We analyze the effect of reflector curvature on the angular dependence of reflection amplitude using ray theory. Defining the curvature effect, CE, as the ratio of reflected amplitude from a curved boundary to that from a flat boundary at the same depth, we obtain l/CE² = (1 + Z/a^X cos²θ) (1 + Z/a^y), where θ is the angle of incidence, Z the depth of the boundary, and a^x and a^y are the principal radii of curvature of the reflector in the plane of incidence and in the perpendicular plane respectively. At θ=0 this reduces to the formula given in reference 1. The angular dependence of CE involves only a^x, which appears to shorten at wider angles, causing an augmentation of the dimming effect of an anticlinal geometry at far offsets. For synclinal structures, the amplitude increases with offset when |Z/a^x | < 1 and decreases with offset when |Z/a^x | > 1.

In addition we examine the effects of wavefront curvature and of a layered overburden in modulating the curvature effect. There is a significant difference in the curvature effect between plane waves and spherical waves impacting on a curved boundary. Results are given showing simple examples of the effect of layered overburden in distorting the curvature effect of a horizontal, but curved, reflector and, more interestingly, of a dipping, but planar, bed.

The fact that faults are generally synclinal in character is used to examine the curvature effect for compaction-driven faults which have both exponential and logarithmic porosity decreases with increasing depth into the sediments.

The curvature effect is generally larger over synclines where amplitudes can either increase with offset (exposed focus) or decrease with offset (buried focus). The magnitude of the effect depends on the ratio between the depth to the structure and the radius of curvature of the structure. A phase change of 90° also occurs at a critical offset in the case of an exposed focus syncline, with decreasing amplitude at offsets larger than the critical value. Dip move-out (DMO) dominantly removes the amplitude variation with offset due to curvature. These results suggest that when looking for amplitude variations with offset in a fault prospect, DMO should be applied as a preprocessing step. Compaction-driven faults have an exposed focus and, for an exponential porosity with depth, there is a maximum curvature effect at a  depth roughly the same as the scaling depth for  the porosity. Logarithmic porosity with depth  variations suggest a continued increase in the  curvature effect of faults with increasing depth,  to a maximum amplitude increase of about 35%  relative to a plane interface.