Discussion

We have seen how the proposed SLTFT is applied in ground-roll attenuation, inverse-Q filtering, and multicomponent data registration. As metioned before, the localization scalar $\varepsilon$ is a key parameter in the SLTFT. It controls the balance between time and frequency resolution. Overall, it is similar to the window length in STFT. A small $\varepsilon$ value means a rapid decaying smoothing radius, which leads to higher time resolution and lower frequency resolution. In contrast, a large $\varepsilon$ value means a slow decaying smoothing radius, which leads to higher frequency resolution and lower time resolution. The $\varepsilon$ value should be set according to the specific requirements of the seismic data processing task. For example, in the ground-roll attenuation and inverse-Q filtering tasks, a larger $\varepsilon$ value can be used to achieve better frequency resolution. The frequency varying scalar can also be set using the same principle, according to the desired frequency-varying resolution.