The subsurface media are not perfectly elastic, thus anelastic absorption, attenuation and dispersion (aka
Q filtering) effects occur during wave propagation, diminishing seismic resolution. Compensating for anelastic effects is imperative for resolution enhancement.
Q values are required for most of conventional
Q-compensation methods, and the source wavelet is additionally required for some of them. Based on the previous work of non-stationary sparse reflectivity inversion, we evaluate a series of methods for
Q-compensation with/without knowing
Q and with/without knowing wavelet. We demonstrate that if
Q-compensation takes the wavelet into account, it generates better results for the severely attenuated components, benefiting from the sparsity promotion. We then evaluate a two-phase
Q-compensation method in the frequency domain to eliminate
Q requirement. In phase 1, the observed seismogram is disintegrated into the least number of
Q-filtered wavelets chosen from a dictionary by optimizing a basis pursuit denoising problem, where the dictionary is composed of the known wavelet with different propagation times, each filtered with a range of possible values. The elements of the dictionary are weighted by the infinity norm of the corresponding column and further preconditioned to provide wavelets of different values and different propagation times equal probability to entry into the solution space. In phase 2, we derive analytic solutions for estimates of reflectivity and
Q and solve an over-determined equation to obtain the final reflectivity series and
Q values, where both the amplitude and phase information are utilized to estimate the
Q values. The evaluated inversion-based
Q estimation method handles the wave-interference effects better than conventional spectral-ratio-based methods. For
Q-compensation, we investigate why sparsity promoting does matter. Numerical and field data experiments indicate the feasibility of the evaluated method of
Q-compensation without knowing
Q but with wavelet given.
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