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There is an underground vault containing something very valuable. To prevent robbers from tunnelling to it, the security personnel regularly scans the ground with sound and geophysic sensors. Some robbers are aware of it, but they want to build a tunnel anyway. They have a lot of time, but only access to common building materials. Can they come up with some lining for the tunnel walls which will hide the tunnel?

Just to make it clear, the mechanism to detect tunnels is the following. In a basement there is a heavy piston that at regular interval hits the ground to produce a booming noise. There is an array of fixed sensors that pick up not only reflected sounds, but also secondary transversal waves.

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  • $\begingroup$ There is a plethora of geophysical tests that can be run - some look only straight down, some need signals from some distant source (explosions, neutrinos, AC) - is the security team only carting some kind of detector in a circle around the facility, or is this a huge operation with off-site personnel and static installations that can help? --- Also: what ground-makeup? - if the vault sits on granite, there is no way the robbers can get through this if security is listening into the ground (three microfones around the vault will give you precise location of any underground scratching) $\endgroup$
    – bukwyrm
    Nov 11 '21 at 9:03
  • $\begingroup$ The more immediate problem is that even 50-years old sound technology can hear the tunnel as it is being dug. The audio setup to just listen for digging is much cheaper and simpler than any kind of geo-sonar rig. $\endgroup$ Nov 12 '21 at 15:08
  • $\begingroup$ Also, what I don't get about every heist film ever, with super hi-tech multi-million dollar protection schemes: why not just put a microphone and/or camera in the fricking vault itself. Costs about $100 to do this. $\endgroup$ Nov 12 '21 at 15:14
  • $\begingroup$ @RBarryYoung "even 50-years old sound technology can hear the tunnel as it is being dug." Unless you are in a busy area. Someone might be building a new skyscraper nearby. Or you might have an underground train and dig by exploding microcharges every time a train passes. They built the undergrounds in Oslo and Stockholm using dynamite and the builders claimed that their method created less noise and vibrations than conventional methods. $\endgroup$
    – FluidCode
    Nov 14 '21 at 13:06
  • $\begingroup$ @RBarryYoung "why not just put a microphone and/or camera in the fricking vault itself". If you have an accomplice inside you can disable a sensor for a while. But digging takes a long time and usually the guards are rotated. The access to the vault is a problem not addressed in this question, that would involve passing a lot of other defensive systems. $\endgroup$
    – FluidCode
    Nov 14 '21 at 13:06

13 Answers 13

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No!

Because hiding from ground sonar requires you to not reflect sound back AND not make a "shadow". This is not something common materials and tunnel construction can do.

What is a shadow? Well, if you are used to seeing certain things in your sonar, and suddenly you stop receiving those signals because something is in the way, you are seeing the shadow of the thing. It is the lack of a signal or blocking a signal. Our robbers cannot simply stop the incoming sonar waves- they will cast a shadow if they only do that.

Obviously, a shadow becomes especially concerning when it is slowly making its way to the thing you are trying to protect. Even if it isn't robbers, you likely wouldn't want whatever that is to collide with your vault.

But With More Science...

They COULD achieve this; essentially, you bend the waves around the tunnel to make it seem like it is not there. It is called acoustic cloaking. (https://en.wikipedia.org/wiki/Acoustic_metamaterial) As far as I can tell, this has never been attempted but is possible.

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    $\begingroup$ This is assuming that authorities are using active sonar and not just passive sensors. $\endgroup$
    – Alexander
    Nov 10 '21 at 18:14
  • $\begingroup$ @Alexander Definitely! I inferred this from the question saying "regularly scanning". A passive sensor would imply a computer system monitoring it rather than actual people- which is a different situation indeed! This opens up exploits, depending on what the system is trained to look for, etc. $\endgroup$
    – PipperChip
    Nov 10 '21 at 18:18
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    $\begingroup$ What about first going pretty deep down (like, say, 300 meters or more), then turning perpendicular and tunnelling towards the vault until they're directly beneath it, and then tunnelling directly upwards? Also keep the tunnel as small as possible. The scans won't show up anything directly beneath the vault and a small tunnel very deep would appear so tiny (simply due to the distance) as to be practically invisible. No? $\endgroup$
    – Vilx-
    Nov 10 '21 at 22:44
  • $\begingroup$ @Vilx you may want to make that an answer $\endgroup$
    – TCooper
    Nov 11 '21 at 22:11
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Dig deep and create a distraction

You can avoid being spotted by ground penetrating radar and similar technologies by digging deep. The Woodingdean Water Well was dug by hand to a depth of 1,285 feet.

Secondly, you can avoid detection from sound sensors by making a lot of noise elsewhere. In Better Call Saul, the bad guys cover the sound of underground blasting by having a large truck drive over a road plate at the exact moment of the explosion. If you team has more time and resources, they could come up with an even bigger source of noise. Maybe buy the land nearby and have a never-ending construction site? It would be hard to pick up the sound of tunneling when there's a pile driver next door.

Finally, you could try flooding your tunnel, possibly with a substance that's more viscous than water. That would lower the difference in density between the rock and the tunnel. Install a small airlock on either end. Either equip your robbers with SCUBA gear or use a robot. A robot would have the added advantage of requiring a very very small tunnel and it could support much higher density liquid without needing decompression (which wouldn't be practical here). Combined with depth and the noise and vibrations coming from next door, you'd have a shot at avoiding detection.

(Edited to add last paragraph.)

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  • $\begingroup$ I didn't mean to disguise digging sound. Geophysics is on land an evolution of what sonars do in water. So they actively create the sound source. With a small explosion you can scan the ground for thousands of meters, that's how they look for oil. $\endgroup$
    – FluidCode
    Nov 10 '21 at 14:05
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    $\begingroup$ Your final point deserves a big heading to make it distinct- it is a way to disguise the tunnel. (Effectivity is another issue...) $\endgroup$
    – PipperChip
    Nov 10 '21 at 14:55
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    $\begingroup$ +1 for including a point of interest local to me :D $\endgroup$ Nov 11 '21 at 11:00
  • $\begingroup$ Explosions is how they try to look for the appropriate rocks to look for oil- that needs lots of calibration. $\endgroup$ Nov 13 '21 at 8:01
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There are several tunnels. Each one is tiny.

robot surgery

https://dilipraja.com/robotic-surgery/

Your robbers are going to use a surgery robot to do their heist. As opposed to traditional surgery where an opening is made big enough to visualize structures with the naked eye and grab them with a gloved hand, robotic surgery uses laparoscopic ports and robot-assisted manipulators.

So too the robbers. Your robbers make several tiny tunnels to permit passage of the remote cameras and manipulators. They are detected but are so small they are considered to be animal burrows.

The robbers never enter the vault. They enter remotely, via the robot.

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    $\begingroup$ Great idea, but I am unsure if this falls under the "with common building materials" stipulation. I guess remote controlled cars and servos are pretty common in certain circles, it just is not what I understood from the question. $\endgroup$
    – PipperChip
    Nov 10 '21 at 14:44
  • $\begingroup$ Answers like this also assume the valuable item(s) can be removed through a tunnel of this size. What if the valuable item is a solid golden bull from the biblical times holding king tuts mummified head and the holy grail in its belly? $\endgroup$
    – TCooper
    Nov 11 '21 at 22:15
  • $\begingroup$ @TCooper - ok for the bull the robbers enter the vault. The robot unlocks it from the inside and opens the door. $\endgroup$
    – Willk
    Nov 11 '21 at 23:23
  • $\begingroup$ @Willk and the robot also disarms and disables all the unspecified number of security personnel with at least enough counter measures that tunneling in even though you know they have this level of sensing is your best option? Got it. I still think this is a great answer for a small object, pointless answer for a large object. You already got my +1 for the idea - just saying I think its a hard limitation. $\endgroup$
    – TCooper
    Nov 12 '21 at 17:00
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An interface between solid ground and air will reflect back a good part of the sonar wave, because of the high mismatch in acoustic impedance.

You can overcome the issue in different ways:

  • shape the tunnel in such a way that the sonar waves will be reflected away from the receiver. Basically mimic the early stealth technology
  • create a disturbing layer above your tunnel, so that it masks the underlying layer. The same way you can't see through a smoke curtain. You can do this by for example creating several air sacks above the tunnel.
  • you can try to tune the impedance of the tunnel wall so that the mismatch is lowered. The same way one uses a gel to remove air and better couple the echo-scan head to the body of the patient during a scan, you will basically make the tunnel less visible by reducing the reflected sonar wave.
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If they were to drill small holes into the tunnel walls about 10ft deep, they could insert tiny microphones that would pick up the sonar (but are too small to set it off themselves). The microphones would connect to computers with a fiber optic cable.

Light is faster than sound, so that you can actually see the sonar coming now a split second before it hits the tunnel walls.

The computer then uses that split-second advantage to creating a dampening wave that makes it impossible for the sonar wave to bounce off the wall of the tunnel. It might also be necessary to send a false echo back up to several seconds later, it could do that as well.

This only muffles the sonar ping, but wouldn't eliminate it completely. Which is probably ok... the stealth bomber doesn't have zero radar signature. It just looks so small that it doesn't appear to be aircraft at all. In the same way, sonar-stealthing the tunnel doesn't have to be perfect. Just has to minimize the signature so that it looks like some void or natural soil/rock boundary.

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  • $\begingroup$ I was wondering if anyone was going to suggest active cloaking. Note that you can also listen to the other side of the tunnel, to replicate the "rebound" sound as well. $\endgroup$ Nov 12 '21 at 14:46
  • $\begingroup$ I like this overall, but how do you write off a void or natural soil/rock boundary that is slowly showing up closer and closer to what you're guarding? $\endgroup$
    – TCooper
    Nov 12 '21 at 16:54
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    $\begingroup$ @TCooper I doubt that they'd see it as a tiny void moving forward, so much as they would see voids blink in an out due to the noisy nature of imaging such things. It's like looking at something in the dark, you see a bunch of shadows as your eye imperfectly picks up what light it can. If you see a shadow moving towards you, is something moving towards you, or are your eyes just playing tricks? $\endgroup$
    – John O
    Nov 12 '21 at 17:13
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    $\begingroup$ @JohnO As long as there is 0 time-series analysis, sure $\endgroup$
    – TCooper
    Nov 12 '21 at 17:38
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Build it under a rock shelf:

First, let me say nothing is perfect. A sophisticated enough, determined enough foe will detect anything, because he will use multiple different techniques and carefully analyze minute differences over time. But a sloppily placed facility (like one placed historically and not with radar in mind) could be snuck up on.

This requires that the local environment has soft soil over a hard rock shelf with soft materials under it. If the hard rock shelf can be tunneled under, then most ground-penetrating radar will travel through the soil and bounce off the hard rock surface. as long as the hard surface doesn't change appreciably (like people digging a shaft UP to a vault...) then the overall appearance of the underground won't change much. The electrical conductivity of the ground can change the ability of detectors, as can the type of soil and the amount of water in the soil. Perhaps building the tunnel under buried power lines might work, but I don't have a source on that.

A tunnel dug through waterlogged materials (good luck!) will be very hard to detect (maybe a dig/pump/seal cycle?). Maybe dig the tunnel in wet materials, then drain the tunnel, dig, and reflood when the detectors are switched on? Or dig in SCUBA gear, if available. It would be a miserable process, but the tunnel might even look like natural erosion in a flooded space, and could be passed off as natural (I mean, who would use a flooded tunnel?)

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  • $\begingroup$ I can't classify a 'rock shelf' as a common building material. $\endgroup$
    – Trioxidane
    Nov 11 '21 at 8:23
  • $\begingroup$ For tunneling though water, consider freezing the water to make it solid. This i used in construction sites when they want to dig a hole below the ground water level $\endgroup$
    – Ferrybig
    Nov 11 '21 at 13:19
  • $\begingroup$ @Ferrybig It's a good idea, but I don't know how the ice would show up on sensors. The water inside the walls would be frozen, and I'm guessing the signature of a tunnel in ice might be like a tunnel through rock. I just don't know, too many variables. $\endgroup$
    – DWKraus
    Nov 12 '21 at 0:01
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There are two ways I see that could work, assuming that you need to build the tunnel right where the ground is scanned:

Active cloaking

Cancelling the tunnel's effect on active sonars is possible by using technology similar to that in today's noise cancelling headphones. The tunnel could in that way cloak itself by sending out "anti-sound" that cancels any reflection or shadow.

I imagine one could record the incoming waves and use some kind of transform (similar to the Fourier transform) to figure out from which directions the waves come, and then send out the sound required to cancel any reflections and create new sonic waves in place of the shadowed waves. Even though this would technically be possible with today's technology and would not be mathematically that advanced, this would require acoustic sensors and actuators (i.e., microphones and speakers for recording sending out sound waves in the ground) all along and all around the tunnel.

Passive acoustic coupling to make the tunnel transparent to sonic waves

A couple of years ago, Steve Mould releases a YouTube video in which he explained why some interfaces reflect sound waves and why some interfaces don't reflect sound waves. He gave ultrasound gel as an example, which is used during ultrasound scans as an acoustic coupler to prevent sound waves from reflecting back once it hits the skin. Basically, a sonic wave will be (partially) reflected when it encounters an interface between two mediums with different acoustic impedance.

This is analogous to when a light wave hits an interface between two objects with different refractive index, such as the interface between air and water or between air and glass. A medium that transmits light and has the same refractive index as air will be invisible in air, and a medium that has the same refractive index as water will be invisible when submerged into water (note that the reason for example glass is not completely invisible is because it has a different refractive index than air and will therefore both bend light as well as reflect some of the light that hits it).

The same goes for sonic waves—an interface between two medium with the same acoustic impedance will not reflect any sonic waves. Now, depending on how the tunnel is constructed, there may be several parts of a tunnel which all have different impedance. If the tunnel has some kinds of walls to prevent earth from falling in, those may have one impedance. The air inside of the tunnel have another impedance, probably much, much lower than that of the ground (for example, the human body has about 3,000 the impedance of air according to the video and it's probably not to dissimilar with the ground relative to air). All of those interfaces might reflect sonic waves. There are however several ways to tackle this.

Perhaps a bit unintuitively, the sonic waves will be reflected less the more interfaces they have to pass, assuming that that allows the relative change in impedance across each interface to be lower. The ideal would be to have an impedance gradient between the ground and the air inside the tunnel, but several interfaces that helped transition the impedance in several small steps would probably be good enough. This would allow sonic waves to propagate into the air inside of the tunnel without being reflected. However, the sound waves would will still travel slower inside of the tunnel than outside of it, making them become out of phase when they exit the tunnel again compared to the waves that passed next to the tunnel and never were slowed down, giving rise to diffraction patterns with constructive and destructive interference which could give the tunnel away.

Another strategy would be to add some kind of structure inside of the tunnel that could transmit the sonic waves straight through the tunnel with the same speed as waves in the ground outside of the tunnel, effectively making the sonic waves propagate through that structure instead of through the air inside the tunnel. For example, metal rods between the tunnel walls going in all possible directions could be added, or perhaps some sort of thredimensional metal grid. This would of course make it difficult to walk inside the tunnel, but perhaps it would be possible to create the structure in such a way that the waves propagated around the innermost part of the tunnel, freeing that for walking or crawling. This type of structure would of course make the tunnel take up a significantly larger volume, and it's not really clear to me exactly how you would design the structure to make the waves propagate with the correct speed in all directions, but maybe there is some clever way to design it that would make the tunnel as good as transparent to sonic waves.

Clearly, this is a rather advanced concept (both mathematically and technically, I would guess). But maybe the team of robbers can pull it of if they know a mathematician who can come up with a theory that describes how a tunnel can be constructed that is coupled acoustically to the ground in an effective way, and an engineer who can help them build such a tunnel.

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Fill the tunnel

I'm not an expert enough to say the following will definitely work.

Fill the tunnel with special material that acts for the scanners like the material that is being removed. Many kinds of insulation material comes to mind. That means with every scan the ground looks normal, as it is filled with a substitute soil. The substitute must be easy to temporarily remove or compress. That way you can quickly get by all of the substitute soil, giving access to where you'll dig.

The digging area can't be lined according to the question anyway, so leaving a meter or so of working space at the end must not be too bad. It is likely small enough to not be a too big blip on the scanners to get suspicious, as no further tunnel goes to it. It would be easily dismissed as an error, if found at all.

In short, you have a small digging area for advancement. The already created tunnel is filled with a substitute that looks alike to normal soil on the scanners. This can easily be compressed to the walls or removed and reapplied to allow diggers to and from the digging area, as well as removal of the dug soil. This will reduce the time the scanners can notice the tunnel. As scanning is done "regularly", you can time it well. If no one is digging, you can fill up the whole space.

The above does have some logistical challenges with the passage to the digging site. If you make a good system to remove big blocks of material and reinstall them quickly, many cheap and abundant materials can do the trick. You might even just grab oblong blocks and turn them sideways, allowing you to walk past, closing the last one behind you and opening the next.

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No

... unless the vault was built before people got concerned about tunneling (might be if the 'vault' was built without an eye for security, and the location and facilities could not be upgraded later, for reasons, when it became apparent how valuable the contents were)

  • If it is built into solid bedrock, trivial passive listening will be sufficient - the process of removing stone in any quantity will produce sound, which can be picked up and even localized using triangulation. Plot any picked-up noise on a 3D chart, and watch as the tunnel extends towards you.
  • If the land around it is owned and controlled by the people operating the vault, the passive surveillance can be even better, so even if the vault is sitting in gravel, or sand or silt, the scratching noises could be picked up, triangulated and plotted.
  • even if there are caves with fast-flowing-gravel-carrying water, a subway, a glacier, and nuclear shelters remodeled as techno-clubs nearby, you just need more and better microfones in your array to weed out the different sound sources.

If this is a vault that was installed before, and for secrecy reasons you absolutely cannot install microfones around it now, indeed you only can send clandestine teams of security with the sensing gear disuised as a zamboni - then yes. Underground sensing from single points of vantage for static stuff (instead of the microfone-case, where the killer-info is in the development of the distribution of the data) is very hard, getting exponentially less resolution the deeper you go - See any 'geophys'-heavy episode of TimeTeam (and note that they are looking for, and overlooking, stuff that is only a few feet underground). Ground penetrating radar will only get you a few meters depth, and the resolution of acitvely sounding the earth is not sufficient to reliably detect a small tunnel.

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Detecting tunnels using seismic waves not as simple as it sounds

That's literally what references say. Detecting a tunnel with seismic waves is far from guaranteed, and if it's small and relatively deep, it can get undetected. In fact, to detect small irregularities in soil, like shallow pipes or sewers, ground-penetrating radar is more useful than seismic waves, and that is far from perfect and has a very limited range.

Therefore, the answer is to go deep, to make the tunnel small, not to change the environment so much, and not to get scared by seismic detectors because they aren't great at detecting tunnels.

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  • $\begingroup$ Interesting article. But not conclusive, because it is based on one off searches. If you take a picture of the underground nearby your area it might be confused, but still you could detect changes over time. $\endgroup$
    – FluidCode
    Nov 14 '21 at 13:13
  • $\begingroup$ Well, there are people actually interested in finding tunnels who have a lot of resources and they quite often fail to find them. If your vault is going to be well protected by seismic detection of tunnels, detectors must work better than at the Gaza strip - Egypt border. $\endgroup$
    – Pere
    Nov 15 '21 at 10:25
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In addition to any of the tunneling methods in other answers, it sounds like you should also consider some other tools in thieves' arsenals while performing this heist.

Social Engineering

Are any of the guards or technicians involved at the vault being underpaid or treated poorly? Are any of them horny? Really gullible? Bribe, seduce, threaten, or trick them into helping you.

  • Get them to disable some of the sensors or the thumper machine itself to create an opening where you could tunnel undetected.
  • If the person manning the sonar sensor system can be turned fully to your side, they can simply never notify anyone else that a tunnel is being dug.
  • Get them to help with some of the suggestions in "Misdirection", below. The more benign what you ask them to do appears, the easier it is to get them to do it.

If you find anyone willing to openly turn on their employers, you'll have to cut them in on a share of the loot, but you were already splitting the payout with the dig team anyway.

Hacking

Can you (or a socially-engineered insider) get physical access, even briefly, to the sensors or the computers?

  • Lock up the computers in the sonar sensor system with ransomware. That gives you a few days where no scanning is happening or the results aren't getting back to the humans. Perhaps long enough to dig your tunnel. As a bonus, if the vault's owners are dealing with a digital attack, they may be unlikely to expect a simultaneous physical breach. And if they pay off the ransom to regain control of their systems before your tunnel finishes, you still have a consolation prize.
  • Take over the computers and modify the data so the end users don't see any tunnel. This would get the same result as if you could perfectly disguise the tunnel against sonar.
  • Take over individual sensors, some of which are likely in less secure locations than the thumper or the computers. Have them to send back data masking your tunnel's presence. You might have to dig a winding tunnel to follow the sensors you control, but it'll still let you go undetected. Alternately or additionally, you could send fake data indicating an opening forming on the other side of the vault.

Sabotage

Can you damage or disable the scanning system? Can you do it in a way that will take time to repair and which appears to be benign in origin?

  • Cause a neighborhood-wide, multi-day power outage in the area the vault is situated. The vault may have a battery/generator backup. If it's batteries, they'll run out eventually. If it's a generator, try to put something in the fuel to break it when they try to refuel it.
  • Cause a major water leak near the vault. They'll have to dig up next to the vault to repair the broken pipe or fill in a sinkhole. Get in the work crew, or access the work area after dark. Then you can break into the vault without having to dig a tunnel at all. Or at the very least you could use the disruption in the sensor system as a cover for tunneling in on the other side.
  • Damage, e.g. by fire, the facility with the vault enough to trigger its contents being moved to another location while the facility is repaired. Cargo vehicles are often easier to rob than entrenched facilities. The faster they have to move to protect the vault's contents, the more chaotic it'll be and thus be easier to rob. Or maybe the temporary storage location is much less secure, making a heist there much easier than at the vault. Just make sure the damage doesn't actually reach whatever you're trying to steal.

Misdirection

Is the sonar system sophisticated enough to interpret a tunnel appearing and notify a human on its own, or does a human have to review and compare the results to come to the conclusion something is amiss? If the sensor system can't tell on its own that you're breaking in, you only need to keep the humans tending it busy somewhere else while your tunnel is being dug. Are there other avenues you could pursue at the same time which would draw their attention away, ideally for several days?

  • Infect other, more-accessible systems in the facility with ransomware.
  • Get the sensor system's handlers sick so someone less competent has to keep an eye on the scans.
  • Use government bureaucracy to force the owners to disable their thumper over concerns about how it's affecting wildlife or citizens living nearby. Whip up an angry mob of protestors outside the facility with rumors that the thumper is making them sick. Pseudoscience and wild accusations are your friend here.
  • Get the facility's manager promoted to a new site, ideally without a successor lined up. Or get them fired.
  • Trick the facility's manager into thinking they've been promoted and/or given a raise. When it doesn't materialize, they'll go on the warpath against their corporate overlords. You could use this technique on anyone you want to social engineer. Disgruntled employees are much more willing to take bribes or sabotage critical systems.
  • Start (or take advantage of) some noisy construction next to the facility. Get the construction crew to "accidentally" damage something at the facility - could be a wall, a power- or water line, whatever; it has to be enough to disrupt the facility for a few days. If you can't get the crew to do it for you, just use one of your team in disguise.
  • Hire a second, incompetent team to attempt their own heist. When they inevitably get caught, you cut contact and hang them out to dry. (And if by some miracle they succeed, then being their employer you have also succeeded. Pay them fairly and do not double-cross them.)
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  • $\begingroup$ Unfortunately these solutions might work for a short time. In the timespan the tunnel is build guards will be rotated and technicians would check that everything is working. $\endgroup$
    – FluidCode
    Nov 14 '21 at 13:16
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Yes, if you know a) the origin of the signal and b) the wavelength of the signal.

It is entirely possible to construct an arrangement of reflectors such that it does not reflect a wave signal back to its source for some set of directions (geometric stealth) nor does it obscure a signal of a given wavelength (geometric transparency).

A tunnel, being acoustically a boundary between two materials of very different acoustic impedance values (air vs rock), is effectively a reflector (it also refracts some amount of sound through it--the walls transmit sound to the air, which retransmits to the other side, and sound can also travel along the boundary--but this can all be mitigated by appropriate acoustic insulation). Thus, if an appropriately complex tunnel is dug, it is possible to obtain a reflector with both geometric stealth and geometric transparency, provided you know the direction the signal is coming from and what wavelength it is.

Making a reflector be geometrically stealthy is trivial--just don't have any surfaces reflecting the signal back to the detector.

Making a reflector be geometrically transparent can be much more difficult. Why? If the reflector is much smaller than the signal wavelength, it will not obscure the wave--the wave will go right through/around it with minimal energy loss--there is no "shadow". This is why small metal objects don't block radio waves. If the reflector is much larger than the signal wavelength, it will cast a shadow. This is why light is blocked by small metal objects. If the reflector is about the same size as the signal wavelength, it will refract about it in interesting ways. If you have a large tunnel which casts an acoustic shadow, many smaller tunnels near the size of the signal wavelength may possibly curve the acoustic signal around the wave in such a way that its presence is indistinguishable from its absence, after a certain distance. Here is an example (note that it is a VERY reflective structure, however). This is why you often hear the term 'metamaterials' thrown around in regards to invisibility--if a material is made to be transparent to visible light despite being very large, it must have extremely fine structure on the wavelength of the light to bend it around itself.

Of course, this is all probably a moot point because the wavelength of geophysical acoustic methods is much larger than human-sized tunnels & so it won't be noticed as long as it is not reflective. GPR may be a problem however, as its wavelength is much finer. Still, casting an acoustic shadow doesn't matter if you don't have buried receivers below you--nobody cares if there's a shadow if there's nobody to see it; and surface receivers will only detect reflections back at them. Which brings me to my next point...

The biggest issue is that if you have multiple receivers, it doesn't matter how geometrically transparent you are if you aren't geometrically stealthy. While it is easy enough to defeat a single emitter/detector system (provided there's not a lot of other reflectors nearby that may eventually kick your signal back at them, if there are many detectors, or worse, many emitter and many detectors, it is impossible if not difficult to avoid returns to all of them unless you have perfect data... and even then it's still very unlikely. This is why modern stealth aircraft aren't as angular as early ones, and rely more on absorption of the signal than minimizing reflection back to a single detector.

Still, in theory it is possible. Whether it is practicable depends on the details.

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  • $\begingroup$ Possibly using many layers of different materials to coat the tunnel may help to make a diffuse acoustic boundary & make a more effectively-absorptive surface. Such a boundary, devoid of any sharp jumps in acoustic impedance would curve sound through it rather than reflect or refract it, similar to the deep mantle on tectonic scales (its density increases with depth & thus its impedance continuously decreases with depth; why seismic signals curve through it) $\endgroup$
    – neph
    Nov 16 '21 at 21:57
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Build many nearby tunnels for legitimate reasons.

as you increase the number of tunnels, scanners become less and less useful. For example, have the thieves build a legitimate goldmine next door

Pick a legitimate reason for needing to dig neighboring tunnels, such as

  • mining for salt, gold, ore, rocks, etc..
  • archeology finds (maybe they found ancient ruins nearby and want to discover what the ancient civilization left behind, or at least they pretend to)
  • burying cable lines
  • building an Underground Railroad
  • laying water pipes very low
  • tunnels for geothermal energy
  • tunnels just for fun
  • car tunnels to speed up traffic
  • pick a reason that's legitimate for them to need to dig tunnels, and make sure there's a labyrinth of tunnels already in place that are already close enough to the vault, so when the theft-day arrives, all they have to do is connect the vault to their already existing network of legitimate tunnels that was nearby.

This question was edited from originally saying: "Dig millions of tunnels."

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    $\begingroup$ Look at en.wikipedia.org/wiki/Chaff_(countermeasure) A countermeasure for radar is making too many things show up in the scan results. It's a legitimate military tactic to fool scanners, and it helped the Allies invade Normandy beach, due to rendering aircraft scanners useless. And the author said "They have a lot of time", a lot of time can mean decades, and with enough hands, it can be done. As time and the number of hands helping to dig increases, the radar spoofing also increases. $\endgroup$ Nov 12 '21 at 15:40
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    $\begingroup$ @TCooper the term "As X approaches infinity" is a calculus term. It means "as you increase the number of tunnels, the radar becomes less and less useful." Here's a definition of mathematical limits: en.wikipedia.org/wiki/Limit_(mathematics) $\endgroup$ Nov 12 '21 at 15:50
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    $\begingroup$ @Tortliena here are my rebuttals to your 3 mentioned problems: 1. As for the ground becoming Swiss cheese: with placement of supports, a Swiss cheese tunnel system can hold up. 2: as for triggering alarm, an alarm that is always on for years is not an alarm, it's just background noise. 3: as for critizicing that my answer is not instant and not cheap: the author said he has "a lot of time" so time isn't a concern. $\endgroup$ Nov 16 '21 at 18:13
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    $\begingroup$ @Nick Bonilla the problem with an alarm that is triggered is that it's triggered in the first place, leading to investigations, not a wave of the hand :). $\endgroup$
    – Tortliena
    Nov 16 '21 at 18:24
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    $\begingroup$ @Tortliena my answer was abstract and mathematical. Build lots of tunnels, and scanners become useless. As for how to do that, my answer doesn't provide the concrete implementation, but I've edited in some more examples into the answer. $\endgroup$ Nov 16 '21 at 19:53

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