Theoretically,
in order to calculate the ray influence as accurately as possible the vector
(see section 5.1)
is required to be perpendicular to the polarization vector
(or, alternatively, parallel to
).
For an arbitrary position of the hydrophone such condition implies traveling along the ray,
until the condition
is fullfiled.
In such case the normal corresponds to

Numerical calculations indicate that there is no significant loss of accuracy
(and requires much less computations) to take

(i.e., at each hydrophone range one interpolates ray depth,
so
becomes a vertical vector,
connecting the ray to the hydrophone)
and to calculate the normal as

Orlando Camargo Rodríguez
2012-06-21