An earthquake location involves pinpointing the origin of the seismic event, finding both the epicenter and the hypocenter. The epicenter is the point on the Earth’s surface directly above where the rupture begins, while the hypocenter is the actual location of the rupture within the Earth’s crust. Accurately locating an earthquake relies on analyzing ground motion data collected from a global network of monitoring stations. These stations use a seismograph, an instrument that records the shaking as a trace called a seismogram.
The Essential Data Recorded by a Single Seismogram
A single seismogram provides the fundamental data necessary to begin calculating the distance to an earthquake’s origin. Earthquakes generate two primary types of body waves that travel through the Earth’s interior: the P-wave and the S-wave. The P-wave, or primary wave, is a compressional wave that travels fastest and is the first to arrive at a seismic station. The S-wave, or secondary wave, is a shear wave that travels slower and arrives later.
The difference in arrival time between the P-wave and the S-wave, known as the S-P interval, is the critical measurement used for distance calculation. Because P-waves travel approximately 1.7 times faster than S-waves, the time difference between their arrivals increases the farther the station is from the earthquake. Seismologists use a travel-time curve, a standardized graph relating the S-P interval to distance, to convert this time difference into a measurement of how far the seismic station is from the epicenter. While a single seismogram can determine the distance to the earthquake, it cannot determine the direction or the specific location.
The Minimum Number Required for Location
The minimum theoretical number of seismograms required to locate an earthquake’s epicenter is three. This requirement stems from the geometric principle used to fix a point in two-dimensional space. One seismic station can only calculate the distance to the epicenter, meaning the earthquake could have occurred anywhere on a large circle surrounding that station.
If data from a second station is added, the two resulting distance circles will intersect at two possible points. Without additional information, it is impossible to determine which of these two points is the correct epicenter. The data from a third seismic station is needed to resolve this ambiguity, narrowing the possible locations down to a single intersection point.
Pinpointing the Epicenter Using Trilateration
The process of locating the epicenter using data from three stations is known as trilateration, a method that uses distance measurements to find a unique point. The first step involves calculating the distance from the earthquake to a seismic station, Station A, using the S-P interval. A circle is then conceptually drawn on a map around Station A with a radius equal to that calculated distance.
Next, the same distance calculation is performed for a second seismic station, Station B, and a corresponding circle is drawn. These two circles will cross at two distinct points, creating two potential epicenters. The third and final circle is drawn using the distance calculated from Station C. The single point where all three circles intersect is the confirmed location of the earthquake’s epicenter.
In real-world application, because of slight inaccuracies in time measurement and variations in the Earth’s structure, the three circles may not intersect at a perfect point. Instead, they often overlap to form a small triangular area. Seismologists identify the center of this triangle as the most probable location of the epicenter.
Determining Depth and Improving Accuracy
While three seismograms are sufficient to fix the two-dimensional epicenter on a map, real-world seismology uses many more stations to determine the complete three-dimensional location, known as the hypocenter. Determining the hypocenter requires finding the depth of the rupture in addition to the latitude and longitude of the epicenter. The arrival times of waves at multiple stations provide a complex set of equations that can be solved simultaneously to find the depth.
Modern seismic monitoring networks often use data from dozens or even hundreds of stations for a single event to maximize accuracy. Using numerous stations helps to minimize errors caused by a factor called the velocity model, which describes how wave speed varies through the Earth’s non-uniform subsurface layers. By incorporating data from many different paths, seismologists can refine the location and gain greater confidence in the calculated depth.