The largest pressure occurs at the location of the event causing it, ie, a valve closing downstream will cause maximum pressure at the upstream face of the valve. When that pressure rises to the maximum, reverse flow begins to carry the pressure wave back to the origin of the pipeline, however frictional resistance to that reversed flow causes the pressure along the pipeline now to fall from that maximum at the face of the valve toward the pipeline's origin. In effect the face of the valve becomes the new pipeline "inlet" and you now have to deduct friction from the reverse flow velocity for each and every foot that the reverse flow travels as it goes back to the pump. When that wave reaches the pump and presumedly a now closing discharge check valve there, the pressure has been decreased from the maximum considerably. When the wave hits the closed check, now at a slower velocity, the pressure spike from that reflection is not as high as the first one originally created at the downstream valve, and it reverses again; flow is once again in the original direction, but now at slower velocity. That occurs 3 to 5 times, each reflected spike less than the previous, before things eventually calm down. The time between spikes is the time that the pressure wave takes to move between original closed valve and pump at the sonic velocity of water, close to 3000 ft/sec. So if the valve was 3000 feet from the pump, it would be 1 second before you saw the first reflection reach the discharge check and 2 more seconds before you see the next spile reach the pump, now the 3rd reflected wave. At about 4 or 5 reflections, there probably isn't much left of the original max pressure wave.
BTW a partially closed valve, or a reducer in the pipeline will reflect a spike proportional to the amount of x-sectional flow area reduction it gives, ie a valve 40% open will reflect 60% of the wave back to the pump while allowing 40% to pass through. A 6 x 3 reducer will reflect 75% of the spike allowing 25% of the spike to pass.
Checks in the line would probably stop most of the reflections from traveling from the closed valve back to the pump, but wouldn't do much of anything to mitigate the original pressure spike at the face of the closing valve. IMO.
From "BigInch's Extremely simple theory of everything."