When ringing derivatives are used in seismic modeling, migration, and other wave propagation problems in heterogeneous media, they interact with boundaries of blocks or layers of different physical properties, generating noncausal and nonphysical waves. These spurious waves can be as strong as reflected or converted waves and other legitimate physical events, leading to errors and misinterpretations. Therefore, compact (i.e., short and nonringing) derivatives should be used.

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