Perfectly matched layers simulation in 2-D VTI media

Abstract: Implementing computational boundary conditions, such as perfectly matched layers PML does have advantages for forwarding modeling of the earth's crust. The mathematical modeling of many physical problems encountered in industrial applications often leads to a system of linear partial differential equations-PDEs. It considerably improves the visualization of seismic events relevant to oil and gas exploration. In this work, we present an efficient numerical scheme for hyperbolic partial differential equations where a computational technique takes care of reflections at the borders domain using a linear 2-D elastic-wave system of decoupled equations with PML-type boundary conditions. The key idea is to introduce a layer that absorbs the reflections from the borders improving images visualization. Anisotropy has been reported to occur in the Earth's three main layers. The crust, the mantle, and the core; but this implementation refers to the case of a vertical transversal anisotropic medium VTI in the crust-layer. Images and screen-shots of the longitudinal P impulse-response and the SV transverse impulse-response are obtained at different times. This computational method enables us to achieve images for the P and SV response-impulses, and to obtain high quality synthetic seismograms for the PP and PS reflection events in a 2-D VTI two-layer model.