Until recently, the interpretation of data obtained in seismic exploration has been based on comparatively simple representations of the Earth. The most commonly used representation for the Earthhas been a set of thick layers, each characterized by a single value for the propa- gation speed of seismic waves. During the last several years, more complicated representa- tions in the form of thin layers with vertical velocity gradients, as weIl as homogeneous thin layers have been considered. New methods for studying propagation speeds in a medium, particularly ultrasonic logging methods, and the...