Partitions of unity (POUs) that track geological features give an effective means to reduce computational complexity in time-frequency methods. Such methods typically localize operators using windowed Fourier transforms to implement Gabor multipliers or more general pseudodifferential operators. We give a description of a method to create nonuniform partitions of unity and show the approximations obtained by these non-uniform versions are as good as the uniform method, while reducing complexity and numerical errors due to window edge artifacts. This windowing is a key step in Gabor decon and Gabor wavefield extrapolation.
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