Offset dependent amplitudes: Fault curvature effects and dip move-out corrections

Equations have been presented previously which predict that reflector curvature can affect significantly seismic reflection amplitudes at both zero and nonzero source-receiver offsets. Here the fact that faults are generally concave-upward is used to examine the curvature effect for compaction-driven faults which the sediments have both exponential and logarithmic porosity decreases with increasing depth.The curvature effect is generally larger over upwardly concave reflectors 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 concave-upward reflector, 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 variation of 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.