Abstract
Quality factor estimation (Q estimation) of vertical seismic profile (VSP) data are necessary for the process referred to as inverse Q-filtering, which is used, in turn, to improve the resolution of seismic signals. In general, the performances of Q estimation methods, based on the standard Fourier transform, are severely degraded in the presence of heavy-tailed distributed noise. In particular, these methods require a bandwidth detection which is difficult to estimate due to instabilities caused by outliers or gross errors, leading to an incorrect Q estimation. In this paper, an improvement of the Q-factor estimation based on the peak frequency shift method is proposed, where the signal spectrum is obtained using a robust transform algorithm. More precisely, the robust transform method assumes that the perturbations that contaminate the signal of interest can be characterized as random samples following a zero-mean Laplacian distribution, leading to the weighted median as the optimal operator for determining each transform coefficient. The proposed method is validated on synthetic datasets using different levels of noise and its performance is compared to those yielded by various methods based on the standard Fourier transform. Furthermore, a non-Gaussianity test is performed in order to characterize the noise distribution in real data. From the non-Gaussianity test, it can be observed that the underlying noise is better characterized using a Laplacian statistical model, and therefore, the proposed method is a suitable approach for computing the Q factor. Finally, the proposed methodology is applied to estimate the Q factors of real VSP data.
Quality factor estimation of JPEG images using a statistical model