Mixed Phase Seismic Wavelet Estimation using the Bispectrum

Summary The ability to estimate a mixed phase wavelet is a useful tool for processing and quality control in seismic imaging. The wavelet is estimated using higher order statistics of the data. In practice, these methods tend to show some instability issues when the wavelet length is increased. To improve the stability of the solution, this abstract proposes a new formulation of the wavelet estimation problem that constrains the solution to be a finite duration, phase-only compensation applied to a known base wavelet. The proposed solution works in the frequency domain and consists of three steps. First, the bispectrum of the data is deconvolved using the bispectrum of the base wavelet to increase its bandwidth. This helps to improve the sensitivity of third order statistics to phase information. Then, a phase-only wavelet is estimated from the deconvolved bispectrum using an iterative least-squares approach without phase unwrapping. Finally, the estimated phase-only wavelet is conditioned using a projection onto convex sets type algorithm to enforce the constraint of the finite time duration giving the user a control on the amount of phase deviation from the base wavelet. Test examples on synthetic and real data both show reliable results with robustness to noise contamination.