MBA mid 2011: Artifacts on screen after wake from deep sleep
Those are very characteristic failures of a hardware nature.


the LVDS cable that carries the signal could be faulty or loose
the GPU could be having problems (perhaps heat related, perhaps not)
the LCD panel could be physically failing or loose or electrically failing
much less likely causes would be RAM, Storage or software (erase and reinstall)


I would start with contacting support in the country of sale and/or country where you are now:


http://support.apple.com/kb/HE57


They will be able to advise you where and how to request a quote for service and then you can decide to pursue hardware repair or further troubleshoot software. Faulty software could cause this, but it's unlikely to come and go and you might waste time reinstalling the OS, clearing preferences, etc…

If the issues only happen after sleep, you might also consider a failure of the RAM or storage where the sleep image becomes corrupt or the part of the RAM that backs the GPU has problems. Again, on an Air, there are no parts that Apple recommends anyone but a trained technician to service, and they have access to additional resources and can send the diagrams to engineering if they don't have enough experience on that particular model. Most Apple store geniuses would know typical failure modes of each model since they see so many broken machines, but they don't work from home or by phone unless you have a paid support plan.