1. A computer-implemented method for pseudo acoustic quasi-P wave propagation which remain stable in variable tilt anisotropic media and is not limited to weak anisotropic conditions, the method includes; acquiring a seismic exploration volume for a subsurface region of interest; determining a modeling geometry for the seismic exploration volume; propagating at least one wavefield through the seismic exploration volume utilizing the modeling geometry for initial conditions and preventing the accumulation of energy along the axis of symmetry of anisotropic regions within the seismic exploration volume and ensuring positive stiffness coefficients in the stress-strain relations utilizing finite quasi-S wave velocities thereby producing a stable wavefield; and utilizing the stable wavefield to generate subsurface images of the subsurface region of interest.