Ben-Z ion, Eystein Husebye,John McRaney, Haruo Sato, and Willie Lee under the title ‘‘QuantitativeSeismology: Advances in Studies of Fine-scale Heterogeneities in a DeformingEarth’’. Since Kei studied (and was instrumental in developing) most aspects ofquantitative seismology, including source, propagation and site effects over the entirerange of observed frequencies, it was difficult to pick a subset of topics that wouldform a reasonably focused scientific session. The title was finally chosen to reflect aset of pro blems that was central to Kei’s interests, while having a somewhat differentfocus than those of two earlier 2000 symposia that commemorated Kei’s retirementsfrom academia.The description of the 2004 AGU session in honor of Aki is as follows: In the past25 years, there have been tremendous advances in many aspects of quantitative seismologyusing physics-based approaches. New fronts were made possible by many factors: Largedata sets with unprecedented resolution and bandwidth; innovative computationaltechniques; new theoretical models for seismic phenomena; and integrative researchaccounting for broad ranges of space and time scales. These advances were stimulated bymany pioneering papers, and were aided strongly by the publication of the two-volumetreatise ‘‘Quantitative Seismology: Theory and Methods’’ by Keiiti Aki and PaulRichards in 1980. This session will focus on integrative physics-based seismologicalstudies, with an emphasis on the nature of fine-scale he terogeneities and earthquakes.Contributions from theory, observations, and applications are welcome. The citation forthe Bowie medal (Appendix 1) was given by Tom Jordan.In contrast to the two earlier 2000 symposia honoring Kei Aki, which had onlyinvited participants, the 2004 AGU meeting provided a venue that allowed anyonewho wished to contribute or attend to do so. The special AGU session and a relatedfollow-up banquet wer e highly successful, both in terms of covering current state-of-the-art research results and celebrating lasting fundamental contributions of Kei Aki.The scientific session received an overwhelming response of 85 contributions. Thesewere given over four oral sessions which included an opening speech by PaulRichards (Appendix 2), an introduction and response by Kei at the beginning an d theend of the oral sessions (Appendix 3), and 27 papers. The remaining 58 papers werepresented in a poster session. Many participants wrote ‘‘tributes’’ to Kei, some ofPure appl. geophys. 163 (2006) 259–2660033–4553/06/030259–8DOI 10.1007/s00024-005-0029-3Ó Birkha¨user Verlag, Basel, 2006Pure and Applied Geophysicswhich were read at the banquet. The tributes provide interesting windows intoaspects of Kei’s personal and scientific interactions with students and colleagues andare posted at http://www.iris.edu/seismo/quakes/1964niigata/.The present volume has 13 papers on topics related to the theme of the special 2004AGU session in honor of Kei, which is a small fract ion of the 85 presentations thatwere given in the meeting. The papers belong generally to three broad categories:Studies related to dynamic earthquake rupture, studies associated with imaging ofearthquake locations and structures using coherent (P and S) seismic phases, andstudies associated with imaging source and structure properties using scattered (coda)seismic waves. In the first group of papers, CHEN and ZHANG provide analytical andnumerical results on dynamic rupture along a dipping fault in a 3-D elastic half space,using a recently-developed boundary integral formulation that accounts for the freesurface and numerical regularization of the associated singular integral kernels. Thecalculations show that waves reflected from the surface can affect signi ficantly therupture growth, especially at shallow depth. A resolution test suggests that the methodprovides accurate results with larger grid size than is required by some othercomputational methods of dynamic rupture. DOR et al. present detailed geologicalmapping of rock damage in the structure of several faults of the San Andreas system insouthern California. The results show strong damage asymmetry across the faults thatis correlated with available information on seismic velocity structures at seismogenicdepth. The observations are compatible with theoretical resul ts on dynamic rupturealong mate rial interfaces in the fault zone structures, with preferred propagationdirection associated with the velocity structure.In the second group of papers, RICHARDS et al. outline the double-differencetechnique for relative earthquake locations, using arrival-time data obtained bywaveform cross correlations and catalog phase picks, and illustrate the method withapplications to regions with different size and different density of seismicity andstations. They conclude that the double-difference method and accurate arrival-timedata obtained by waveform cross correlations can improve considerably the precisionof relative locations, and that routine application of the double-difference andwaveform cross correlation techniques is now possible at local and regional scales.ZHANG and THURBER review a recently-developed double-difference tomographymethod for simultaneous derivation of earthquake locations and velocity structure,based on a mixture of absolute and more accurate differential arrival times. Thematerial includes theory, implementations, and applications of the method to syntheticand observed data at several scales. The results indicate that double-differencetomography provides generally more accurate results than standard tomography. GOTet al. review an alternative treatment of double-difference tomography that incorpo-rates probabilist ic optimization of results, and discuss effects of various errors in dataand model parameters. Application of the method to the structure of the Kilaueavolcano in Hawaii resolves internal velocity variations, and comparison to results ofseveral other algorithms suggests that the approach is advantageous for imaging260 Yehuda Ben-Zion and William H. K. Lee Pure appl. geophys.,heterogeneous structures, especially