Seismic propagation studies made in the Delaware Basin of West Texas by the Field Research Laboratories of the Magnolia Petroleum Company have disclosed several unusual kinds of traveling waves. The near-surface zone in this area is characterized by alternating high- and low-velocity layers, with a thin high-velocity cap. Physical characteristics of the recorded waves have been correlated with this layering.Five types of waves have been identified: 1) Waves refracted along the tops of high-speed near-surface markers which have been multiply reflected, at the critical angle, between the marker beds and interfaces nearer the surface. 2) Shear waves refracted at shear velocity along a competent bed several hundred feet deep. 3) Compressional waves propagated by normal-mode transmission in the wave guide formed by a low-speed layer situated between two high-speed layers. 4) A single-cycle, apparently non-dispersive Rayleigh wave propagated in a thin limestone surface layer and in an underlying low-speed layer of sand and gravel. 5) An inversely dispersive Rayleigh wave train in which the group velocity appears to decrease with increasing wave length; this type of dispersion, just the opposite of the kind ordinarily recorded, is attributed to the fact that the low-speed surface layer is unusually thick compared with the wave length corresponding to the cut-off frequency of the instrumental system.