Head waves – also called refraction arrivals, lateral waves,

or conical waves – have been used extensively in near-earthquake studies,

geophysical prospecting, and deep-crustal seismological investigations. In the past,

research was confined largely to the kinematic characteristics of the waves, but

emphasis is now being given to the dynamic characteristics: amplitudes, spectra, and

wave forms. In the last fifteen years, several new mathematical and computational

techniques have been developed to study these waves.

This is an advanced,

technical book presenting a consistent theory of head waves, using methods developed

in the famous Leningrad school under G.I. Petrashen and his colleagues. It proceeds

from a consideration of the simplest problem of one interface to a study of the

situation in which there are many interfaces (some of which may not be plane or

parallel to one another) and the material between the interfaces is not necessarily

homogenous. The method is used principally, though not exclusively, that of ray

series in which the displacement vector is expressed in terms of an asymptotic

series in inverse powers of frequency. The volume includes numerical data and an

extensive bibliography.

This book is intended as a text for graduate and

senior undergraduate students in geophysics, and as a reference work for practising

seismologists and research workers.