Running and disc height loss occurs with moderate intensity after 30 minutes.
Many people complain about spinal related pain in and around the act of running. Here is a wonderful article from Medicine and Science in Sports and Exercise. Running is a form of spinal compression but it is also a form of decompression.
These researchers found that the net result of 30 minutes of moderate running caused significant disc height loss in the spine. They found the discs lost about 6% of their height which can be quite substantial if the discs are already compressed.