Wavelet transform and instantaneous attributes analysis

IP (instantaneous parameters such as instantaneous frequency) of a signal computed with HT (Hubert transform) method usually do not well characterize the signal when its S / N is poor. So a theorem is proposed for the calculation of the analytic signal of a real-velued signal in L₂ (R). Based on the theorem, a wavelet-based method (called WT method). of computing the IP is given. The numerical simulation results and theoretical analysis show that the WT method has higher precision and antinoise capacity than the HT method does. On the basis of the convolutional model in the analysis of reflection seismogram, the meaning of wavelet transform of seismogram and corresponding IP at different scales is investigated. This is very important to practical seismic data processing and interpretation using wavelet transform.