Forward modeling of pseudo P waves in TTI medium using staggered grid

A tilted transversely isotropic (TTI) medium is a good approximation for anisotropic problems. We discuss the property of a 3D tilted transversely isotropic (TTI) medium and use pseudo P waves to simulate the P component of the elastic wave field in the weak elastic anisotropy approximation. We compare forward features of 3 second-order difference equations of pseudo P waves based on Hooke's law, elastic wave projection and dispersion equation, respectively. Now numerical calculation of these equations uses regular grid finite difference method, which is of low efficiency, low accuracy and is unstable in TTI simulation. In order to improve the calculating accuracy, this paper builds the staggered grid finite difference format for each forwarding simulation. Comparing three different numerical expressions of pseudo P wave equation in a 3D TTI medium, we find that the method based on dispersion equation is more convenient to simulate elastic P wave propagation and has lowest numerical noise. By analyzing the frequency dispersion characteristics based on different angles of isotropic symmetry axis, we introduce appropriate SV wave velocity in calculation to keep calculation stable. An example of a 2D simple synthetic model shows that the staggered grid forwarding method allow us to obtain a smooth and stable pseudo P wave field. With this strategy, 2D BP TTI reverse time migration can also achieve basically stable migration results.