High-order Staggered-grid Finite-difference Method Research Articles

Numerical simulation of the seismic wave propagation and fluid pressure in complex porous media at the mesoscopic scale

In this study, we apply an improved high-order staggered-grid finite difference method to model seismic wave propagation in complex heterogeneous porous media with cracks. Upon changing the mesh step and applying a broadband wavelet, we obtain numerical simulation results at the mesoscopic scale. As a fundamental result of applying Biot’s theory, three types of waves are also found. We discuss the relationship between the shear wave splitting parameter and the crack density of an equivalent medium in detail. Based on Darcy’s law, the finite element method is used to investigate the distribution of the fluid pressure field in porous media at the mesoscopic scale. A flat ellipse is used as an approximation of a crack. According to the simulation results, we further study the influence of variations in the crack angle on the distribution of the fluid pressure. Moreover, the formulas derived from the Fourier transform are used to calculate the inverse attenuation quality factors and phase velocities of the fast compressional wave, slow compressional wave and shear wave. The effects of the porosity and elastic modulus of an equivalent medium on wave attenuation are also taken into account in this study.

Numerical simulation of ultrasonic wave transmission experiments in rocks of shale gas reservoirs

Shale gas reservoirs have risen in importance in China’s new power source exploration and development program. The investigation of the propagation of ultrasonic waves in shale forms the basis for the full waveform application of acoustic logging data to the exploration of shale gas. Using acoustic wave theory, initial conditions, vibration source conditions, and stability conditions are developed in combination with experimental background of ultrasonic wave transmission. With improved boundary conditions, we performed numerical simulations of the ultrasound transmission experiments in shale using the high-order staggered-grid finite difference method (second-order in the time domain and fourth-order in the space domain). With programs developed within MatLab, the results obtained from numerical simulations agree well with experimental results based on physical models. In addition, using snapshots of the wave field that give a microscopic perspective, the propagation laws for ultrasonic waves can be analyzed. Using this method, human error is avoided, transmission experiments costs can be reduced and efficiency improved. This method extends the scope of experimental investigations regarding the transmission of ultrasonic waves in a shale gas reservoir with increasing stratification, and thus has great theoretical value and practical significance.

Prestack reverse-time migration with a time-space domain adaptive high-order staggered-grid finite-difference method

With advanced computational power, prestack reverse-time migration (RTM) is being used increasingly in seismic imaging. The accuracy and efficiency of RTM strongly depends on the algorithms used for numerical solutions of wave equations. Hence, how to solve the wave equation accurately and rapidly is very important in the process of RTM. In this paper, in order to improve the accuracy of the numerical solution, we use a time-space domain staggered-grid finite-difference (SFD) method to solve the acoustic wave equation, and develop a new acoustic prestack RTM scheme based on this time-space domain high-order SFD. Synthetic and real data tests demonstrate that the RTM scheme improves the imaging quality significantly compared with the conventional SFD RTM. Meanwhile, in the process of wavefield extrapolation, we apply adaptive variable-length spatial operators to compute spatial derivatives to decrease computational costs effectively with little reduction of the accuracy of the numerical solutions.

P- and S-wavefield simulations using both the first- and second-order separated wave equations through a high-order staggered grid finite-difference method

In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equations. In this study, we compare two kinds of such wave equations: the first-order (velocity–stress) and the second-order (displacement–stress) separate elastic wave equations, with the first-order (velocity–stress) and the second-order (displacement–stress) full (or mixed) elastic wave equations using a high-order staggered grid finite-difference method. Comparisons are given of wavefield snapshots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corresponding first-order or second-order full elastic wave equations. These mixed equations are computationally slightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-component processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.

Multi-Azimuth Three-Component Surface Seismic Modeling in Cracked Monoclinic Media

The snapshots of the seismic wave propagation in monoclinic media are simulated using high-order staggered-grid finite-difference method. The monoclinic medium is a typical anisotropic model in fractured reservoir which includes two sets of non-orthorhombic vertical fractures in isotropic background and with different fracture infill. The modeling results show that the velocities of wave propagation in anisotropic models vary greatly in different directions, and the property of the fracture infill has a strong effect on velocity anisotropy. Then the axial rotation method is used in the modeling of multi-azimuth three-component surface seismic data in layered monoclinic media. The results illustrate that seismic velocities vary in directions not only with the polar angle, but also with the azimuth angle. Furthermore, the numerical modeling results may provide a theoretical basis for the inversion of anisotropic parameters and the fracture parameters by using the surface multi-azimuth seismic attributes.