Earthquake fault zones exhibit hierarchical damage and granular structures with evolving geometrical and material properties. Understanding how repeated brittle deformation form the structures and how the structures affect subsequent earthquakes is a rich problem involving coupling of various processes that operate over broad space and time scales. The diverse state-of-the-art papers collected here show how insight can come from many fields including statistical physics, structural geology and rock mechanics at large scales; elasticity, friction and nonlinear continuum mechanics at intermediate scales; and fracture mechanics, granular mechanics and surface physics at small scales. This volume will be useful to students and professional researchers from Earth Sciences, Material Sciences, Engineering, Physics and other disciplines, who are interested in the properties of natural fault zones and the processes that occur between and during earthquakes.

Considerable progress has been made recently in quantifying geometrical and physical properties of fault surfaces and adjacent fractured and granulated damage zones in active faulting environments. There has also been significant progress in developing rheologies and computational frameworks that can model the dynamics of fault zone processes. This volume provides state-of-the-art theoretical and observational results on the mechanics, structure and evolution of fault zones. Subjects discussed include damage rheologies, development of instabilities, fracture and friction, dynamic rupture experiments, and analyses of earthquake and fault zone data.

This second special issue is in honor of Keiiti Aki. It focuses on recent advances in quantifying and interpreting heterogeneities in lithosperic structures and earthquake behavior. The volume provides a combination of reviews, methodological studies and applications on topics related to Aki's pioneering contributions. The discussed subjects include research associated with dynamic earthquake rupture. It also includes material on Aki and a list of his publications.

Statistical Seismology aims to bridge the gap between physics-based and statistics-based models. This volume provides a combination of reviews, methodological studies, and applications, which point to promising efforts in this field. The volume will be useful to students and professional researchers alike, who are interested in using stochastic modeling for probing the nature of earthquake phenomena, as well as an essential ingredient for earthquake forecasting.

Geophysicists use seismic signals to image structures in the Earth's interior, to understand the mechanics of earthquake and volcanic sources, and to estimate their associated hazards. Keiiti Aki developed pioneering quantitative methods for extracting useful information from various portions of observed seismograms and applied these methods to many problems in the above fields. This volume honors Aki's contributions with review papers and results from recent applications by his former students and scientific associates pertaining to topics spawned by his work. Discussed subjects include analytical and numerical techniques for calculating dynamic rupture and radiated seismic waves, stochastic models used in engineering seismology, earthquake and volcanic source processes, seismic tomography, properties of lithospheric structures, analysis of scattered waves, and more. The volume will be useful to students and professional geophysicists alike.