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 information inside the data. Considering the nonstationary nature of seismic data, time-frequency spectra can be obtained by applying a local time-frequency transform (LTFT) method that matches the input data by fitting the Fourier basis with nonstationary Fourier coefficients in the shaping regularization framework. The key part of LTFT is the temporal smoother with a fixed smoothing radius that guarantees the stability of the nonstationary 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 nonstationarity in the data by LTFT and dealing with the nonstationarity in the model by nonstationary smoothing. We evaluate the performance of our nonstationary LTFT method in several standard seismic applications via synthetic and field data sets, e.g., arrival picking, quality factor estimation, low-frequency shadow detection, channel detection, and multicomponent data registration, and we benchmark the results with the traditional stationary LTFT method.

中文翻译：

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非平稳局部时频变换

时频分析是解决许多地震问题的基本方法。时频分解将输入的地震数据从时域转换到时频域，从而提供了一个新的维度来探测数据中的隐藏信息。考虑到地震数据的非平稳性质，可以通过在整形正则化框架中使用非平稳傅立叶系数拟合傅立叶基础，通过应用与输入数据匹配的局部时频变换（LTFT）方法来获得时频谱。LTFT的关键部分是时间平滑器，具有固定的平滑半径，可确保非平稳最小二乘拟合的稳定性。我们开发了一种新的LTFT方法来处理所有时间，频率和空间（x和y通过将固定半径的时间平滑扩展到在所有物理维度上具有可变半径的非平稳平滑，来输入地震数据的方向。所得的时频变换称为非平稳LTFT方法，可以显着提高时频变换的分辨率和抗噪能力。非平稳性有两种含义，即通过LTFT处理数据中的非平稳性和通过非平稳平滑处理模型中的非平稳性。我们通过合成数据和现场数据集评估了非平稳LTFT方法在几种标准地震应用中的性能，例如，到达选择，质量因子估计，低频阴影检测，通道检测和多分量数据配准，