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Taking velocity to be a rough (bumpy) function of depth, different offset traces might be fundamentally different thus providing different information (i.e. more information hence potentially more bandwidth). The bumpy velocity model seems artificial since it requires to be known a rough velocity as a function depth. Never-the-less, the idea could be helpful because we sometimes have well logs, or we might later learn how to bootstrap our velocity estimate from a smooth velocity to a rougher one.

Many people think about rough impedance. Here we consider a rough interval velocity.