Reparing a sloping lawn

I've got this side yard (photo link below) on a slope where water has been washing top soil away for a year or so. There is only dried thatch now. I made some terrace-like rows using a shovel, hoping this would collect enough water to get some new grass seed going.

So far the openings are catching the water. Think it has a chance of working?

LR&T

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I forgot to say.... this area still has a little Bermuda grass. I did not want to damage the roots any more than necessary, so I just pushed the shovel down about 4 inch and then levered it back just enough to leave a 1/2-inch or so V-shaped trench for the water to have a place to soak.