Rotated Staggered Grid Finite-difference And The Combined Boundary Conditions In TTI Media

Anisotropy is a rather common phenomenon, and may be caused by the periodic thin layers and vertical fractures. Theoretically, we use tansverse isotropy with a vertical axis(VTI) and tansverse isotropy with a horizontal axis(HTI) models to describe these two kinds of media. For the tilted near-parallel cracks, the tilted tansverse isotropy(TTI) model is more realistic to describe the crack. On the basis of rotated staggered grid high-order finite-difference scheme of first-order velocity-stress elastic wave equations in TTI media, wavefields are simulated under the combined boundary conditions consisting of Non-spliting Perfect Match Layer (NPML) absorption conditions and the free-surface boundary conditions.The main ideas using the rotated staggered-grid finite-difference (SSG) is to change the direction of derivation, in order to get a new distribution of the wave field and parameters in media on the finite-difference grid. In the rotated staggered-grid finite-difference (SSG) schemes, spatial derivatives of variables are calculated on the diagonal of the corresponding grid. That is to say, the spatial derivatives are calculated along two diagonal in each finite difference cell. This method can realize any even-order difference approximation. On this basis, the paper established first-order velocity-stress elastic wave equations in TTI media by using rotated staggered-grid finite-difference scheme.Not only to avoid the complexity and the huge storage of auxiliary variables in solving wave equation under the splitting PML boundary conditions, but also to overcome the convolution computing problem in time domain involved in Non-splitting PML, this paper approximately calculates the time integrals by trapezoidal integration, and make further efforts to realize the Non-splitting PML boundary conditions taking advantage of the recursive integration. Moreover, this paper introduces the image method for free-surface boundary conditions. On the basis of the above, the thesis implements the wavefields modeling under the combined boundary conditions consisting of Non-splitting PML and free-surface boundary conditions.Using the rotated staggered-grid finite-difference scheme of first-order velocity-stress elastic wave equations in TTI media and the combined boundary conditions, the paper realize the modeling of wavefileds in TTI media. Numerical simulation results show that the NPML works particularly well for absorbing reflection from the artificial boundary. Moreover, applying the combined boundary conditions, Rayleigh surface wave propagating along the free-surface, the ghost reflection, and the PS converted shear wave generated from the free-surface are simulated. The results indicate the rotated staggered-grid finite-difference numerical simulation of elastic wavefields in the TTI media based on the combined boundary conditions is feasible and valid.