how prominate is the "thud"? you cant hear it, but where do you feel it and to what intensity? is it like hitting a pothole jolt, or someone closing a door, or something lite like someone tapping on the steeringwheel or the back of your seat?

if there is a tick along with the thud and it sounds electrical, it might be. id say run the car at night with the lights off and watch the spark plugs and wires, you might be grounding out or arcing from the plugs/wires or between them and the motor somewhere, you should be able to clearly see a blue flash at the problem sight if its external...or you could pull the wires off of the plugs CAREFULLY and confirm the "snap snap snap" sounds goes away when you push the boot back on the plug. you could through a dab of dielectric in there to help, but your wires might be cracked inside where they angle to go back into the wire (the clip that actually connects to the back of the plug.) follow the wires back too, perhaps they are arcing or grounding somewhere along they way, are they touching or too close to the exhuast manifolds? or the plugs might have crosstheaded or have cracked insulators (white porcelain part) they might have burned up there, or back by the coil. Be carefull with the coil though, obseve it best you can with a mirror, but dont touch the thing unless the cars off, batterys disconnected and you give it a good sit period to discharge and risidual current. your plugs culd also not be in correctly or completly fouled, they go bad quick if they are missfiring, they could ash up or black out with carbon...and with the spark with no where to go but to the motor you could hear the pop, see it most likely, and you would feel a slight shudder from the missfire. speeding up the rpm MIGHT be enough to muffle the vibration or popping or cause enough voltage to gap the plug and have it function at speed...if thats what you are noticing that is...

i doubt its the sai pump, but if one of the connections was loose or the valves not accuating (or the pump itself broken or housing lose/cracked) youd get a very audible change like a low rumbling or loud hairdrier sound, and only for the first 30 seconds on a cold start...after which the sound would go away. it wouldnt be enough to "detonate" fuel in the exhuast from a missfire, if it where, youd hear a pop through the exhuast pipe rather noticebly.

if your intake valves are dirty, bend or not seated, you could have a backfire wave into the intake manifold which you would also hear very clearly, not a tick but a definat bang or pop, so i dont think its that either.

bottom line, id check the entire ignition system first, rule out the simple stuff that go bad regulalry from wear (tune up items) and go from there.