Why are some parts of this ice block cloudy and other parts clear? I had a sprain in my leg a few days back. The doctor recommended dipping my foot alternately in ice-cold and hot water to aid blood circulation. It is here that I discovered something interesting.

The picture above shows the piece of ice that was put in the bucket. The above picture shows the ice cube from above.
If you look at the large piece of cube from the side (see below), you can see that the upper part of the cube, that was near the open surface of the container in which the ice froze, seems to be almost transparent and has a crystalline appearance. The lower part does not have this appearance, and it is white and opaque.


Why is there a difference in the layers of ice in the large cube? Is it because the water was from tap and not completely pure? The water was put in the refrigerator for a period greater than 12 hours, so the ice has frozen properly. Can anyone explain this unique structure of ice? I've never seen this before.
Update:
This update is to simply demonstrate the bubble formation in the ice,which causes the cloudiness. Out of the two answers, I had accepted the one by @IliaSmilga . Today, the ice formed demonstrated this idea clearly. Given below are the pictures in which the bubbles of dissolved gas are clearly visible.




The last two pictures are the best.
 A: As @pr1268 explained, tap water is not pure: it contains dissolved gases (basically air) and dissolved minerals.
However, I do not think stratification causes this phenomenon: I think that as long as water remains unfrozen, the dissolved gas concentration remains approximately constant throughout the solution (basically equal to the saturation concentration). Here is an alternative explanation.
When ice crystals start to form, they naturally tend to exclude the impurities; so the impurities are "squeezed out" into the part of the water that remains liquid. Eventually the impurity concentration exceeds the saturation threshold, and they start to precipitate out of the solution. But by this time, the ice has already formed an airtight enclosure around the liquid water which prevents gas bubbles from escaping to the surface; and the mineral crystals stay no matter what.
For this reason, on a big lake where only a small portion of the total water freezes, you can get crystal clear ice (unless the water surface has snow, slush or other impurities to begin with).
A: The cloudiness is caused by dissolved air bubbles.  Plus, tap water is notoriously rich in mineral particles (giving nucleation sites).
Seeing how you placed the tap water in the freezer, the cold temperature kept the dissolved gases and minerals in solution, and only partial stratification occurred before the water froze.  The expanding ice1 "magnified" the dissolved gas bubbles, causing the cloudy appearance.  The clear section is that portion of the water from which the gas bubbles and solute had precipitated (sinking in the container, so to speak).
1 Water is one of the very few substances that expands when transitioning from a liquid to a solid state.
