  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.
