High-resolution seismic data enables better well ties, structure delineation, stratigraphic mapping, and reservoir characterization. Differential resolution (DR) is a data-driven method to improve seismic resolution, but it can introduce a false spatial amplitude variation in the seismic output due to whole trace normalization. The newly proposed normalization technique decomposes the input seismic trace using a translating Gaussian window and then implements the DR algorithm on each window. The introduced weight factors give the interpreter control of the degree of spectral broadening. These developments enable the algorithm to account for the nonstationary properties of the seismic trace, reduce spurious spatial amplitude variation, and provide broader bandwidth seismic data for detailed analysis. We described the mathematical derivation of the nonstationary differential resolution (NSDR) algorithm and its implementation on synthetic and real seismic data. A comparison of NSDR with the original and DR shows better relative amplitude preservation.