  For a locally nilpotent integrable connection on a proper (strict) semistable
family over a small polydisc with a relative horizontal simple normal crossing
divisor, we construct a canonical section in derived categories inducing an
isomorphism from the log de Rham cohomology of it on the log special fiber of
this family to the stalk of the higher direct image of it at the origin modulo
the maximal ideal of the localization of the structure sheaf at the origin. As
an application of the existence of this section, we prove the following: (1):
the locally freeness of the higher direct image by a purely algebraic method;
(2): the existence of a canonical isomorphism between the base change of the
log de Rham cohomology of the log special fiber to the small polydisc and the
higher direct image above. The result (2) tells us that the higher direct image
has the crystalline nature: the invariance of the higher direct image.
