Using the forced-oscillation method, we measure the dispersion of Young's modulus, extensional attenuation, and Poisson's ratio of tight sandstone and carbonate samples at seismic frequencies (1-1000 Hz) under a constant confining pressure of 20 MPa and for a water saturation varying between 0% and 100%. The experimental data suggest that the dispersion of Young's modulus and attenuation of tight rocks is significant in a broad frequency band spanning over 1-1000 Hz. A comparison with the high-porosity and high-permeability sample data shows a contrasting dispersion and attenuation characteristics. For the tight sandstone, Young's modulus reaches a maximum dispersion of 16% at 60% water saturation and a 13% dispersion at 100% saturation. Attenuation is insignificant in dry condition and for water saturation ≤30%. In contrast with the peak attenuation occurring at very high water saturation (e.g., 80-100%) in partially saturated high-porosity rocks, peak attenuation of tight sandstone takes place at a water saturation of 60%. For the tight carbonate, the magnitude of dispersion (~3%) and attenuation are markedly lower for all saturation levels. In the explored frequency range (1-1000 Hz), Young's modulus increases monotonously, and no obvious attenuation peak is observed when saturation levels are greater than 10%. Using well-established theoretical models based on physical properties and microstructure of the tested rocks, we suggest that the observed attenuation characteristics are possibly attributed to the combined physical mechanism of microscopic (squirt) flow, mesoscopic flow in partially saturated rock, and shear dispersion due to viscous flow in grain contacts. Key Points:• Dispersion and attenuation of both tight sandstone and carbonate are distributed across frequency range of 1-1000 Hz • Extensional attenuation in tight sandstone is saturation dependent with a maximum at 60% saturation, which contrasts with that of porous sandstones • The coupled pore fabric and fluid distribution heterogeneity in tight rocks might cause complex dispersion and attenuation characteristics

S transform (ST) proposed by Stockwell et al. is the unique transform that provides frequency‐dependent resolution while maintaining a direct relationship with the Fourier spectrum. This feature is very important for applications. However, the ST can't work well for seismic data analysis since its basic wavelet is not appropriate. In this paper, the ST is generalized with two steps, and two kinds of new transforms are obtained, which are called generalized S transform (GST). First, the basic wavelet in ST is replaced by a modulated harmonic wave with four undetermined coefficients, and then a new transform and its inverse are given, called GST1. Second, taking a linear combination of the basic wavelets in step 1 as a new basic wavelet, called GST2, and its inverse is constructed. To compare ST with GST, the ST and GST method are used to analyze several typical models of thin beds, respectively. The results show that the resolution of GST is better than that of ST. The GST method can determine accurately the location of interfaces of acoustic impedance in thin interbeds of thickness being only an eighth wavelength, while ST method can't. In this study, the effectiveness of GST method is also verified by processing results of real data.

Beamlet migration based on local perturbation theory is proposed. The method is formulated with a l o c a l bac kground velocity and local perturbations for each window of the wave eld decomposition using Gabor-Daubechies frame and local cosine basis. The propagators and phase-correction operators are obtained analytically for the G-D tight-frame, and numerically for the local cosine basis. The numerical test using the SEG-EAEG salt model poststac k data demonstrates the great potential of this approach.

We have developed a new sparse-spike deconvolution (SSD) method based on Toeplitz-sparse matrix factorization (TSMF), a bilinear decomposition of a matrix into the product of a Toeplitz matrix and a sparse matrix, to address the problems of lateral continuity, effects of noise, and wavelet estimation error in SSD. Assuming the convolution model, a constant source wavelet, and the sparse reflectivity, a seismic profile can be considered as a matrix that is the product of a Toeplitz wavelet matrix and a sparse reflectivity matrix. Thus, we have developed an algorithm of TSMF to simultaneously deconvolve the seismic matrix into a wavelet matrix and a reflectivity matrix by alternatively solving two inversion subproblems related to the Toeplitz wavelet matrix and sparse reflectivity matrix, respectively. Because the seismic wavelet is usually compact and smooth, the fused Lasso was used to constrain the elements in the Toeplitz wavelet matrix. Moreover, due to the limitations of computer memory, large seismic data sets were divided into blocks, and the average of the source wavelets deconvolved from these blocks via TSMF-based SSD was used as the final estimation of the source wavelet for all blocks to deconvolve the reflectivity; thus, the lateral continuity of the seismic data can be maintained. The advantages of the proposed deconvolution method include using multiple traces to reduce the effect of random noise, tolerance to errors in the initial wavelet estimation, and the ability to preserve the complex structure of the seismic data without using any lateral constraints. Our tests on the synthetic seismic data from the Marmousi2 model and a section of field seismic data demonstrate that the proposed method can effectively derive the wavelet and reflectivity simultaneously from band-limited data with appropriate lateral coherence, even when the seismic data are contaminated by noise and the initial wavelet estimation is inaccurate.

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In this paper, we study the existence of mild solutions for a class of semilinear fractional differential equations with nonlocal conditions in Banach spaces. The results are obtained by using convex-power condensing operator and fixed point theory. An example is presented to illustrate the main result.MSC 2010 : Primary 26A33: Secondary 33E12