Global geometrical optics method is a new semi-classical approach
for the high frequency linear waves proposed by the author in
[13]. In this paper, we rederive it in a more concise way. It is shown that the right
candidate of solution ansatz for the high frequency wave equations is
the extended WKB function, other than the WKB function used in the
classical geometrical optics approximation. A new and main
contribution of this paper is an interface analysis for the
Helmholtz equation when the incident wave is of extended WKB-type.
We derive asymptotic expressions for the reflected and/or transmitted
propagating waves in the general case. These expressions are valid
even when the incident rays include caustic points.