Thread by @geophysichick

A Seismic Rant, by Geophysichick:

Rather annoyed, as I prepare my class on seismic waves for tomorrow. Nearly every website I find has a subtle but maddening error in how they discuss the speed of seismic waves. [A rant, but hopefully an educational rant, follows]

For the most part, seismic waves move faster in denser materials. We see this as waves propagate into the deep mantle (they go faster!) and we see this when we compare how fast waves move in different types of rock (e.g. v = 6 km/s in basalt but 3 km/s in sandstone).

From this, many website infer that denser = faster. Seems reasonable, no? Well, it's not necessarily true.

Let's look at a profile through the Earth and compare density and seismic velocity. This figure shows PREM, the Preliminary Reference Earth Model (Dziewonski and Anderson, 1981).

The left panel shows the speed of seismic P waves as a function of depth (the center of earth is at the bottom of the plot). P wave speeds range from ~1-14 km/s (fast!).

The right panel shows density with depth--you can see that things get more and more dense as you approach Earth's center. There's a HUGE jump in density 3500 km from Earth's center--that's the core/mantle boundary.

If we just look at the upper half of Earth...mostly the mantle...speed and density both increase. So it's reasonable to assume they are related. BUT...!

If dense = fast, then we would expect that the densest part of the Earth would see the fastest waves. But this isn't the case! Earth is densest at its center, but the fastest P waves are actually in the lowermost mantle. Clearly there must be more to the story!

To dive deeper into this, let's look at the equation that describes the speed of a P wave:

In this equation, K and u are called "elastic moduli". They describe how hard a material is to deform. If K and u are high, it's *really* hard to deform, but a softer material has lower values. Density is represented here by the Greek letter rho, in the denominator.

Wait...WHAT? Density is in the denominator? This means that if density increases, the speed should drop! How can this be?

Well, guess what? That's exactly what should happen. If density increases and nothing else changes, waves *should* slow down. But in general, that's not what we observe. So what gives?

Here's the important point: denser materials tend to be harder to deform. K and u are much higher in dense materials. And if they increase faster than density, then velocity increases too.

So ultimately it comes down to this: seismic waves go faster in more rigid materials--materials that are hard to deform. Density plays something of a secondary role.

Maddeningly, though, this is often, often misrepresented on line and even in (intro level) textbooks. Once students see the equations, they get really confused. So I'm trying to nip these misconceptions in the bud.

By the way--you may be wondering why P wave velocities drop so much at the core/mantle boundary. The answer to this lies in what S waves do there:

S wave speeds drop to zero in the outer core--they can't enter it. This tells us that the outer core is liquid S waves do not propagate in fluids because fluids cannot resist shearing, and that's what S waves do.

The whole purpose here is to say two things:

(1) Denser does not necessarily mean faster
(2) Seismic waves move fastest through materials that are hardest to deform.

There's no reason for books or websites to get this wrong!!

[rant over]

Wait...one more thing (more a rave than a rant). One of the coolest things about P and S waves is that their speeds depend only on the physical characteristics of the stuff their moving through: density and elastic moduli.

It doesn't matter how big the quake was. It doesn't matter what the frequency of oscillation is. All that matters is what the waves are moving through. THIS is how we know what the interior of the Earth is like.

Isn't that beautiful?

[rant really over now]

I might add that the site that set me off on this rant was a @khanacademy video on refraction--it specifically, and inaccurately explained that dense = fast (it said that tighter packing = faster transmission of energy, where it's actually quicker restoration of shape = faster).

Oh. My. God. I misspelled "they're". I'm mortified. I swear I know when to use the various there/their/they'res.

Oy.