Seismic waves generated by earthquakes have been interpreted to provide us information about the Earth's structure across a variety of scales. For short periods less than 1 second, the envelope of seismograms changes significantly with increased travel distance and coda waves are excited by scattering due to randomly distributed heterogeneities in the Earth. Deterministic structures such as horizontally uniform velocity layer models in traditional seismology cannot explain these phenomena. This book focuses on the Earth heterogeneity and scattering effects on seismic waves. Topics covered in this book are recent developments in wave theory and observation including: coda wave analysis for mapping medium heterogeneity and monitoring temporal variation of physical properties, radiation of short-period seismic waves from an earthquake fault, weak localization of seismic waves, attenuation of seismic waves in randomly porous media, synthesis of seismic wave envelopes in short periods, laboratory investigations of ultrasonic wave propagation in rock samples. This title also covers: understanding new methods for the analysis of short-period seismic waves to characterize the random heterogeneity of the Earth on many scales; observations of seismic wave scattering; discussion of techniques for mapping medium heterogeneity and for monitoring temporal change in medium characteristics; and, up-to-date techniques for the synthesis of wave envelopes in random media.