In 3-D the eikonal equation is
For a spherical-coordinates system
The cross derivative equation (4) is transformed into the spherical coordinates system
In equation (11), the Engquist-Osher scheme is applied twice, once for calculating the values of across three points of consecutive values of , and second for calculating the values of across three consecutive values of .The computational front advances in spherical shells, and on each shell the computations advance a circle at a time. The angle is the horizontal angle while the angle is the vertical angle. The Engquist-Osher scheme is applied along each three consecutive points on the circle with constant vertical angle to determine from the equation .For each circle of constant vertical angle the Engquist-Osher scheme is applied for three points (), and (), which are perpendicular on the circle in the coordinates. The scheme is completely vectorizable.