Extremum criteria for optimal suppression of coherent noise in seismic data using the Karhunen–Loève transform

We present a method for suppressing the ground roll that combines the Karhunen–Loève (KL) transform with optimization procedures based on thermodynamic-like extremum criteria. The region in the seismic record where the ground roll is located is first mapped onto a horizontal rectangular region, which is decomposed with the KL transform, with the first few KL modes being removed to extract the coherent noise. Extremum criteria are then used to identify the best region to be processed by the KL filter, thus allowing the filtering to be performed in an automated manner.