A method for processing seismic data acquired using the same seismic survey setup over long periods of time includes acquiring sets of seismic data using the same seismic survey setup over multiple days, the sets being gathered as repeated seismic data. The method further includes estimating a time-variable wavelet corresponding to unwanted waves, and determining a propagation of the time-variable wavelet, which propagation is assumed to be constant in time, by solving an inverse problem using the repeated seismic data and the estimated time-variable wavelet. The method also includes extracting signal data by subtracting a convolution of the estimated time-variable wavelet and the propagation from the repeated seismic data.