Imaging thin beds using attributes achieved in spectral decomposition by short time Fourier transforms



One of the most fundamental reservoir characteristics is the thickness. The analysis of thin bed tuning on seismic reflectivity has been studied extensively by Wides (1973) and Neidel and Pogiaggliomi (1977), who discussed the limits of seismic resolution. During the past decade, the industry has developed a plethora of new attributes in studying thin beds by employing spectral decomposition (Peyton et al., 1998; Partyka et al., 1999), and attributes which are obtained from it (Marfurt and Kirlin, 2001). Spectral decomposition refers to all methods that generate frequency spectrums consisting of amplitude spectrum, phase spectrum, change of phase with frequency and power spectrum in windows with the center of each time sample of a trace. These methods are used in studying geological features, thin beds, hydrocarbon reservoirs and noise attenuation. The most important of these methods are short time Fourier transform (STFT), continuous wavelet transforms, S-transform, Wigner-Ville distribution and matching pursuit decomposition. The result of a trace spectral decomposition is a time-frequency map.
In this paper, the STFT method is applied for imaging thin beds in 2D seismic sections. In this method, a short time window with constant size is multiplied by a trace for each of its time samples of it then Fourier transform is applied on it. So, there is a local frequency spectrum for each time sample. The main factor of this method to be considered is the effect of the existence of two boundaries of a thin layer inside a time window. This affects local frequency spectrum and changes it so that by choosing some quantities of local spectrum as attributes it is possible to image the thin bed. The spectral attributes that are studied are the peak frequency, peak amplitude and change of phase with frequency. Detectable layers are related to the size of the time window. In this paper, frequency spectrums of a bed response and their reflection with minimum and zero phase wavelets are considered. Then, the effect of changing of thickness on frequency spectrums is studied. For controlling the main factor of this method, STFT algorithm is applied on a synthetic seismic section. It is shown that with the peak frequency and the peak amplitude obtained from a small portion of each local amplitude spectrum, and local change of phase with frequency in a particular frequency a good conclusion can be obtained. After that the STFT algorithm is applied on a part of a real seismic section and the place of layers with thickness up to 10 ms, between 10 to 18 ms and more than 18 ms are defined. It should be noted that the main idea of detecting thin beds on seismic sections is deference of frequency spectrum of a bed and a boundary. It is necessary to use more than one attribute for achieving more accurate results. It is shown that in particular frequency portions, thin beds are detected better. The minimum thickness that can be detected by this method depends on the frequency content of the seismic wavelet and the time sampling interval. It should be considered that applying STFT in more stages and less difference of size of windows in alternative stages increases accuracy of estimated thickness ranges.