The depth required is different at all locations on the globe... it changes due to proximity to a water source, soil composition, elevation, any number of factors really...
To be honest with you this idea is too costly to implement. the metal tubing that you will have to drop into the ground would be a coil of copper about 50 ft (25 ft min, 25 coils of 1 ft circumference) with an ID of 1/4; that right there will run you about $40 USD.
Then you have to dig the hole or in most cases have someone dig it for you. with the transfer sink being 1ft coils the hole will only have to be about 1/2 ft diameter and 6-50 ft deep. no sense in diging it by hand at that point.
as you can see the cost adds up fast, it really isnt practical.
I have built a geo-thermal air conditoner for my house. it incorporates copper tubing, a fan, some hose, and a cooler of ice, I kept away from diging up the backyard when i realized the significant cost involved.
When i get a second to run out to my car I will grab my air-conditoner and snap a pic to show everyone.