How Do Scientists Find Where an Earthquake Began, and Why Is Its Depth Harder to Pin Down?

1. One Seismometer Gives a Distance but No Direction

Earthquakes send out two main kinds of waves. The P wave is faster and arrives first, usually as a small jolt. The S wave is slower and arrives later, usually as the bigger shaking. The farther away the earthquake, the longer the wait between the two. A seismogram, the wiggly record from a seismometer, shows both arrivals, so the wait can be measured. If you want the full story of that gap, the earlier article on the two waves covers it.

Two words come up all the time. The hypocenter (also called the focus) is the point underground where the rock first slipped. The epicenter is the point on the surface directly above it. The Japan Meteorological Agency (JMA), Japan's national weather and earthquake agency, calculates hypocenters from the arrival times of P and S waves [1].

Here is the catch. A longer wait means farther away, but the wait says nothing about north, south, east or west. One station can only say, "the earthquake began somewhere about this far from me." In three dimensions, that is the whole surface of a sphere around the station. So how do several stations turn many possible places into one?

2. Several Stations Narrow Many Possible Places Down to One

A simple way to picture it is to draw on a map. Put a dot where each station is. Around each dot, draw a circle whose radius is the distance that station worked out. The earthquake sits somewhere on the first circle. A second station's circle crosses the first in two points. A third station's circle usually leaves only one of those two points. That is why classroom lessons say you need at least three stations.

This drawing is a picture, not what scientists really do. Real measurements have small errors, so the circles never meet in a perfect point. And the real Earth is three-dimensional, with waves traveling faster at greater depth, so the paths are not straight lines.

What agencies do instead is let a computer search. JMA's own guide says hypocenters are calculated from P-wave and S-wave arrival times, using pre-computed travel-time tables that give the expected travel time between a source and a station. The computer tries places and keeps the one whose predicted arrival times match the observed ones best. Stations whose times fit badly are left out of the calculation [1]. So the map position comes from the best overall agreement, not from a clean crossing point.

The position on the map is the easier half. The depth is where things get tricky.

3. Why the Depth Can Stay Uncertain, and What Agencies Do About It

Earthquakes happen at very different depths. The U.S. Geological Survey (USGS) says they occur anywhere from the surface down to about 700 kilometers (about 435 miles). It splits that range into shallow (0 to 70 km), intermediate (70 to 300 km) and deep (300 to 700 km) [2].

Seismometers sit at the surface, so their records mix the sideways distance and the depth together. Think of a quake that is directly under a station: the waves have to travel straight down-and-up either way, and a small change in depth changes the timing only slightly. When no station is close to the epicenter, many different depths can fit the arrival times almost equally well.

JMA handles this openly. Its guide says the depth is first calculated without restrictions. If the solution is unstable, the computer holds the epicenter fixed, changes the depth in steps of 1 km, and picks the depth with the best match. For shallow earthquakes around the Kuril Islands, north of Japan, where stations are far away, the depth is simply fixed at 30 km [1].

That means a depth number can be either measured or assumed. It is worth remembering when you read a news report. Is there a better way to measure depth? Yes, and it uses an echo.

4. How an Echo From the Surface Gives the Best Depth Clue

When an earthquake is deep, some of its P wave first travels up and bounces off the Earth's surface near the epicenter, then goes back down and travels on. Seismologists call that echo the pP phase. At far-away stations it arrives a little after the direct P wave. USGS explains that this gap, "pP minus P," changes slowly with distance but quickly with depth. The deeper the earthquake, the longer the echo's detour and the bigger the gap. Reading it from a seismogram and comparing it with published tables is, in USGS's words, the most accurate method of finding the focal depth [2].

USGS also describes a second echo, called sP, in which an S wave bounces off the surface and turns into a P wave. It shows up after pP, roughly half the pP-minus-P gap later. If both pP and sP can be identified, an accurate depth can be found [2].

There is a human catch: the method only works if the right wave is picked out of a messy record. For that reason, the depth stays a result of careful reading, not an automatic fact.

5. Why Early Warnings Trade Accuracy for Speed

If careful depth work takes time, how can an alert go out before the strong shaking arrives? JMA's earthquake early warning system, called Kinkyu Jishin Sokuho in Japanese, works from wave data recorded by seismographs near the epicenter. It quickly estimates the focus and the size of the quake, then announces expected shaking and arrival times so that trains can slow down and people can protect themselves [3].

Speed has a price. An early estimate uses only the first few stations and the first seconds of data, so its location and depth can differ from the careful recalculation made later, once more stations have recorded the shaking. This trade-off is my reading of how the pieces fit, not a quote from the agency, and the same idea applies to any quick alert: the earlier it goes out, the less data it can use.

6. Try It: Find a Hidden Epicenter With Paper and String, and Where to Read More

On a large sheet of paper, mark three dots as "stations." Secretly mark a fourth dot somewhere else as the "epicenter." With a ruler, measure the distance from the secret dot to each station. Tie a string to a pencil, hold the string at one station, and draw a circle with that distance as the radius. Do the same at the other two stations. Do the three circles meet at your secret dot? Then try with only two circles and notice that two places remain.

For a harder challenge, draw each circle slightly too large or too small, as measurement errors would. What happens to the crossing point?

To read more, JMA publishes a user's guide to its earthquake catalog, which describes the calculation [1], and USGS has a short article on determining depth [2]. A question to carry with you: if two agencies report the same earthquake with different depths, how could both be honest?

Sources

Revision history

October 25, 2026: First published.