Multiscale seismic attributes: source‐corrected wavelet response and application to high‐resolution seismic data - Ker, Stephan; Le Gonidec, Yves; Gibert, Dominique (Geophysical journal international, 2012)
ABSTRACT A wavelet‐based method was presented in a previous work to introduce multiscale seismic attributes for high‐resolution seismic data. Because of the limited frequency bandwidth of the seismic source, we observed distortions in the seismic attributes based on the wavelet response of the subsurface discontinuities (Le Gonidec et al.). In this paper, we go further in the seismic source‐correction by considering Lévy alpha‐stable distributions introduced in the formalism of the continuous wavelet transform (CWT). The wavelets are Gaussian derivative functions (GDF), characterized by a derivative order. We show that a high‐resolution seismic source, after a classical signature processing, can be taken into account with a GDF. We demonstrate that in the framework of the Born approximation, the CWT of a seismic trace involving such a finite frequency bandwidth can be made equivalent to the CWT of the impulse response of the subsurface and is defined for a reduced range of dilations. We apply the method for the SYSIF seismic device (Marsset et al.; Ker et al.) and show that the source‐corrections allow to define seismic attributes for layer thicknesses in the range [24; 115 cm]. We present the analysis for two seismic reflectors identified on a SYSIF profile, and we show that the source‐corrected multiscale analysis quantifies their complex geometries.