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.