Earthquake Waveguide

this is a method for for protecting a city from an earthquake.

first of all what causes most of the damage? this is a surface wave called Rayleigh wave:

this kind of wave can be guided in nature by a flat layer of rock and then it's called Lamb wave:

in fact ANY wave can be guided and we can "steal" the vibrating energy from one vibrating mass and transfer it away into another vibrating mass.

we know this in electromagnetic waves and sound waves, and this "siphon tube" is called a wave guide:

but lately with smart materials we see that we can manipulate seismic waves just like electromagnetic waves (manipulate light to make "invisibility cloak")

if you haven't heard of this cool new way to engineer existing materials into metamaterials, check it out here

Metamaterials and The Science of Invisibility | John Pendry | TEDxImperialCollege

here in this TED lecture he talks about manipulating the seismic wave by reshaping ordinary materials:

Metamaterials matter: smart material of future | Nicolò Maccaferri | TEDxUniversityofLuxembourg

so my idea is to take the dangerous Rayleigh wave and guide it away from the city, like a lightning rod takes the dangerous energy of the lightning (electromagnetic wave) and transfer it to the ground.


we know roughly where the waves will come from, by looking at geology maps that show fault lines.

United States Geological Survey (USGS)

for example in this map by the USGS from Wikipedia (San Andreas fault line), wherever there is a red-orange color (danger) next to a green color (dense population) we want to take the guide the red away from the green. so i added the yellow "lightning" to show in what direction we need to direct the energy away from dense population:


if you've never seen coupled pendulums, i'm putting a few videos here:

Coupled Pendulums - Sixty Symbols

Coupled Pendulum (minus the bagpipe music) by Dan Russell

the last one is "how does it work" to the "how does it work" section:

Footnote †: Double Pendulums Are Crazy   by    minutephysics

in our case instead of 2 pendulums close to each other, we have 2 masses of land close to each other, let's say this hill and the neighboring hill.

suppose we can connect them with something, let's say a tunnel with a paved road inside, that will convey the vibrations between them, like in the demos you saw with the pendulums.

what will happen with the 2 hills?

the first one will start to shake because the earthquake hit it first, and normally (without the tunnel) it will transfer energy to all it's neighboring hills equally.

but once we have the tunnel then almost all the vibrations move fast into the second hill, and then back and forth, because the walls of the tunnel are more solid then the surrounding ground, and it's easier for the vibrations to travel inside a solid medium.


so what we need is something like a coil spring that can conduct the vibration from one "block" of area on the map (with many people) into another neighboring "block" (with few people). let's say 100 kilometers away.

because there is a lot of energy to transfer i suggest our spring will actually be a straight metal bar, i think steel is the best. where do we get 100 kilometer (km) long steel bar? we need to cast the metal on the spot.

we first dig a long ditch 100 km long, because we need to steel bar to be buried underground in the depth where this kind of waves travel. i couldn't find this depth anywhere but from this article:

Dobrin, M. B., Simon, R. F., & Lawrence, P. L. (1951). Rayleigh waves from small explosions. Transactions, American Geophysical Union, 32(6), 822. doi:10.1029/tr032i006p00822

i guesstimate about we need to put the steel bar buried under 20 feet of earth, which is 6 meters.

the wave will "want" to travel through the bar because it travels faster which means more easily there:

Rayleigh waves have a speed slightly less than shear waves by a factor dependent on the elastic constants of the material.[1] The typical speed of Rayleigh waves in metals is of the order of 2–5 km/s, and the typical Rayleigh speed in the ground is of the order of 50–300 m/s.

the Golden Gate Bridge contains about 88,000 tons of steel which is 75,000 metric tons of steel.

1 metric ton equals 1000 kilograms (kg)

so the Golden Gate Bridge weight is 75,000,000 kg.

so if our steel bar is shaped like a cylinder of 100 km height which is 100,000 meters, and a radius of 1 meter, it's volume would be PI * radius^2 * height.
volume would be 3.14 * 1 * 100000 = 314,000 cubic meters of steel.

the weight of 1 cubic meter of steel is 7850 kilograms.

so a steel bar would have a weight of ‭2,464,900,000‬ kilograms.

so we need almost 33 Goldlen Gate Bridges for one steel bar.

but in a bridge we have a limiting constraint which is the weight because it needs to hold it's heavy weight above the water so that ships can pass below the bridge.

here we do not have this limiting constraint, so we can use reinforced concrete which is concrete with very thin steel bars inside it, and it has compressive strength (strong against pushing), and because of the thin steel bars inside it it's also strong against tensile strength (strong against pulling).

So how much steel do we need now?

The relative cross-sectional area of steel required for typical reinforced concrete is usually quite small and varies from 1% for most beams and slabs to 6% for some columns.

so let's go with 6% then we need almost 2 Golden Gate Bridges. of course we also need concrete, but concrete is a lot cheaper then steel.

according to Les McLean from Quora, steel costs 1 cubic metre would cost approximately $US 3,905

and according to Kent Aldershof from Quora, 1 cubic meter of concrete would cost  $US 78.5

so the 95% of the mass of our "lighting rod" is made from concrete which is 50 times cheaper than steel!

so i think the best way is to dig one long 100 big ditch for the concrete, and running alongside it one furrow for each steel rod that we want, then cast the steel rods and let them harden.

after we have the steel rods ready, we cast simultaneously all along the ditch some concrete, and then lower a rod simultaneously into the mix, and repeat this concrete-rod-concrete-rod etc.


but remember we said the energy will travel back and forth between the two neighboring "hills" or blocks of land, and we want to send the energy away with a one-way-ticket and disperse there, we don't want it to come back!

so what we need is to engage at the beginning, normally we have 45 seconds or so, in the beginning of the earthquake.

we need something that with a switch of a button will connect our "lightning rod" to the ground, and with a flick or a button will disconnect, once the energy moved away from the city.

it also must be very strong against pushing, ideally as strong as the concrete and the steel that we're using, because the vibrations ("the pushes") will pass through this thing.


Why Bridges Move... by Practical Engineering (this effect can be seen in minute 4:00 of the video)

so in long straight sections of the "lightning rod" we need to make gaps so that our one "lightning rod" is built from a series of many "lightning rods" that almost touch.

when we make the "lightning rod", before we bury it in the ground we need to connect electrodes to both sides of each section, so that we can run electricity through the thin steel rods inside the concrete.

this will cause the steel to heat up and expand and also the concrete will expand because it takes heat from the steel and concrete has almost the same thermal expansion as steel.

so when we "activate" the rod all its parts are touching and connected so they are pressed hard against each other and they transfer the vibrations.

when the energy was transferred far away, we quickly disconnect the electricity, the rods cool down and shorten, they are separated by gaps, and the energy cannot return.


you might ask yourself about the two "lightning rods" nearest to San Francisco in the picture, that are located in the sea.

how can we cast steel and concrete on the bottom of the sea?

for drilling we can use all the oil and gas rigs that are pumping carbon into the air from off shore drilling. instead of killing people let's use them to save people.

"Rayleigh wave" can not travel in the ocean, but there is something similar called "Scholte wave"

which can travel along the border between sand on the seafloor and water.

maybe we can translate the energy from one kind of seismic wave (Rayleigh) into another kind of seismic wave (Scholte) ?

i think that the answer is yes because we see an analogue to this in the physical phenomenon of "Wilberforce Pendulum"

see a nice video here:

PH ME CE DEMO 70041A V0241 Wilberforce Pendulum by UniServeScienceVIDEO

and also a video here:

Wilberforce Pendulum by  BerkeleyLectureDemos

it looks like nature is happy to trade the energy in any oscillator with the energy in any other oscillator!

so to build underwater is of course more challenging, we would need to make a "tent" of air for which would be upside down, just like a diver's bell

i think we should build this at first from some soft material, like the baloon that you see here:

Michael Lombardi: Inventions Enable Diving to New Depths | Nat Geo Live by  National Geographic (you can skip over the first 10 minutes)

so we can connect this kind of baloons and anchor them to the seafloor, and make a tunnel of air where people (or better yet robots because it's dangerous) can work and cure a half pipe of concrete. basically do what we did on ground but under this long tent. the problem is that we are limited to how long a tent we managed to stitch together. for this we need to make a process which is not all in once but instead it's an "assembly line"

we have a "tent of air" that covers the length of 2 kilometers (units one and two), and under its cover the robots are curing the first kilometer, and after they move on to work on the second kilometer meanwhile the first kilometer is hard enough to be exposed to water, and now we advance the "tent of air" forward to cover the next two units (unit two and three). and so on.