Karhunen–Loève spectral analysis in multiresolution decomposition

In this work we develop a method for pinpointing the scales in a multiresolution decomposition where coherent structures appear. A sequence of images yielded from the wavelet multiresolution analysis of seismic signals are analyzed in the Karhunen–Loève ( KL ) space. Using KL decomposition we distinguish two coherent structures in the scale–images: the ground roll and the hyperbolic lines characteristic of geologic layers. Moreover, the KL spectrum also points out the high frequency noise. In this way the method allow us to split three energy mode regimes in the data and, as a consequence, to select the relevant geologic information. The method can be extended to other problems where coherent structures need to be recognized.