Functions that are rough in the frequency domain will be long in the time domain. This suggests making a short function in the time domain by local smoothing in the frequency domain. Let the notation denote smoothing by local averaging. With longer filters we use numerical methods. Corrections need to be made for hyperbolic traveltime resulting from lateral separation between shot and receiver.
Diffractions are a result of lateral imperfections in the generally flat sea floor.
We will investigate them here in only a limited way.