The projection onto convex sets (POCS) interpolation method is well-known to interpolate the randomly sampled and aliased seismic data in geophysical community. To manipulate the thresholding step in this method with ease, we suggest using a percentage thresholding scheme. To combat the spectral leakage, we proposed to employe a redundant DFT frame by excessive zero-padding to exploit the Fourier domain sparsity. Empirically, double excessive zero-padding and less than 20% Fourier coefficients are enough to obtain a satisfying result, supported by the theory of spectral compressive sensing.
Seismic instantaneous frequency (IF) is a useful attribute for characterizing depositional features from seismic data. However, commonly used IF estimations methods are sensitive to noise and also suffer from meaningless values. In this paper, we propose an IF regularization method based on time-frequency analysis. The Stockwell transform (ST), which has an advantage in providing multi-resolution time-frequency analysis while retaining the absolute phase of each frequency component, is used for IF regularization. We firstly decompose the estimated IF into the ST domain. By considering that most geologic changes are expressed only in certain local spectral ranges, we utilize an instantaneous amplitude parameterized low pass filter to identify the spectral ranges of IF from the multi-resolution results. After inverse ST is taken, noise and meaningless values are removed, and the regularized IF becomes more useful for describing geological features. The synthetic and real data examples demonstrate the effectiveness of our method.
Based on the diffusive-viscous theory, we have investigated characteristics of frequency-dependent reflection coefficient as a function of incident angle at an interface between two dispersive media or between a non-dispersive medium and a dispersive medium. We observe that significant attenuation occurs in fluid-saturated layer because of high velocity dispersion and the attenuation in gas- and oil-saturated rocks is larger than that of water-saturated rocks. Furthermore, the results show that reflection coefficients of fluid-saturated layers vary significantly with frequency. Three cases are considered and show that 1) the amplitude and phase angle of reflection coefficient from an interface between air- and water-saturated medium change insignificantly with frequency because of its lower dispersion. 2) the amplitude of reflection coefficient at an interface between air- and oil-saturated medium increases toward higher frequencies because of high dispersion when the incident angle is less than 50°, which agrees with the low-frequency dim-out response, and the phase angle increases with incidence angle and decreases with increasing frequency. 3) The amplitude of reflection coefficient at an interface between oil- and water-saturated medium increases toward lower frequencies because of significant dispersion when the incident angle is less than 50°, which coincides with the low-frequency bright-spot response, and the phase angle is always negative and varies complicatedly with frequency.
The method of arbitrary high-order discontinuous Galerkin finite element solves the elastic wave equations with arbitrary high-order accuracy in space and time on unstructured triangular meshes; however, the absorbing boundary condition proposed by Käser & Dumbser has some problems at corners or for grazing incidence of waves. In this paper we introduced new scheme which combine the unsplit convolutional perfectly matched layer with the absorbing boundary condition. The numerical scheme maintains the uniform high order of accuracy in space and time in the perfectly matched layer region. In the modeling test, we discussed the behavior of the attenuation coefficients in our scheme and demonstrate the efficiency for body wave and Rayleigh wave.
We proposes a new approach to the seismic blind deconvolution problem in the case of band-limited seismic data with a low dominant frequency and short data records, based on the Csiszár’s f-divergence. In order to model the probability density function of the deconvolved data, and obtain the closed form formula of Kagan divergence, mixture Jones’ family of distributions (MJ) is introduced, by which a new criterion for blind deconvolution is constructed. By applying N. S. Neidell’s wavelet model to the inverse filter, we then make the optimization program for multivariate reduce to univariate case. Examples are provided showing the good performance of the method even in low SNR.
In this paper, a robust method for the extraction of instantaneous attributes is proposed in wavelet domain. A new class of analytic wavelets, the Generalized Morse Wavelets (GMWs), which have some desirable properties, are applied during the procedure of the proposed method. Compared to the conventional method based on Hilbert transform (HT), the new method is proved to yield higher precision and better anti-noise performance. Experimental results on synthetic signals and real seismic data show the validity of the method.