Nonstationary local time-frequency transform

Time-frequency analysis is a fundamental approach to many seismic problems. Time-frequency decomposition transforms input seismic data from the time domain to the time-frequency domain, offering a new dimension to probe the hidden informa-tion inside the data. Considering the nonstationary nature of seismic data, time-frequency spectra can be obtained by apply-ing a local time-frequency transform (LTFT) method that matches the input data by fitting the Fourier basis with nonsta-tionary Fourier coefficients in the shaping regularization frame-work. The key part of LTFT is the temporal smoother with a fixed smoothing radius that guarantees the stability of the non-stationary least-squares fitting. We have developed a new LTFT method to handle the nonstationarity in all time, frequency, and space (x and y) directions of the input seismic data by extending fixed-radius temporal smoothing to nonstationary smoothing with a variable radius in all physical dimensions. The resulting time-frequency transform is referred to as the nonstationary LTFT method, which could significantly increase the resolution and antinoise ability of time-frequency transformation. There are two meanings of nonstationarity, i.e., coping with the non-stationarity in the data by LTFT and dealing with the nonstatio-narity in the model by nonstationary smoothing. We evaluate the performance of our nonstationary LTFT method in several stan-dard seismic applications via synthetic and field data sets, e.g., arrival picking, quality factor estimation, low-frequency shadow detection, channel detection, and multicomponent data registra-tion, and we benchmark the results with the traditional station-ary LTFT method.