Could anybody tell me how I can use sed to modify lines following specific lines? the file is as following:

"TEST/SI1573.lab"
3670 8920 h#
8920 9530 hh
9530 10694 ih
.
"TEST/DR1/FAKS0/SI2203.lab"
9730 9580 h#
9580 9840 dh
9840 10652 ix
10652 11997 r
........

I want to modify the first fields to 0 of the lines which follows the lines started with "TEST. The file after operation should be:
"TEST/SI1573.lab"
0 8920 h#
8920 9530 hh
9530 10694 ih
.
"TEST/DR1/FAKS0/SI2203.lab"
0 9580 h#
9580 9840 dh
9840 10652 ix
10652 11997 r
........
could anybody tell my how to do that? Thanks in advance.