The calculation of an earthquake’s distance begins with the detection of its initial tremors, which travel through the Earth as seismic waves. These waves are categorized into two main types: P-waves and S-waves. P-waves, or Primary waves, are compressional waves that move by pushing and pulling the material they travel through in the same direction as the wave itself. Since P-waves are the fastest seismic waves, their early arrival at monitoring stations makes them the first signal of an earthquake and the foundational step for determining the earthquake’s origin.
P-Wave Fundamentals and Velocity Factors
The speed at which a P-wave travels is dependent on the physical properties of the Earth material it propagates through. P-wave velocity generally increases with the stiffness of the medium and decreases with its density. This relationship means that a wave moves faster through rigid, incompressible rock layers than through softer, less dense materials. In the Earth’s crust, P-wave speeds typically range from about 1.5 kilometers per second in loose sediments up to 8 kilometers per second in solid, crystalline rock.
Two primary physical factors govern this velocity: the material’s density and its stiffness, which seismologists quantify using the bulk modulus and the shear modulus. The bulk modulus measures the material’s resistance to compression, while the shear modulus measures its resistance to shearing or shape change. Materials with a high bulk modulus are extremely incompressible, resulting in a faster P-wave speed. Since P-waves are compressional, they can travel through solids, liquids, and gases.
P-wave velocities increase significantly with depth, reaching values up to 13.5 kilometers per second in the Earth’s lower mantle. This variation requires seismologists to use complex models of the Earth’s interior to accurately track the wave’s path and determine its speed.
Calculating Distance Using Arrival Time Differences
Determining the distance to the earthquake from a single seismic station relies on the difference in speed between the P-waves and the slower S-waves (Secondary waves). Both waves are generated simultaneously at the earthquake’s focus, but the P-wave will always arrive first. The time interval between the first arrival of the P-wave and the first arrival of the S-wave is known as the S-P interval, which is measured directly from the seismogram.
The S-P interval increases the farther the station is from the earthquake source because the slower S-wave falls progressively further behind the faster P-wave over a greater distance. Seismologists convert this measured time lag into a precise distance measurement using standardized travel-time curves. These curves are graphs that plot the expected travel time of P and S waves against the distance from the epicenter, based on decades of observations and models of the Earth’s velocity structure.
To find the distance, a seismologist takes the measured S-P interval and locates where that exact time difference fits vertically between the P-wave and S-wave curves on the travel-time graph. The corresponding value on the distance axis represents the distance from the recording station to the earthquake’s epicenter. For a quick estimate, scientists can use a simplified linear relationship where every second of S-P delay corresponds to a specific distance. This calculation provides the radius of a circle on which the earthquake must have occurred.
Locating the Epicenter Through Triangulation
Once the distance from the earthquake to a single seismic station is calculated using the S-P interval method, that distance is used as the radius of a circle drawn around the station on a map. Every point on the circumference of this circle represents a possible location for the earthquake’s epicenter. One station’s data alone is insufficient to pinpoint the event’s location.
To solve this problem, a minimum of three separate seismic stations must independently perform the S-P interval calculation to determine their individual distances to the source. A second station’s data generates a second circle on the map, which intersects the first circle at two possible points. A third station’s distance calculation is then used to draw a third circle. The three circles will ideally intersect at a single, precise point, and this unique intersection marks the location of the earthquake’s epicenter on the Earth’s surface. This requirement of three distinct distance measurements is why this final location process is known as triangulation.