First of all, the vector sum is rarely used and should be ignored unless there is a need for it to be referenced. Each time the seismograph takes a sample, there is a value for the radial (longitudinal), vertical and transverse. The vector sum at that sample is the square root of the sum of the squares of those values.
At time t = 1.0 Second
Radial = 0.30
Vertical = -0.15
Transverse = 0.27
Vector Sum = Sqrt(0.09 + 0.0225 + 0.0729) = 0.43
This is just the vector sum at a time of 1.0 second. At the next sample time there will be another vector sum value. The peak vector sum is the largest of all of these values.