Geophysical Prospecting - Volume 72, Issue 6, 2024

When compared to traditional seismic data acquisition, irregular blended acquisition significantly promotes the acquisition efficiency. Yet, the blending noise of subsampled blended data introduces new obstacles for the subsequent processing of seismic data. Due to the predictability of linear events in the frequency–space domain, the constructed Hankel matrices exhibit low‐rank characteristics. However, the blending noise of subsampled blended data increases the rank, so deblending and interpolation can be implemented via rank‐reduction algorithms such as the singular spectrum analysis. The significant computing cost of the singular value decomposition, however, makes the traditional singular spectrum analysis inefficient. An alternative algorithm, known as the randomized singular spectrum analysis, employs the randomized singular value decomposition instead of the traditional singular value decomposition for rank‐reduction. The randomized singular spectrum analysis significantly enhances the efficiency of the decomposition process, particularly when dealing with large Hankel matrices. There still remains some random noise when using the singular spectrum analysis or randomized singular spectrum analysis for subsampled blended data, because the noise subspace and signal subspace are coupled together. Thus, we incorporate a damping operator into the randomized singular value decomposition and propose a novel damped randomized singular spectrum analysis method. The damped randomized singular spectrum analysis combines the advantages of the randomized singular value decomposition and the damping operator to enhance the computational efficiency and suppress the remaining noise. Moreover, an iterative projected gradient descent strategy is introduced to achieve deblended and interpolated seismic data for subsequent processing. Examples from synthetic data and field data are used to demonstrate the effectiveness and superiority of the proposed damped randomized singular spectrum analysis method, which enhances the accuracy and efficiency during simultaneous deblending and interpolation.

The inverted velocity model obtained from the reflection tomography based on the angle domain common‐image gathers has a certain fuzziness. The inverted velocity model's stratigraphic interface is always not clear enough in areas with complex stratigraphic structure. In order to improve the accuracy and resolution of the inverted velocity model, a double‐difference constraint condition is added on the basis of minimizing the absolute travel‐time residual at the subsurface imaging points. This constraint makes the inverted velocity model local structure information more refined by minimizing the differential travel‐time residual at adjacent imaging points (i.e. closely spaced points within the same layer) and makes the variation of velocity model information within a certain range more accurate. The method in this paper is based on angle domain common‐image gathers, the tomography inversion equation is established by using the ray tracing method, and the conversion relationship between the traveltime residual and the residual curvature of the angle domain common‐image gathers. Then, by adding differential constraint and double‐differential constraint conditions and using the least squares QR decomposition method to solve the set of equations, the inverted velocity model can be obtained through multiple iterations, which provides a high‐precision velocity field for the migration and improves the accuracy of seismic imaging. Numerical experiments on both one typical model and a field data example demonstrate the effectiveness of the proposed double‐difference constrained elastic reflection tomography in generating high‐precision velocity models.

Organic‐rich shales contain large amounts of oil and gas and are anisotropic because of fine‐scale layering and the partial alignment of organic matter and anisotropic clay minerals with the bedding. An example is the Wolfcamp Shale in the Permian Basin. Elastic anisotropy needs to be accounted for in the characterization of such formations using seismic data and plays a role in hydraulic fracturing and in the evaluation of stress changes and geomechanical effects resulting from production. Using extensive well log data acquired in the Midland Basin, the eastern sub‐basin of the Permian Basin, we estimate and compare the elastic anisotropy in the Middle and Upper Wolfcamp Shale by combining data from a vertical pilot well with two lateral wells, one (6SM) drilled in the Middle Wolfcamp and one (6SU) drilled in the Upper Wolfcamp. The data used were acquired at the Hydraulic Fracture Test Site 1, located in the eastern part of the Midland Basin. Thomsen's anisotropy parameter calculated from the fast and slow shear sonic is higher on average for the 6SM lateral than for 6SU, consistent with there being less carbonate content in 6SM than in 6SU. However, the anisotropy parameter in some regions with higher carbonate content in well 6SU is higher than in well 6SM. This may indicate the influence of natural fractures. The primary set of steeply dipping fractures observed in the lateral wells at Hydraulic Fracture Test Site 1 acts to increase if the ratio of the normal‐to‐shear fracture compliance is less than about 0.5. Sub‐horizontal fractures may also increase and could affect the vertical extent of hydraulic fractures. Relations between elastic moduli C33 and C55 in the Upper and Lower Wolfcamp in a vertical pilot well allow C33 to be predicted in a lateral well using measurements of C55 in that well. Comparison of Thomsen's anisotropy parameters and , with calculated from the measured values of C55 and C66 and calculated from the measured values of C11 and predicted values of C33, show that  is mostly greater than .

The total magnetization of an underground magnetic source is the vector sum of the induced magnetization and the natural remanent magnetization. The direction of the total magnetization serves as important a priori information in the inversion and processing of magnetic data. We demonstrated that the total gradient of the magnetic potential with vertical magnetization constitutes the envelope of the vertical component of the magnetic field for all directions of the Earth's field and source magnetization. The total gradient of the magnetic potential with vertical magnetization and the reduction‐to‐the‐pole field simultaneously tend to achieve maximum symmetry near the correct total magnetization direction. As a result, the total magnetization direction can be estimated by computing the correlations between the reduction‐to‐the‐pole and the total gradient of the magnetic potential with vertical magnetization. The proposed method yields accurate magnetization directions in synthetic model examples. The total gradient of the magnetic potential with vertical magnetization is less susceptible to data noise than transforms which are derived from the high‐order magnetic field derivatives or tensors. The estimation results are slightly affected by changes in the source magnetization direction. In a field example in the Weilasito region (North China), the reduction‐to‐the‐pole fields calculated using the estimated magnetization directions are well centred over the source. The proposed method obtained a more focused magnetization direction than that of a three‐dimensional magnetization vector inversion. The total gradient of the magnetic potential with vertical magnetization therefore provides a novel and accurate approach to determine the total magnetization direction from the total field anomaly in a variety of situations.

The accurate identification of water‐bearing structures is urgently required for the safe construction of tunnel engineering. Currently, the direct current resistivity method is an effective method for detecting water‐bearing structures in tunnels. In the advanced detection of the direct current resistivity based on the finite element method, the traditional hexahedron mesh performs poorly for the discretization of models of complex tunnel structure sections such as horseshoe‐shaped and round sections. Therefore, this study adopts unstructured grid generation technology combining tetrahedra and hexahedra to achieve more accurate modelling of complex structures, such as round and horseshoe‐shaped sections, and establishes a forward modelling method of the direct current resistivity in tunnels based on an unstructured mesh. The maximum error between the numerical simulation and theoretical results for an infinite tabular body in full space is less than 0.8%. It is more complicated to calculate the sensitivity matrix and model constraint term for the inversion region containing two types of grid than for one. For this purpose, the sensitivity matrix of different types of grid areas is calculated, a model constraint term based on the dual constraints of volume and distance is constructed, and finally, a partitioned domain‐weighted least‐squares inversion method based on an unstructured mesh is proposed. Synthetic examples of typical water‐bearing structures are analysed, and the results show that the proposed forward and inverse methods of the direct current resistivity in tunnels based on an unstructured mesh can effectively capture the position and morphology of the water‐bearing structure. Finally, an on‐site application was conducted in the Yellow River Diversion Project in central Shanxi. The proposed method could effectively identify the water body in front of the tunnel face and guide the on‐site construction of the project. These results can improve the interpretation of the direct current resistivity data in tunnels and play a positive role in promoting the use of the direct current resistivity method to prevent and control water‐inrush disasters in tunnels with complex structures.