Wavelet Based Semblance Analysis

Semblance filtering compares the phases of two datasets as a function of frequency. Because it is based on the Fourier transform its application suffers from all the problems associated with that transform, in particular its assumption that the frequency content of the data does not change with time. Semblance is here extended in two ways, using the continuous and the discrete wavelet transforms. When calculated using the continuous wavelet transform, semblance analysis allows the local phase relationships between the two datasets to be studied as a function of scale (or wavelength). Additionally, the efficient inverse transform of the discrete wavelet transform allows datasets to be filtered based on their local semblance, which offers considerable advantages over previous Fourier methods.