Seismic weak responses from subsurface small-scale geologic discontinuities or inhomogeneities are encoded in 3D diffractions. Separating weak diffractions from a strong reflection background is a difficult problem for diffraction imaging, especially for the 3D case when they are tangent to or interfering with each other. Most conventional diffraction separation methods ignore the azimuth discrepancy between reflections and diffractions when suppressing reflections. In fact, the reflections associated with a specific pair of azimuth-dip angle possess sparse characteristics, and the diffractions adhering to Huygens’ principle behave as low-rank components. Therefore, we have developed a 3D low-rank diffraction imaging method that uses the Mahalanobis-based low-rank and sparse matrix decomposition method for separating and imaging 3D diffractions in the azimuth-dip angle image matrix. The advantages of our 3D diffraction imaging method not only includes the handling of interfering events but also includes ensuring a better protection of weak diffractions. The numerical experiment illustrates the good performance of our method in imaging small-scale discontinuities and inhomogeneities. The field data application of carbonate reservoirs further confirms its potential value in resolving the masked small-scale cavities that can provide storage spaces and a migration pathway for petroleum.

Diffractions are the seismic responses of subsurface small-scale geologic discontinuities or inhomogeneities, whose energy is much weaker than that of reflections. To eliminate the masking effect of strong reflections on weak diffractions, a prestack diffraction separation method is proposed based on the common virtual source gather (CVSG) and the median filter. The reflection generated from a reflector can be regarded as originating from a virtual source (or a focused area). According to this behavior, the reflection can be transformed into its corresponding virtual source position to build the CVSG. Unlike the reflection, diffraction cannot be regarded as originating from one virtual source. Therefore, diffractions have a curved shape, whereas reflections are flat in the CVSG. Based on the traveltime moveout method, the reflection traveltime is calculated for describing reflection events and generating CVSG. Theory and a simple synthetic data test demonstrate that there is almost no energy lost when transforming between a shot gather and CVSG. Then, for removing the reflection, the median filter is used in the CVSG where the reflection appears as a linear event. Complex synthetic and field examples demonstrate that the proposed method can flatten reflection events and thus can separate diffraction events from strong reflections in the prestack domain.

Seismic diffractions are ideal carriers of information on small-scale, discontinuous objects and can therefore be used to detect these geologic objects. However, recognizing diffractions is difficult because specular reflection with strong energy masks the weak diffraction. In this study, we propose a diffraction separation and imaging method based on a Mahalanobis-based and phase-based attenuation function used to modify the Kirchhoff migration formula in the full-azimuth dip-angle domain. In this domain, reflections are restricted to within the first Fresnel zone and are distributed in the vicinity of the stationary point, while diffractions are located across a wide range of azimuth and dip angles. Synthetic and field data applications suggest that this new method can effectively separate and image diffractions. The results also demonstrate the efficiency of the new method in clarifying subsurface small-scale objects, which can provide finer information about these structures for seismic interpretation.

Random noise attenuation is one of the most essential steps in seismic data processing and effective denoising methods can significantly improve the accuracy of structural imaging and data inversion. To address this issue, we propose a novel low-rank approximation method that uses a CUR matrix decomposition algorithm instead of the traditional truncated singular value decomposition (SVD). The low-rank method is applied along the structural direction of seismic data produced by plane-wave structural prediction to strengthen the low-rank property. The CUR decomposition exhibits a matrix as a product of three matrices, C, U, and R, to obtain a low-rank approximation. The decomposed matrices are formed by randomly selecting a subset of columns and rows from the data matrix. The subspace sampling algorithm is considered as a column selection principle to compute CUR decompositions. The proposed CUR-based low-rank denoising method is directly exploited to perform low-rank approximation in the Hankelization space, thus avoiding the time-consuming SVD. To improve the accuracy of slope estimation, a robust plane-wave destruction algorithm with nonstationary shaping regularization is provided to enhance the slope estimation of noisy data. Synthetic and field examples are used to demonstrate the effectiveness performance of the proposed CUR-based low-rank denoising method both in eliminating seismic random noise and improving computational efficiency.

Seismic diffractions encoding subsurface small-scale geologic structures have great potential for high-resolution imaging of subwavelength information. Diffraction separation from the dominant reflected wavefields still plays a vital role because of the weak energy characteristics of the diffractions. Traditional rank-reduction (RR) methods based on the low-rank assumption of reflection events have been commonly used for diffraction separation. However, these methods using truncated singular-value decomposition (TSVD) suffer from the problem of reflection-rank selection by singular-value spectrum analysis, especially for complicated seismic data. In addition, the separation problem for the tangent wavefields of reflections and diffractions is challenging. To alleviate these limitations, we have developed an effective diffraction separation strategy using an improved optimal RR (ORR) method to remove the dependence on the reflection rank and improve the quality of separation results. The improved RR method adaptively determines the optimal singular values from the input signals by directly solving an optimization problem that minimizes the Frobenius-norm difference between the estimated and exact reflections instead of the TSVD operation. This improved method can effectively overcome the problem of reflection-rank estimation in the global and local RR methods and adjusts to the diversity and complexity of seismic data. The adaptive data-driven algorithms indicate good performance in terms of the trade-off between high-quality diffraction separation and reflection suppression for the ORR operation. Applications of our strategy to synthetic and field examples demonstrate the superiority of diffraction separation in detecting and revealing subsurface small-scale geologic discontinuities and inhomogeneities.