Phase mismatches sometimes occur between final processed sections and zero-phase synthetics based on well logs, despite best efforts for controlled-phase acquisition and processing. The latter are often based on deterministic corrections derived from field measurements and physical laws. A statistical analysis of the data can reveal whether a time-varying nonzero phase is present. This assumes that the data should be white with respect to all statistical orders after proper deterministic corrections have been applied. Kurtosis maximization by constant phase rotation is a statistical method that can reveal the phase of a seismic wavelet. It is robust enough to detect time-varying phase changes. Phase-only corrections can then be applied by means of a time-varying phase rotation. Alternatively, amplitude and phase deconvolution can be achieved using time-varying Wiener filtering. Time-varying wavelet extraction and deconvolution can also be used as a data-driven alternative to amplitude-only inverse-Q deconvolution.