Residual static correction Using Tunable Q Factor Discrete Wavelet Transform

Document Type : Research Article


1 M.Sc. Student, Department of Earth Sciences, Faculty of Sciences and Modern Technologies, Graduate University of Advanced Technology, Kerman, Iran

2 Associate Professor, Department of Earth Sciences, Faculty of Sciences and Modern Technologies, Graduate University of Advanced Technology, Kerman, Iran


The derivation of the static reference corrections was generally based on a fairly simple geological model close to the surface. The lack of detailed information near the surface leads to inaccuracies in this model and, therefore, in static corrections. Residual static corrections are designed to correct small inaccuracies in the near-surface model. Their application should lead to an improvement of the final section treated compared to that in which only static corrections is applied. For example, if the final stacked section is to be inverted to produce an acoustic impedance section, it is important that the variations in amplitude along the section represent the changes in the reflection coefficient as close as possible. This is unlikely to be the case if small residual static errors are present. In addition, static reference corrections are not a unique set of values because a change in reference results in a different set of corrections. Due to variation in the Earth's surface, velocities, and thicknesses of near-surface layers, the shape of the travel time hyperbola changes. These deviations, called static, result in misalignments and events lost in the CMP, so they must be corrected during the processing. After correcting the statics of long wavelengths, there are still some short-wavelength anomalies. These “residual” statics are due to variations not counted in the low-velocity layer. The estimation of the residual static in complex areas is one of the main problems posed by the processing of seismic data, and the results from this processing step affect the quality of the final reconstructed image and the results of the interpretation. Residual static can be estimated by different methods such as travel time inversion, power stacking, and sparsity maximization, which are based on a coherent surface assumption. An effective method must be able to denoise the seismic signal without losing useful data and have to function properly in the presence of random noise. In the frequency domain, it is possible to separate the noise from the main data, so denoising in the frequency domain can be useful. Besides, the transformation areas are data-driven and require no information below the surface. The methods in the frequency domain generally use the Fourier transform, which takes time and has certain limits. Wavelet transformation methods always provide a faster procedure than Fourier transformation. We have found that this type of wavelet transform could provide a data-oriented method for analyzing and synthesizing data according to the oscillation behavior of the signal. Tune able Q Factor Discrete Wavelet Transform (TQWT) is a new method that provides a reliable framework for the residual static correction. In this transformation, the quality factor (Q), which relates to the particular oscillatory behavior of the data, could be adjusted in the signal by the user, and this characteristic leads to a good correspondence with the seismic signal. The Q factor of an oscillatory pulse is the ratio of its center frequency to its bandwidth.
TQWT is developed by a tow channel filter bank. The use of a low-pass filter eliminates high-frequency data; these high-frequency components are the effect of residual static. After filtering, the data will be smoother; this amount of correction gives the time offset for the residual static correction. This time difference must apply to all traces. Applying this method to synthetic and real data shows a good correction of the residual static.


Main Subjects

سیدآقامیری، س. ح. و غلامی، ع.، 1395، حذف اثر استاتیک باقیمانده با نوفه‌زدایی در حوزه مکان- فرکانس (f-x)، پژوهش‌های ژئوفیزیک کاربردی، 2(1)، 1-9.doi: 10.22044/jrag.2016.652
Barnes, A., 1993, Instantaneous spectral bandwidth and dominant frequency with applications to seismic reflection data. GEOPHYSICS, 58(3), 419-428.
Daubechies, I., 1990, Orthonormal bases of compactly supported wavelets., 41, 909-996.
Elboth, T., Geoteam, F., Hayat Qaisrani, H. and Hertweck, T., 2008, Denoising seismic data in the time-frequency domain, SEG Las Vegas 2008Annual Meeting.
Gholami, A., 2013, Residual statics estimation by sparsity maximization, Geophysics, 78 (1), 11-19
Goudarzi, A. and Riahi, M., 2013, TQWT and WDGA: innovative methods for ground roll attenuation. Journal of Geophysics and Engineering, 10(6).
Grosman, A., Martinet, R. and Morlet, J., 1989, Reading and understanding continuous wavelet transform, Proc, Int'l Conf. Wavelets, 2-20.
Haar, A., 1910, Zur Theorie der orthogonalen Funktionensysteme, Mathematische Annalen, 69 (3), 331–371, doi:10.1007/BF01456326.
Hatherly, P., Urosevic, M., Lambourne, A. and Evans, B. J., 1994, A simple approach to calculating refraction statics corrections, Geophysics, 59, 156-160.
Ronen, J. and Claerbout, J. F., 1985, Surface-consistent residual statics estimation by stack-power maximization, Geophysics, 50, 2759-2767.
Selesnick, I. W., 2011, Wavelet transform with tunable Q-factor. IEEE Transactions on Signal Processing, 59, 3560-3575.
Sheriff, R. E. and Geldart, L. P., 1982, Exploration Seismology, Cambridge University Press.
Taner, M. T., Koehler, F. and Alhilali, K. A., 1974, Estimation and correction of near-surface time anomalies, Geophysics, 39, 441-463.
Wiggins, R. A., Larner, K. L. and Wisecup, R. D., 1976, Residual statics analysis as a general inverse problem, Geophysics, 41, 922-938
Yilmaz, Ö., 2001, Seismic data analysis, Society of exploration geophysicists Tulsa.