Wavelet distortion correction due to domain conversion

Abstract

Converted-wave (PS) data, when converted to PP time, develop time- and location-varying compression of the seismic wavelet due to a variable subsurface [Formula: see text] [Formula: see text]. The time-dependent compression distorts the wavelet in a seismic trace. The lack of a consistent seismic wavelet in a domain-converted PS volume can eventually lead to an erroneous joint PP/PS inversion result. Depth-converted seismic data also have wavelet distortion due to velocity-dependent wavelet stretch. A high value of seismic velocity produces more stretch in a seismic wavelet than a low value. Variable wavelet stretch renders the depth data unsuitable for attribute analysis. A filtering scheme is proposed that corrects for distortion in seismic wavelets due to domain conversions (PS to PP time and time-to-depth) of seismic data in an amplitude-preserving manner. The method uses a Fourier scaling theorem to predict the seismic wavelet in the converted domain and calculates a shaping filter for each time/depth sample that corrects for the distortion in the wavelet. The filter is applied to the domain-converted data using the method of nonstationary filtering. We provide analytical expressions for the squeeze factor [Formula: see text] that is used to predict the wavelet in the converted domain. The squeeze factor [Formula: see text] for PS to PP time conversion is a function of the subsurface [Formula: see text] whereas for PP time-to-depth conversion [Formula: see text] is dependent on subsurface P-wave velocity. After filtering, the squeezed wavelets in domain-converted PS data appear to have resulted from a constant subsurface [Formula: see text], which we denote as [Formula: see text]. Similarly, the filtered depth-converted data appear to have resulted from a constant subsurface P-wave velocity [Formula: see text].