<p>To add a bit of a quantitative perspective to James' answer.</p>
<p>Tsunamis occur in the wake of large earthquakes. They grow in amplitude because the speed of a water gravity wave is influenced by water depth, causing the wave to 'pile up'. In particular, if the wavelength is (much) greater than the depth of the water, the speed at which a wave will travel is roughly:</p>
<p><span class="math-container">$$v \sim \sqrt{gd}$$</span></p>
<p>where v is the speed, g is the gravity, and d is the depth. So by keeping the dimensions consistent as a wave enter shallower water the wave length (L) is squished proportionally to the change in speed and amplitude (A) grows accordingly:</p>
<p><span class="math-container">$$ \dfrac{A_1}{A_2} \sim \dfrac{L_1}{L_2} \sim \dfrac{v_2}{v_1} $$</span></p>
<p>such that</p>
<p><span class="math-container">$$A_2 \sim A_1 \sqrt{\dfrac{d_1}{d_2}}. $$</span></p>
<h3>Plugging some numbers in:</h3>
<p>So even for an earthquake that displaces water over say 500km (e.g. <span class="math-container">$M_w9.1$</span> Tohoku earthquake). If the water changes in depth from 500km to 200km (as OP asks), the change in height will only be a factor of:</p>
<p><span class="math-container">$$A_2 \sim A_1 \sqrt{\dfrac{500km}{200km}} \sim 1.5A_1.$$</span></p>
<p>JeopardyTempest asks, what if the water got as shallow as 20km then:</p>
<p><span class="math-container">$$A_2 \sim A_1 \sqrt{\dfrac{500km}{20km}} \sim 5A_1.$$</span></p>
<h3>How big?</h3>
<p>Now <span class="math-container">$A_1$</span> (the original wave height) is generally comparable to the average vertical displacement from the earthquake. On earth, the plate boundary configuration is such that the largest earthquakes occur on shallow-dipping subduction zones such that the corresponding average vertical deformation would rarely exceed 1 meter even in the largest earthquakes. Tohoku for instance had a maximum sea floor displacement of tens of meters (at a dip of approximately 10 degrees). Should your configuration be better suited on your mystery planet (steeper dip), and should there be a potential for larger earthquakes than on earth (say <span class="math-container">$M_w9.5+$</span>), only then would there be a  potential for a sizable tsunami with an amplitude at least as large as the sea floor displacement and potentially larger should the bathymetric change. Certainly a <span class="math-container">$M_w10+$</span> would generate a lot (10s of meters) of seafloor displacement, but then, of course, the wavelength would be much bigger than the amplitude.</p>

CC BY-SA 4.0
2022-11-18T04:31:05.670Z
2022-11-18T19:07:09.207Z
2022-11-18T19:07:09.207Z
Kélian Dascher Cousineau
<p>Tsunami are caused by sudden changes in the sea floor. An earthquake that causes a slump or surge in the seabed can cause a tsunami.</p>
<p>Tsunami travel as shallow water waves; they have a wavelength comparable to, or longer than the depth of the water.  A large earthquake can cause rupturing on a scale of hundreds of km, (the <a href="https://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake_and_tsunami" rel="noreferrer">boxing day quake</a> caused a rupture of 200km) and so can create a tsunami even in 200km deep water.  Such a tsunami would have a wavelength of hundreds of km and a wave height of perhaps a few cm. So this is not the <em>great wave off Kanagawa</em> (which was not a tsunami) but it is a true tsunami, and would be undetectable except with high accuracy gauges.</p>
<p>If there is no land, the tsunami will circle the planet several times gradually dissipating due to friction.  With no land, it will remain a few cm in amplitude and be of no practical interest.</p>
<p>A planet with significant earthquakes will probably have plate tectonics, so the seabed won't be flat, which will have consequences for its velocity. It will move faster over deeper water.</p>

CC BY-SA 4.0
2022-11-11T08:55:26.253Z
For those curious about what the "boxing day quake" is, it appears to refer to the 2004 [Indian Ocean earthquake](https://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake_and_tsunami)
Toivo Säwén
CC BY-SA 4.0
2022-11-11T12:30:57.880Z
With regard to *Tsunami travel as shallow water waves*: That's true on Earth because tsunamis have a wavelength in the multiple 100s of kilometers. The depth of the oceans on Earth is less than 1/20 of that long wavelength, which is the borderline of shallow water waves and non-shallow water waves. Deep water waves have a wavelength that is at most half the depth. The OP is positing a planet with a very deep ocean, so the tsunami on that planet would traverse more as deep water waves rather than shallow water waves.
David Hammen
CC BY-SA 4.0
2022-11-11T23:14:23.230Z
To make sure for Zan... what happens when this few cm tall wave (generated in 200 km water) travels into a zone where the seafloor was only 20 km?  Little negligible change because it's a shallow water wave?
JeopardyTempest
CC BY-SA 4.0
2022-11-10T19:54:39.260Z
2022-11-11T21:34:51.740Z
2022-11-11T21:34:51.740Z
James K
<p>Assume a water planet with an ocean depth of about 200-500 km.</p>
<p>Would a very strong ground-quake happening at the very bottom of the planet's ocean floor be able to cause a large tsunami to rise up to the surface of the ocean? If it could, how strong would the ground-quake need to be on the Richter scale in order to do that?</p>

CC BY-SA 4.0
2022-11-10T18:15:25.837Z
From a simplified - shallow-water theory standpoint, tsunamis depend on the conservation of fluid height h and bottom height b. If you don't change b, then h cannot change, hence no tsunami.
AtmosphericPrisonEscape
CC BY-SA 4.0
2022-11-10T18:23:37.897Z
So tsunami most likely can not occur in deep water planet. But what about earthquake? If the earthquake be ridiculously strong, let say about 13.0 magnitude richter scale, it might cause some waves on the ocean surface, right?
ZanMoon-chan
CC BY-SA 4.0
2022-11-11T00:44:51.247Z
You have to compare b+h before and after the event. If the total delta is negligible, then so are the surface waves.
AtmosphericPrisonEscape
CC BY-SA 4.0
2022-11-19T09:42:06.290Z
Tsunami occurs when oceanic tectonic plates uplift water, at sea it is a wave and will dissipate, however upon reaching land, volume it has to expand decreases exponentially and has but one output, to overlap on land. Deep water planets can have tides, geologic plate upheavels..upheavals... but no land, no tsunami 
LazyReader
<geophysics><earthquakes><water><planetary-science>
Is it possible for tsunamis to occur on deep water planets?
ZanMoon-chan
# Is it possible for tsunamis to occur on deep water planets?

(Asked by: username_0 on 2022-11-10)

Assume a water planet with an ocean depth of about 200-500 km.

Would a very strong ground-quake happening at the very bottom of the planet's ocean floor be able to cause a large tsunami to rise up to the surface of the ocean? If it could, how strong would the ground-quake need to be on the Richter scale in order to do that?

**Tags:** geophysics, earthquakes, water, planetary-science

> **Comments:**
> **username_1**: From a simplified - shallow-water theory standpoint, tsunamis depend on the conservation of fluid height h and bottom height b. If you don't change b, then h cannot change, hence no tsunami.  
> **username_0**: So tsunami most likely can not occur in deep water planet. But what about earthquake? If the earthquake be ridiculously strong, let say about 13.0 magnitude richter scale, it might cause some waves on the ocean surface, right?  
> **username_1**: You have to compare b+h before and after the event. If the total delta is negligible, then so are the surface waves.  
> **username_2**: Tsunami occurs when oceanic tectonic plates uplift water, at sea it is a wave and will dissipate, however upon reaching land, volume it has to expand decreases exponentially and has but one output, to overlap on land. Deep water planets can have tides, geologic plate upheavels..upheavals... but no land, no tsunami   

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## 2 answers

### Answer by username_3 on 2022-11-18. Score: 5 | Accepted answer

To add a bit of a quantitative perspective to username_4' answer.

Tsunamis occur in the wake of large earthquakes. They grow in amplitude because the speed of a water gravity wave is influenced by water depth, causing the wave to 'pile up'. In particular, if the wavelength is (much) greater than the depth of the water, the speed at which a wave will travel is roughly:

$$v \sim \sqrt{gd}$$

where v is the speed, g is the gravity, and d is the depth. So by keeping the dimensions consistent as a wave enter shallower water the wave length (L) is squished proportionally to the change in speed and amplitude (A) grows accordingly:

$$ \dfrac{A\_1}{A\_2} \sim \dfrac{L\_1}{L\_2} \sim \dfrac{v\_2}{v\_1} $$

such that

$$A\_2 \sim A\_1 \sqrt{\dfrac{d\_1}{d\_2}}. $$

### Plugging some numbers in:

So even for an earthquake that displaces water over say 500km (e.g. $M\_w9.1$ Tohoku earthquake). If the water changes in depth from 500km to 200km (as OP asks), the change in height will only be a factor of:

$$A\_2 \sim A\_1 \sqrt{\dfrac{500km}{200km}} \sim 1.5A\_1.$$

username_7 asks, what if the water got as shallow as 20km then:

$$A\_2 \sim A\_1 \sqrt{\dfrac{500km}{20km}} \sim 5A\_1.$$

### How big?

Now $A\_1$ (the original wave height) is generally comparable to the average vertical displacement from the earthquake. On earth, the plate boundary configuration is such that the largest earthquakes occur on shallow-dipping subduction zones such that the corresponding average vertical deformation would rarely exceed 1 meter even in the largest earthquakes. Tohoku for instance had a maximum sea floor displacement of tens of meters (at a dip of approximately 10 degrees). Should your configuration be better suited on your mystery planet (steeper dip), and should there be a potential for larger earthquakes than on earth (say $M\_w9.5+$), only then would there be a potential for a sizable tsunami with an amplitude at least as large as the sea floor displacement and potentially larger should the bathymetric change. Certainly a $M\_w10+$ would generate a lot (10s of meters) of seafloor displacement, but then, of course, the wavelength would be much bigger than the amplitude.


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### Answer by username_4 on 2022-11-10. Score: 8

Tsunami are caused by sudden changes in the sea floor. An earthquake that causes a slump or surge in the seabed can cause a tsunami.

Tsunami travel as shallow water waves; they have a wavelength comparable to, or longer than the depth of the water. A large earthquake can cause rupturing on a scale of hundreds of km, (the [boxing day quake](https://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake_and_tsunami) caused a rupture of 200km) and so can create a tsunami even in 200km deep water. Such a tsunami would have a wavelength of hundreds of km and a wave height of perhaps a few cm. So this is not the *great wave off Kanagawa* (which was not a tsunami) but it is a true tsunami, and would be undetectable except with high accuracy gauges.

If there is no land, the tsunami will circle the planet several times gradually dissipating due to friction. With no land, it will remain a few cm in amplitude and be of no practical interest.

A planet with significant earthquakes will probably have plate tectonics, so the seabed won't be flat, which will have consequences for its velocity. It will move faster over deeper water.

> **Comments:**
> **username_5**: For those curious about what the "boxing day quake" is, it appears to refer to the 2004 [Indian Ocean earthquake](https://en.wikipedia.org/wiki/2004_Indian_Ocean_earthquake_and_tsunami)  
> **username_6**: With regard to *Tsunami travel as shallow water waves*: That's true on Earth because tsunamis have a wavelength in the multiple 100s of kilometers. The depth of the oceans on Earth is less than 1/20 of that long wavelength, which is the borderline of shallow water waves and non-shallow water waves. Deep water waves have a wavelength that is at most half the depth. The OP is positing a planet with a very deep ocean, so the tsunami on that planet would traverse more as deep water waves rather than shallow water waves.  
> **username_7**: To make sure for Zan... what happens when this few cm tall wave (generated in 200 km water) travels into a zone where the seafloor was only 20 km?  Little negligible change because it's a shallow water wave?  

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