I want to create a bathymetry map of a gulf using spline with barriers.When the interpolation finished the map in the gulf was created very well but a value is also created around the island. I tried to close the gulf with a line or making a polygon in order to "keep" the prices within it and failed again! Does anyone know the reason?
If I understand your question correctly, the gulf is part of an island and you want to contain interpolation to that region. It appears you're using a polygon of the island as the bounding feature, which is why interpolation continues out of the gulf and around the island. You could just clip your output raster to the desired area around the gulf and be done with it, but another approach is to run Polygon to Line on the island polygon, edit the resulting polyline so it bounds only the gulf and is closed off at the mouth. This new polyline should give you the desired result as the barrier in Spline with Barriers.