High-resolution gathers by inverse Q filtering in the wavelet domain

Abstract

We have developed and applied an inverse [Formula: see text] filter formulation using the continuous wavelet transform (CWT), which provides a natural domain for time-variant operations, such as compensation for propagation in attenuating and dispersive media. The well-known linear attenuation model, given as a function of time and frequency, was applied very efficiently over wavelet coefficients in the time-frequency domain to correct for amplitude and phase distortions, as necessary. The inverse CWT yields the recovered trace with a broader bandwidth. The process works on a trace-by-trace basis, making no distinction if the data is pre- or poststack. Our motivation was to develop gather conditioning tools to enhance prestack interpretation techniques such as amplitude variation with offset (AVO) analysis and inversion — a technique that is often compromised by tuning and other propagation related issues that degrade seismic resolution. Thus, we investigated the AVO fidelity of our filter and the sensitivity of the results to incorrect values of [Formula: see text], using real and synthetic data. Our synthetic data experiments clearly showed that AVO anomalies are recovered and preserved in a stable manner, even with values of [Formula: see text] off by 50% of its correct value. The application in time-migrated gathers shows a very natural increase in the vertical definition of the events, especially due to the partial elimination of the tuning effect. The benefits for imaging are also evidenced by comparing stacked sections before and after inverse [Formula: see text] filtering. The higher resolution of seismic sections leads to a better definition of smaller scale stratigraphic and structural features.

Continuous Wavelet Transform-Based Frequency Dispersion Compensation Method for Electromagnetic Time-Reversal Imaging

“…Furthermore the CWT method provides us with an improved separation between the unwanted noise and our signal [19]. Next step is applying our inverse filter to X[n, a j ] in the wavelet domain to compensate the attenuation caused by the dispersive medium.…”

“…The wavelet function that we used for the CWT method is Morlet wavelet [22]. Morlet wavelet is considered in [19] as the proper choice for analyzing the propagated wave in attenuating and dispersive media. The mother wavelet of Morlet in time domain [23] is…”

“…where a j is a scaling factor which controls the actual frequency f ( fc aj ) of the filter in order to have a variable window size [19] and f c is the central frequency of x[n]. H[n, a j ] uses r of the dominant tissue in the propagating media at f c .…”

“…The inverse filters in [12] and [17] need the non-dispersive version of the propagation media to create the inverse filter which might be unknown in real-life scenarios. The STFT method uses a fixed time window length which provides a lower resolution in determining attenuation when compared with other size-adjustable window methods [18], [19]. In this paper, we propose a compensation method that uses adaptive-window scheme based on the Continuous Wavelet Transform (CWT).…”

Some remarks on Q‐compensated sparse deconvolution without knowing the quality factor Q

“…The Q values are required for most of the above methods (e.g. Wang 2006;van der Baan 2012;Braga and Moraes 2013;Wang and Chen 2014;. The wavelet is additionally required for the methods described by Zhang and Ulrych (2007), van der Baan (2012), Oliveira and Lupinacci (2013), Chai et al (2014Chai et al ( , 2016Chai et al ( , 2018, and Wang et al (2018a).…”