A novel computational method to evaluate the Sommerfeld integral (SI) efficiently and accurately is presented. The method rewrites the SI into two parts, applying discrete complex image method (DCIM) to evaluate the infinite integral while using double exponential quadrature rules (DE rules) for the computation of the finite part. Estimation of signal parameters via rotational invariance techniques (ESPRIT) is used to improve the accuracy and efficiency of extracting DCIM compared to the generalized pencil of function (GPOF). Due to the symmetry of the horizontal layered media, the Green function, representing the seismic fields due to a point source, can be written in the form of Sommerfeld integral in cylindrical coordinate system and be calculated by the proposed method. The performance of the method is then compared to the DE rules with weighted average partition extrapolation (WA), which shows a good agreement, with computational time reduced by about 40%.

One of the significant challenges in processing and analyzing seismic data is the contamination of the seismic signal with noise from various sources. Coherent or incoherent noise, multiples, and other types of noise can all be eliminated using a number of techniques, but it is still complicated to attenuate random noise to the desired level. The non-homogeneous curvelet transform is first applied in this study, and the regularized calculation is then carried out using the inverted operator. Following the application of the linear calculation method, the threshold value is modified to remove the coefficient noise during the iteration process, allowing the homogeneous coefficients and noise-free seismic data to be obtained. We choose some real data as an example and apply the suggested curvelet theory to obtain homogeneous data in order to verify the denoising effect. Tests on real data show that, when the suggested approach interpolates sampled data to be homogeneous, random noise can be effectively reduced. The important benefit of this approach is that features like multi-resolution, and locality introduce minimal overlapping between coefficients representing signal and noise in curvelet domain.

When the grid-based finite difference (FD) method is used for elastic wavefield forward modeling, it is inevitable that the grid divisions will be inconsistent with the actual velocity interface, resulting in problems related to the stepped grid diffraction and inaccurate travel time of reflected waves. The generalized finite difference method (GFDM), which is based on the Taylor series expansion and weighted least square fitting, solves these problems. The partial derivative of the unknown parameters in the differential equation is represented by the linear combination of the function values of adjacent nodes. In this study, the Poisson disk node generation algorithm and the centroid Voronoi node adjustment algorithm were combined to obtain an even and random node distribution. The generated nodes fit the internal boundary more accurately for model discretization, without the presence of diffracted waves caused by the stepped grid. To avoid the instability caused by the introduction of boundary conditions, a Cerjan damping boundary condition was proposed for boundary reflection processing. The test results generated by the different models showed that the generalized finite difference method can effectively solve the problems related to inaccurate travel time of reflection waves and stepped grid diffraction.

Once a coal seam has been weathered and oxidized, the quality of the coal is lost and the coal resources are wasted. At the same time, new risks are introduced to the safe operation of the coal mine. Therefore, it is critical to determine the extent of the weathered and oxidized zone in the coal seam. This paper depicts the electromagnetic characteristics of the weathered and oxidized zone of coal seams, briefly introduces the method of detection by transient electromagnetic method (TEM) and the data processing steps, and performs the numerical simulation for the simplified resistivity model of weathered and oxidized zone in a coal seam. It is observed that after the coal seam has been weathered and oxidized, the electromagnetic characteristics (secondary field potential and resistivity) will be dramatically affected, namely high secondary field potential and low resistivity. For experimental verification purposes, this study selects the test project of the Shixin Minefield in Shanxi, China as an example, and the accuracy for the detection of the weathered and oxidized zone of the coal seam using TEM is successfully verified.

In this study, the meshless generalized finite difference method (GFDM) was used to simulate elastic wave propagation in the frequency domain, and the performance of this method was studied through dispersion analysis and numerical experiments. The dispersion analysis indicated that the GFDM requires approximately 5.6 grid points in a shear wavelength to suppress the dispersion error of 1% with a regular node distribution. To handle the artificial boundary reflection problem, a multiaxial convolutional perfectly matched layer (MCPML) was introduced into the meshless numerical simulation for its good performance. Numerical experiments show that the meshless generalized finite difference method can effectively avoid stepped diffraction and reduce the total number of nodes for the calculation by adopting an adaptive node distribution according to the model parameters. By comparing the memory consumption and calculation time with the 25-points finite difference method (FDM), the method proposed in this study is a reliable numerical simulation method for elastic wave simulation in the frequency domain with high calculation accuracy, less memory consumption, and good boundary absorption effect.