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ABSTRACT The frequency-dependent width of the Gaussian window function used in the S-transform may not be ideal for all applications. In particular, in seismic reflection prospecting, the temporal resolution of the resulting S-transform time-frequency spectrum at low frequencies may not be sufficient for certain seismic interpretation purposes. A simple parameterization of the generalized S-transform overcomes the drawback of poor temporal resolution at low frequencies inherent in the S-transform, at the necessary expense of reduced frequency resolution. This is accomplished by replacing the frequency variable in the Gaussian window with a linear function containing two coefficients that control resolution variation with frequency. The linear coefficients can be directly calculated by selecting desired temporal resolution at two frequencies. The resulting transform conserves energy and is readily invertible by an inverse Fourier transform. This modification of the S-transform, when applied to synthetic and real seismic data, exhibits improved temporal resolution relative to the S-transform and improved resolution control as compared with other generalized S-transform window functions.
Summary Although the S-Transform (ST) has better time resolution than the Continuous Wavelet Transform (CWT) at low frequencies, resolution may still not be adequate for certain seismic interpretation purposes. A modified S-Transform (MST), which reduces from the Generalized S-Transform (GST) is proposed as a simple means of controlling temporal and frequency resolution as a function of frequency. This is accomplished by replacing the frequency in the normalized Gaussian window of the S-transform with a linear frequency function. With appropriate choice of slope and intercept of this linear function, greatly improved temporal resolution can be accomplished at low frequencies, while retaining the temporal resolution of the ST at high frequencies. Synthetic examples show that low frequency ST spectra may suffer from interferences from nearby reflectors, and that this effect can be greatly reduced or eliminated using the MST. Application to real seismic data indicates that the MST can be useful in direct hydrocarbon indication.
- Geophysics > Seismic Surveying > Seismic Processing (0.97)
- Geophysics > Seismic Surveying > Seismic Interpretation (0.67)