Near-Surface Seismology: Wave Propagation

This chapter serves as an introduction to seismic wave propagation for those waves commonly observed in near-surface seismology. A reasonably detailed description is provided for linearly elastic and linearly viscoelastic constitutive models. Dissipation of energy is systematically developed with careful definition of the relationships between energy loss, complex moduli, and the quality factor. The discussion of wave propagation is mostly about plane body waves (viscoelastic case) and plane surface waves (elastic case) in homogeneous (or vertically heterogeneous) isotropic media. The discussion also includes a simple model for head waves, the reflection of plane body waves from a plane interface between homogeneous and isotropic elastic media, and a description of geometric spreading, the radiation pattern, and the near field associated with a point source in an unbounded elastic medium. The appendices contains a significant amount of related information including an introduction to linear system theory, Fourier integral transforms and the convolution theorem, a discussion of the principles that underlie linear viscoelasticity in the general heterogeneous and anistropic case, and details for many of the computations