"ground invasion of North Korea" or any attack of North Korea is a sure way to see the destruction of Seoul and other major cities in South Korea.  Now that NK has nukes and likely many short and intermediate range missiles to carry them, where do you think they are aimed at?  SK, of course, and maybe Japan.

Let's face it, SK has had over 60 years to establish better relations with NK.  They didn't do anything but rely on the U.S. for protection.  They totally underestimated NK.  Now that NK has nukes, the U.S. cannot protect them so they better start talking to NK fast.