Locating Earthquakes
Earthquake Location in a Nutshell
Earthquake waves travel at specific speeds through different materials. By knowing a bit about the ground beneath our feet and the time an earthquake happened, we can determine where the earthquake originated.
A primary function of the Pacific Northwest Seismic Network is locating earthquakes in Washington and Oregon. We locate earthquakes by using a model of the speed of seismic waves through the ground in the Pacific Northwest to estimate the expected time of arrival of waves at seismometers in our network. This is a trial-and-error process, which computers are very good at doing quickly. It works like this:
Guess a starting location and time for the search. It doesn't need to be accurate at all. We usually use the arrival time of the first seismic wave at the first seismic station as an initial guess.
Given our model of wave propagation speeds and our initial guess of the earthquake location, forecast the expected seismic wave arrival times at each of the stations recording the earthquake.
Compare the differences between expected and observed arrival times, and use the differences to adjust the location and make a better-educated guess.
Complete step 2 again, but this time using the adjusted guess from step 3.
Repeat steps 2-4 until the differences between successive location estimates are stable and smaller than some predetermined threshold.
The computer performs the necessary math within a few seconds.
An earthquake location consists of four pieces of information: latitude, longitude, depth, and origin time. We need at least four seismic wave arrival times to estimate these four parameters uniquely.
A Few Notes and Refinements
It sounds simple, but there are a few things to keep in mind when you look at modeled earthquake locations. Here are the graduate-level concerns:
1. Model dependence. The "answer" (location) we get is only as good as the model we use of wave speeds in the region, and models are imperfect. In fact, the only way we know about the wave speeds in the region is from studying seismic waves. That sounds like circular reasoning, and it is. The good news is the more data we get, the more refined and detailed (and hopefully more accurate) our model becomes.
2. Sometimes it fails. Occasionally, the adjustment process fails. The revised location jumps between two (or more) possible spots and cannot converge any closer or decide between the two. Sometimes the location gets "wedged" against a velocity boundary in the regional wave speed model and can't jump across it. In these cases, the computer essentially shrugs its shoulders and alerts a human. Humans are really good at finding an error (like a misidentified arrival time) or thinking our way out of the box to a better answer. Ultimately, all automatically modeled earthquake locations in our public catalog are reviewed by humans.
3. Large earthquakes are not points. All earthquakes occur along a fault plane – a two-dimensional area – as opposed to at a one-dimensional point (see the figure below). The location that we compute and report for an earthquake is the focus, or hypocenter, of the event. This is the initiation point of the earthquake rupture that has a location and depth. The Recent Earthquakes map shows the epicenter, the point on the surface directly above the hypocenter. A large earthquake rupture may occur over a very wide area. For example, the 2002 Mw 7.9 Denali Earthquake ruptured parts of three connected faults for a total of over 330 kilometers. A magnitude ~9.0 Cascadia Subduction Zone earthquake could rupture the entire 1000 km length of the fault.
4. Better scores don't necessarily mean better locations. The computer program judges the quality of a location by the average difference between expected and observed arrival times. On our event pages we call this the "rms," and it is measured in seconds. Theoretically, a small earthquake may use just 4 seismic wave arrival times, and will find the location with 0 rms! Perfect! Right? The problem is that any uncertainty in the selected arrival time due to noise or other interference, and any imperfections in the mathematical model of wave propagation, lead directly to errors in location. In this case, more observed arrivals will inevitably lead to higher rms values and a less precise estimate for location. However, although the precision is lower, we are more certain that the location is accurate – the earthquake was where the model is telling us. Therefore, our location estimates come with numerous "quality factors" that quantify this tradeoff for each earthquake.
5. Location! Location! Location! Even lots of arrival times are insufficient to obtain a really high-quality location if the geometry of the recording stations around an earthquake isn't right. The best locations are from earthquakes where (a) there is at least one station close to the earthquake (no farther than the earthquake is deep, as a rule of thumb), and (b) stations surround the earthquake in all directions. Therefore, our location calculations are generally poorer on the edges of our seismic network, especially offshore and in the eastern and southwestern parts of our coverage area where stations are far apart from one another.