How Deep in the Earth Do Earthquakes Typically Occur?
During the Dynamic Earth course, one of the questions that came up was about the depth at which earthquakes typically occur. There was some confusion around a quiz question and to get to the bottom of the issue I ended up seeking out some data that would illuminate the process. I started down this path because the initial confusion arose when one learner, based in Taiwan, was confused as to why we claimed that most earthquakes happen at depths shallower than 12-15km. He was looking at some recent earthquakes that had happened around Taiwan and the majority of them were deeper than 15km. Surely we must be wrong; look at this data.
Well, I did look at that data. The obvious answer before even looking at the data, though, was just that the sample was limited to a short time frame in a small area of the globe. But another observation this learner drew our attention to was a global dataset of 2.5 or greater magnitude earthquakes over the last 24 hours. The claim was that this dataset also showed that most earthquakes originate deeper than 15km. Again, I was suspicious that this contrary observation (that most earthquakes were happening deeper than 15km) was due to a sampling bias—only looking across a day and only looking at 2.5 or greater magnitude quakes. So I went after a bigger dataset.
The resource linked to was the USGS Earthquake Hazards Program, which releases worldwide earthquake data. I was chiefly interested in depth and magnitude, as that was the comparison being made in the comment thread about the topic and it's also a convenient way to visualize the depth data. Another way to look at this problem would be to make a bar chart of the number of quakes at increasing depth categories. That would summarize the data nicely but I wanted to see it all, so a scatterplot it is. I could also have plotted depth against time of occurrence, but I like the plot of origin depth and magnitude because it also makes a nice comparison beyond the scope of the issue at hand. That is, do stronger earthquakes happen deeper? That's an interesting question with some reason to think (a shaky theoretical ground, if you will) that stronger quakes might happen at shallower depths since the crust is more brittle when cooler and earthquakes are an elastic phenomenon.
So I grabbed data on the last 20,000 earthquake events (USGS limits queries to 20,000 through this interface) and went to R to plot the data. I ended up plotting the natural log of depth because there was such a great number of events between the surface and 15km that seeing all the data was difficult. After sorting out some problems with negative and zero values on the log transformed variable, I have ended up with the plot you see below. The script and dataset I used to make this figure are both on GitHub.
Turns out, about 70% of earthquakes happen at a depth of 15km or less (so we were right, but that's no surprise). And there seems to be a trend of stronger earthquakes happening at greater depths, though this is largely driven by some outliers in the dataset. I did a linear regression on the untransformed data (not shown), and the residuals errors plotted against their fitted values show a decided trend around zero, so I don't really trust the model and it's a weak signal anyway. A normal probability plot confirms that the untransformed data is very not normal.
My guess that stronger earthquakes will occur at shallower depths is mostly driven by detection bias–we tend to notice those ones. However, this dataset shows that lots of very strong earthquakes happen deep in the earth. We don't experience them much likely because of that depth. Many of those deep earthquakes occur along subduction zones in oceanic plates, where brittle crust is being forced down deep into the earth, and these brittle rocks can still hold stress up (which ductile rocks won't do) and then break, causing deep quakes, same as at shallower depths. And sometimes those quakes are big.
What I really learned in this whole process is the relationship between rock elasticity and temperature. So, returning to the question of the seismogenic layer, the reason that most earthquakes happen at a depth less than 15km is because the rocks aren't ductile at that range—they can't flow, they sustain pressure, crack, and snap. And that's an earthquake. But at deeper depths, rocks can flow. That's really crazy.