Spectral Decomposition of Seismic Data with Continuous Wavelet Transform

In this paper we present a new methodology for computing a time-frequency map for non-stationary signals using the continuous wavelet transform (CWT). The conventional method of producing a time-frequency map using the Short Time Fourier Transform (STFT) limits the time-frequency resolution by a pre-defined window length. In contrast, the CWT method does not require pre-selecting a window length and does not have a fixed time-frequency resolution over the time-frequency space. The CWT utilizes dilation and translation of a wavelet to produce a timescale map. One scale encompasses a frequency band, and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a timescale map into a time-frequency map by taking the center frequencies of each scale. We transform the timescale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a timescale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a non-stationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT can potentially be utilized to detect frequency shadows caused by hydrocarbons and identify subtle stratigraphic features for reservoir characterization.