To the interpreting geologist, lateral velocity variation produces a strange distortion in the seismic section. And the distortion is worse than it looks. The geophysicist is faced with the challenge of trying to deal with lateral velocity variation in a quantitative manner. First, how can reliable estimates of the amount of lateral velocity variation be arrived at? Then, do we dare use these estimates for reprocessing data?
Our studies of dip and offset have resulted in straightforward procedures to handle them, even when they are simultaneously present. Unfortunately, increasing lateral velocity variation leads to increasing confusion--confusion we must try to overcome. Strong lateral velocity variation overlies the largest oil field in North America, Prudhoe Bay. Luckily, however, we have many idealized examples that are easy to understand. Any ``ultimate'' theory would have to explain these examples as limiting cases.
Let us review. The double-square-root equation presumably works if the square roots are expanded and if we accept the usual limitation of accuracy with angle. Our problem with the DSR is that it merely tells us how to migrate and stack once the velocity is known. Kjartansson's method of determining the distribution of (some function of) v(x,z) assumes straight rays, no dip, and a single, planar reflector. On the other hand, stacking along with prestack partial migration allows any scattering geometry but enables determination of v(z) only under the presumption that there is no lateral variation of velocity. Clearly, there are many gaps. We begin with comprehensible, special cases but ultimately sink into a sea of confusion.