Basing on a particle network model, we have developed a dynamic lattice approach to simulate seismic wave propagation in transversely isotropic (TI) media with tilted symmetry axis (TTI). Different from other wave-equation-based numerical methods, the dynamic lattice approach calculates the micromechanical interactions between particles in the lattice instead of solving the wave equation. We implement Lagrange’s equations to transform these interactions into elastic forces acting upon each particle. By solving the equations of motion, we obtain the disturbances of particles. Therefore, seismic wave motions in continua are approximated by displacements of these particles. Elastic features of the continuum are represented by properties of the particle lattice, including the physical properties of particles and the micromechanical interactions between particles. In the case of TI media, it is a challenge to find the correct particle lattice model that can reflect the anisotropic nature of TI media. We have determined the theoretical connection between the TI medium and the particle lattice model, allowing us to model elastic seismic waves in heterogeneous TI media. Furthermore, we have linearized the propagator to improve the CPU efficiency of our method for seismic wave simulation. We have applied the method to reverse time migration on a TI model to test its usefulness in complex media imaging.

One advantage of one-way wave equation-based migration is its low computational cost. However, due to the limited wavefield propagation angle, it is difficult to use one-way wave equation-based migration for high-precision imaging of structures with large inclinations due to issues such as inaccurate amplitudes and migration image artifacts. In addition, when the model has large horizontal velocity differences, it is difficult for the one-way wave propagator to calculate an accurate wavefield phase. Reverse time migration (RTM) based on the two-way wave propagator has a high resolution and avoids the issues associated with one-way wave propagators; however, it has a high computational cost in practical applications. We develop a convolutional neural network (CNN) application mode that improves one migration method by learning from another one and design a CNN with a structure similar to U-net that combines the advantages of both migration methods. The CNN label is the RTM result, and the corresponding input is the result of one-way wave migration with a generalized screen propagator (GSP). The trained CNN model improves the amplitude in the one-way wave migration image and removes the errors caused by large lateral velocity perturbations. Moreover, by maintaining the high migration calculation efficiency, our CNN model allows for a high resolution, few artifacts, and accurate images of steep structures in the one-way wave migration result. With our method, the accuracy of the one-way wave migration result is close to that of the RTM result. The use of GSP-based migration in our CNN model rather than conventional RTM to generate prospecting images can considerably reduce the calculation costs.

The discrete particle-based dynamic lattice method (DLM) offers an approach to simulate elastic wave propagation in anisotropic media by calculating the anisotropic micromechanical interactions between these particles based on the directions of the bonds that connect them in the lattice. To build such a lattice, the media are discretized into particles. This discretization inevitably leads to numerical dispersion. The basic lattice unit used in the original DLM only includes interactions between the central particle and its nearest neighbours; therefore, it represents the first-order form of a particle lattice. The first-order lattice suffers from numerical dispersion compared with other numerical methods, such as high-order finite-difference methods, in terms of seismic wave simulation. Due to its unique way of discretizing the media, the particle-based DLM no longer solves elastic wave equations; this means that one cannot build a high-order DLM by simply creating a high-order discrete operator to better approximate a partial derivative operator. To build a high-order DLM, we carry out a thorough dispersion analysis of the method and discover that by adding more neighbouring particles into the lattice unit, the DLM will yield different spatial accuracy. According to the dispersion analysis, the high-order DLM presented here can adapt the requirement of spatial accuracy for seismic wave simulations. For any given spatial accuracy, we can design a corresponding high-order lattice unit to satisfy the accuracy requirement. Numerical tests show that the high-order DLM improves the accuracy of elastic wave simulation in anisotropic media.

An element-free method (EFM) has been demonstrated successfully in elasticity, heat conduction and fatigue crack growth problems. We present the theory of EFM and its numerical applications in seismic modelling and reverse time migration. Compared with the finite difference method (FDM) and the finite element method (FEM), the EFM has unique advantages: 1) independence of grids in computation and 2) lower expense and more flexibility (because only the information of the nodes and the boundary of the concerned area is required). However, in EFM, due to improper computation and storage of some large sparse matrices, such as the mass matrix and the stiffness matrix, the method is difficult to apply to seismic modelling and reverse time migration for a large velocity model. To solve the problem of storage and computation efficiency, we propose a concept of Gauss points partition (GPP) and utilise the Graphics Processing Unit (GPU) to improve the computational efficiency. We employ the compressed sparse row (CSR) format to compress the intermediate large sparse matrices and attempt to simplify the operations by solving the linear equations with CULA solver. To improve the computation efficiency further, we introduce the concept of the lumped mass matrix. Numerical experiments indicate that the proposed method is accurate and more efficient than the regular EFM.

Reverse time migration (RTM) is a powerful seismic imaging tool that suffers from high computational complexity when dealing with massive data. The simultaneous-shot method can effectively reduce the amount of migration by assembling several sources, although it adds crosstalk noise, which seriously affects the quality of the RTM results. To avoid this problem, we have adopted a time-domain scheme that combines time-delay encoding and amplitude encoding to reduce crosstalk artifacts in simultaneous-source imaging results. This scheme modulates the wavefields of multiple sources to fit the wavefield of a suspended super-virtual shot (SVS), which can eliminate crosstalk artifacts because they are absent in single SVS migration. Numerical examples on a steeply dipping model and the 2D SEG/EAGE salt model show the feasibility of the proposed method. SVS encoding can generate a qualified imaging result and takes less time than plane-wave encoding in the migration process.