Time-frequency analysis, Heisenberg-Gabor uncertainty principle, windows Fourier transform, continuous wavelet transform, marginal distributions (Wigner-Ville) for real seismic signals and their discrete versions, adaptive pursuit methods-orthogonal/non-orthogonal matching pursuit. Discrete wavelet transform, definition of multi-resolution analysis (MRA). Approximation spaces, scaling function, and the dilation equation, detail spaces. Mother wavelet and the wavelet equation. A view from the frequency domain. Orthogonal wavelets, Daubechies wavelets, Daubechies' least asymmetric filters, coiflets, biorthogonal wavelets. Local trigonometric bases and transforms - discrete sine and cosine transforms. Wavelet packet transform (WPT) and local sine and cosine packet transform. Shift-invariant wavelet transform (MODWT) and WPT's algorithms for pattern recognition. Image segmentation, signal detection and edge identification in seismic signals and images. Wavelet threshold and noise reduction, the minimum squared error threshold. General cross validation (GCV) methods and their applicability for seismic signals. The Bayesian approach or denoising signals and images. Wavelet packet and best basis methods for compression of seismic signals. Algorithms and methods for identification and clustering methods in automated identification of seismic phases, phase and group delay, polarization analysis, locally earthquakes effects. 

Type of methodology: Combination of lecture and hands-on

Participants receive the certificate of attendance: Yes

Paid training activity for participants: Yes, for all

Participants prerequisite knowledge: Numerical methods (linear algebra, statistics) Domain-specific background knowledge