Improvement of seismic vertical resolution using time scaling property of Fourier transform

Summary The improvement of seismic data resolution in hydrocarbon exploration, especially in complex structures is of great importance. There are two types of resolution in surface reflection seismic data: horizontal resolution and vertical resolution. Vertical or temporal resolution is expressed by means of the tuning thickness and horizontal or spatial resolution is expressed by means of the Fresnel zone. Tuning thickness is defined as a quarter of the dominant wavelength at the position of the target layer. It is the minimum thickness by which the top and bottom of the layer is separable. The tuning thickness is related to interval velocity of the target layer and the dominant frequency of traveling wave at the depth of the target layer. Thus, the increase in the dominant frequency of seismic data can help to increase the vertical resolution.
Introduction Based on the convolution model, the seismic trace is a convolution of the earth reflectivity series with a seismic source wavelet. The seismic source wavelet is a frequency band-limited signal and the earth reflectivity series is assumed to be white noise, which is un-limited frequency bandwidth signal. Many methods have been introduced to enhance the vertical resolution of reflection seismic data. Each of them has advantages and disadvantages that are due to the assumptions and theories governing their issue. Inverse Q-filter, different deconvolution methods and time-variant spectral whitening are the basic methods of the resolution improvement. In the deconvolution procedure, the band limited seismic source signature is compressed by various methods to increase the frequency band of seismic source wavelet.
Methodology and Approaches In this paper, the vertical resolution of surface reflection seismic is increased using scaling property of Fourier transform. According to this property, when the value of scaling factor is selected greater than one, the scaled seismic trace in comparison with original seismic trace is compressed and its amplitude spectra are shifted to higher frequency band. In this way, the vertical resolution of seismic trace is increased. When the value of scaling factor is selected less than one, the scaled seismic trace compared to original seismic trace is extended and its amplitude spectra are shifted to lower frequency band, and thus, the vertical resolution of seismic trace is decreased. In this paper, a filter is designed based on Fourier transform of scaled and original source wavelet. Then, the filter is applied on seismic trace in frequency domain, and as a result, inverse Fourier transform of filtered signal is computed. The obtained signal is an improved resolution seismic trace.
Results and Conclusions The proposed algorithm has been tested on both synthetic and real seismic sections and the results have been compared to the frequency deconvolution method. The synthetic seismic section has been created from a wedge model by a 35 Hz Ricker wavelet. The enhanced resolution seismic section is obtained by applying the designed filter on the seismic traces. In the obtained section, the dominant frequency is shifted to 70 Hz and frequency bandwidth is expanded. Moreover, the tuning thickness after the filtering is reduced from 12.5 m to 6.25 m indicating that the vertical resolution is improved. In the real case, the dominant frequency is increased from 25 to 40 Hz. After filtering the seismic section as described above, we can see that the resolution is increased, and thin layers, which were not clear in the original section, become visible in the filtered seismic section. Therefore, the results of applying the proposed method on synthetic and field data show that we can efficiently obtain high resolution seismic section using the proposed method. Note that there is a trade-off between resolution and signal-to-noise (S/N) ratio in the time scaling transform of seismic trace. The S/N ratio is reduced a little after the filtering the trace.