In Sorting and categorising the world's militaries, I asked about categorising modern human militaries with respect to destroying the Snakebot of Doom, and it was pointed out that this might not be the best way to ask the question. So...
How best might the Snakebot of Doom reduce the threat posed by modern human militaries so that it can get on with its task of flattening human infrastructure in the absence of any meaningful opposition? Where would it best begin its task of flattening human infrastructure?
The SoD's nanites have specific instructions from its programmers:
Only one active military unit - the SoD itself - may be constructed. No duplication or changing form is permitted.
The SoD is to demolish any human structure any larger or more complex than a tent or other improvised shelter. It need not concern itself with portable devices, objects, vehicles or the infrastructure concerned with transmission of power, water, data or any other utility save as necessary to advance its objectives.
Nanites may gather intelligence, but must not reveal their existence to, openly communicate with, allow themselves to be examined by or come into physical contact with humans. Covert communication is permitted as long as it does not have a significant risk of revealling the existence of and its connection with the nanites.
Damage received in the course of the SoD's activities is to be repaired, unless that damage is such that the SoD cannot continue its mission, in which case the SoD and all nanites must self-destruct.
When its task of demolishing human structures is completed, the SoD and all nanites must self-destruct.
Where possible, the natural environment of Earth and its flora and fauna should be preserved, providing that this does not conflict with the previous instructions.
The Snakebot of Doom is 446 metres in diameter, with a body that is cylindrical for 7480m, and then tapers down to a point over a further 669m, the tail matching with a similarly shaped mouth. Its internals are made from a compound functionally similar to an AZ91D/SiC syntactic foam composite, with density of 0.97 g/cc, or 970 kg/m3. Its armour - which is 14 metres thick - is made from Tungsten-depleted Uranium alloy plates with a surface coating of Boron Carbide, and underlaid by an open energy-absorbing magnesium alloy foam.
The Snakebot of Doom weighs 1.486 billion metric tons with an effective density of 1271 kg/m3, has a maximum footprint of 3.34 square kilometres, and a ground pressure when on its belly of 4.3 MPa and when rolling in a hoop, a ground pressure of 13 MPa, on the order of the ground pressure of a woman running in stiletto heels. While these ground pressures are high for a vehicle, this is acceptable, as its purpose is to destroy infrastructure - even below ground - by rolling on it.
The snakebot is equipped with a multitude of sensors on its skin, including optical sensors from the far UV to the far IR, electromagnetic sensors, audio sensors (for what it matters given that it would most likely have to stop moving to hear anything) and radiological sensors. It also has broad-band radar and lidar capabilities. While these sensors are surface-mounted, they may be retracted for defensive purposes (and to protect them if the snakebot rolls), and replacements are available further beneath the armour in case of battle damage.
The snakebot is armed with 512 "small" railguns firing unguided steel 4.5x72mm flechettes at 5000 m/s, at 24 around rounds per second, 128 or so "medium" railguns dispersed over its outer armour, each firing a steel command-guided and optically-self-guided flechette about 18x288mm long at velocities of around 5000 m/s, at around two rounds per second.
It is also armed with six large railguns in its "mouth", only one of which is available for use at any time, the others being retained deeper beneath the mouth's armour as immediate-use backups, firing 144mm diameter, 2304mm long optically-self-guided munitions at a velocity of around 7000 metres per second, at about 40 rounds per minute. These munitions may be single depleted-uranium long-rod penetrators, or they may be capable of breaking up into hundreds of unguided steel sub munitions at some point prior to impact.
As a weapon of last resort, the Snakebot of Doom can launch up to sixteen scramjet-propelled ballistic missiles each containing a fusion warhead in the eighty-megaton range, with built-in ECM, ECCM and anti-anti-missile defences (small command-guided railguns), before having to take around two weeks to build replacements.
Resupply of these munitions (except for the depleted uranium and atomic munitions, which would be used sparingly) would be by the expedient of the snakebot "eating" ferrous human infrastructure and processing it into more ammunition. To address a point made that guided munitions would be difficult to fabricate, these are being produced by nanoassemblers, and are not significantly more difficult for them to produce than an unguided projectile. The limiting factor is surface area and nanobot availability.
The snakebot is supported by a multitude of nanite-controlled birds which act as its spies. The controlled birds act naturally as far as possible, and each bird stays within its species' natural range. They will not attack and neither will they defend themselves from attack beyond those attacks or defences typically used by their species. However, they are able to observe the preparation of human defences and the Snakebot of Doom is able to act on this intelligence, if necessary by destroying the defended area with its stand-off railguns instead of simply flattening the area.
Prior to commencement of the attack, the snakebot's nanites have also tapped into the public internet, however, they cannot rapidly decrypt secure communications, not being equipped with quantum computers (unlike their military nanite brethren, which were not deployed on this mission).
The SoD is not interested in exterminating humanity. Individual humans are of little interest to it unless they are - or are capable of - counter-attacking with any effectiveness, at which point the snakebot will simply eliminate the threat in the most expeditious manner possible given its options. However, neither will it attempt to preserve the life of humans or any other species.
If damaged, the snakebot's controlling nanites will use whatever materials available within the machine's structure and in the environment to effect repairs. The snakebot took around ten years to build beneath the Antarctic ice-cap, and the time to repair damage can be expected to be roughly inversely proportional to the amount of damage - the more damage, the more nanites will be required to repair it, and conversely the slower the repairs will be. Relatively minor damage can be expected to take as little as a few hours, and major damage such as the total loss of one reactor can be expected to take many months to a year or more.
It has been mentioned in previous questions that the SoD is vulnerable to liquid oxygen. This is ridiculous. The SoD's flammable internals are sealed behind 14m of airtight armour, and for good measure, the internals are flooded with pretty pure nitrogen. It would take at least two major breaches of its armour to allow for its internals to be ventilated sufficiently to be sufficiently oxygenated to burn. It is less vulnerable to LOX than a human in full NBC protective gear who is sitting inside a tank is vulnerable to VX.
Secondly, it has been mentioned that near-misses from nukes could destroy the SoD. Don't forget that tungsten & uranium have very high melting points, and there are such things as thermal capacity, thermal conductivity and heats of fusion and vaporisation. Sure, a nuke detonating nearby would raise the external temperature a lot, but a billion tons of W-U armour would take a lot of heat to get hot, it would take time for that heat to penetrate the armour, and it would take still more energy to melt and then vaporise that armour, during which time, the heat from the nuclear detonation would be rapidly decreasing. Sure, some armour might be ablated, but probably not 14m of it. And that is only if a nuke can get close enough without the SoD's very effective point-defense shooting the nuke(s) down. Damaged nuclear warheads don't detonate at full effectiveness - at best they fizzle, if they can detonate at all. Consider that during nuclear tests, warships were exposed to nuclear airbursts, and those that weren't capsized by the shockwave remained afloat with relatively little damage to their bulk structure.
Humanity's best chance of eliminating the SoD is to use nuclear mines to force the SoD to traverse gaps between continents in a less-than-optimal route, where its open-air weapons are largely ineffective, and use nuclear depth-charges on it. However, the SoD is well aware of this...
Prior to its first attack, the SoD may appear by surprise at any point on any coast in the world that it can reach from Antarctica without having to surface to traverse shallow areas. After this, humans will be aware of it, and it must act accordingly.