Peter Hubral’s extension of the raypath migration calculator program to include a lateral velocity gradient is quite ingenious. In such cases where the vertical and horizontal velocity gradients are constant, the net effect is a simple coordinate rotation. The theoretical raypath remains circular, but is only rotated about its intersection with the datum plane.
Abstract
Rayleigh wave dispersion data on Australia by Bolt and Niazi (1964) and Thomas (1969) are examined in detail in the period range of 20 to 40 sec. The dispersion characteristics correspond well to region 7 in Santô's (1965) classification. A further and similar inspection of the African mass, Brazilian shield, Canadian shield etc. reveals that the entire family of shield areas systematically belongs to Santô's regions 6 and/or 7. They are uniformly characterized by the absence of appreciable lateral velocity gradients in clear contrast to corresponding extremely steep gradients for high seismicity areas.
An algorithm for three‐dimensional wave equation migration in the presence of lateral velocity gradients is developed. The algorithm is based geophysically on the exploding reflector model and mathematically on integral solutions to the scalar wave equation. In addition, the velocity is assumed to vary slowly over a seismic wavelength. The primary application of the algorithm is to stacked sections. However, if the velocity is a function of depth only, the algorithm may be used to migrate and/or image common‐depth‐point gathers.
Instability of shallow open channel flow with lateral velocity gradients