> I actually have no idea how large the differences in the distance from the core to the water surface is in different parts of the world

Taking the core to be a point, the distance to the sea's surface would depend on factors such as

* The earth’s variation from a pure sphere (6,378.137 km (3,963.191 mi) at the Equator and 6,356.752 km (3,949.903 mi) at the poles) [0, 1]

* The local depth of the sea (up to 10,984 metres for the Mariana Trench [2])

* Tidal effects [3]

[0] https://en.wikipedia.org/wiki/Spheroid

[1] https://en.wikipedia.org/wiki/Figure_of_the_Earth

[2] https://en.wikipedia.org/wiki/Mariana_Trench

[3] https://en.wikipedia.org/wiki/Tide