The Wolf ramp: Reflection characteristics of a transition layer

The modern use of spectral decomposition has shown that reflection events in practice are always frequency dependent, a phenomenon called reflectivity dispersion. Often, this can be attributed to strong interference effects from neighboring reflection coefficients of the classical type (i.e., parameter discontinuities or jumps). However, an intrinsic frequency dependence from a single layer is possible if the contact is not a jump discontinuity but a gradual transition. We have expanded the normal-incidence theory of a linear velocity transition zone (termed a Wolf ramp) and have shown how it leads to frequency-dependent reflectivity. The development of waveform forward modeling in turn has led to a ramp detection method that we have tested on migrated field data.