The DSR operator defined by (14) is fun to think about, but it doesn't really go to any very popular place very easily. There is a serious problem with it. It is not separable into a sum of an offset operator and a midpoint operator. Nonseparable means that a Taylor series for (14) contains terms like .Such terms cannot be expressed as a function of Y plus a function of H. Nonseparability is a data-processing disaster. It implies that migration and stacking must be done simultaneously, not sequentially. The only way to recover pure separability would be to return to the space of S and G.
This chapter tells us that lateral velocity variation is very important. Where the velocity is known, we have the DSR equation in shot-geophone space to use for migration. A popular test data set is called the Marmousi data set. The DSR equation is particularly popular with it because with synthetic data, the velocity really is known. Estimating velocity v(x,z) with real data is a more difficult task, one that is only crudely handled by by methods in this book. In fact, it is not easily done by the even best of current industrial practice.