Fractional integration of seismic wavelets in anelastic media to recover multiscale properties of impedance discontinuities
Résumé
Multiscale seismic attributes based on wavelet transform properties have recently been introduced and successfully applied to identify the geometry of a complex seismic reflector in an elastic medium. We extend this quantitative approach to anelastic media where intrinsic attenuation modifies the seismic attributes and thus requires a specific processing to retrieve them properly. The method assumes an attenuation linearly dependent with the seismic wave frequency and a seismic source wavelet approximated with a Gaussian derivative function (GDF). We highlight a quasi-conservation of the Gaussian character of the wavelet during its propagation. We found that this shape can be accurately modeled by a GDF characterized by a fractional integration and a frequency shift of the seismic source, and we establish the relationship between these wavelet parameters and Q. Based on this seismic wavelet modeling, we design a time-varying shaping filter that enables making constant the shape of the wavelet allowing retrieval of the wavelet transform properties. Introduced with a homogeneous step-like reflector, the method is first applied on a thin-bed reflector and then on a more realistic synthetic data set based on an in situ acoustic impedance sequence and a high-resolution seismic source. The results clearly highlight the efficiency of the method in accurately restoring the multiscale seismic attributes of complex seismic reflectors in anelastic media by the use of broadband seismic sources.