Borehole-driven sparse-spike deconvolution and seismic bandwidth enhancement

Abstract

Reflectivity estimation approaches are usually driven solely by observed seismic data, leaving other types of a priori information, such as well-log data, out of the equation. This may result in solutions that honor the observed data but are not properly linked to geology. We provide a method for estimating sparse-spike reflectivity solutions that takes into account the observed data and any given sparse-spike model derived from well-log data. Starting with the well-log measurements, we estimate the reflectivities trace by trace by iteratively perturbing the previous solution with a warping function. This procedure is repeated until the synthetic trace formed by convolving with an appropriate wavelet fits the observed data. The assumption that two consecutive reflectivities have the same number of spikes with similar amplitudes and positions ensures lateral continuity. Because it is expected that reflectivity fluctuates smoothly from trace to trace, the technique is appropriate for areas with low to moderate structural complexity. The resulting sparse-spike reflectivity section can be considered as a product in and of itself. Even so, the interpreter might prefer a borehole-consistent frequency-enhanced seismic image, which can be easily produced by convolving the reflectivity with a suitable broadband wavelet. We rigorously test the technique on 1D and 2D synthetic data as well as on a 3D poststack field data set. The results indicate that we can obtain sparse-spike reflectivities with good lateral continuity that honor the observed data. Most importantly, the resulting reflectivity section (or frequency-enhanced data) is guaranteed to honor the well-log information too, which may aid users in seismic data analysis and interpretation.