Discontinuity attribute, seismic reflector picking, interpolation of seismic data, and the assessment of image quality all require a mathematical model of seismic data. A successful model for one application might work for other applications. For example, I derived the discontinuity attribute that is based on the best-fitting plane wave from a dip-picking scheme by Claerbout 1992. Before using prediction error to detect faults, I 1995 used it to interpret seismic data. Claerbout applies a similar prediction error approach to detect lapses in data quality.
Over the years, I painfully learned, however, that the characterization of seismic data greatly varies among its domains, prestack and image domain as well as two-dimensional and three-dimensional domain. A method that works in one domain does not necessarily succeeds in another. For example, prediction-error filters interpolate the superposed plane waves of prestack data, but fail to remove the adjacent plane waves separated by a fault. Wavelet compression succeeds in the high-dimensional, redundant prestack domain but fails for two-dimensional seismic images.