Chapter one, the Fractional Fourier Transforms (FRFT) is introduced.It will show the basis of the FRFT with nostationary behaviors is a chirp-like function related to sinusoid basis of Fourier Transforms. Therefore the FRFT could be considered as the Chirp-like Transforms Chapter two, Curvelet transform is a new multiscale analysis method, and this analysis was developed from the purpose of de-noising. Compare to wavelet, curvelet analysis can solve the characteristic represent of higher dimension and this transform can acquire theoretically the best expression as to curve singularity characteristic. Chapter three, a type of time-frequency representation optimal with respect to time-frequency localization is the Wigner Distribution (WD) . The WD is already used to enhance the seismic event .