Seismic waves are vibrations that propagate outward from an earthquake’s focus, carrying the energy released by the sudden fault rupture. Determining the distance a secondary seismic wave, or S-wave, covers over a fixed time requires understanding the wave’s nature and the highly variable speed at which it travels through different materials. The travel distance is not a single fixed number, but rather a wide-ranging estimate influenced by the specific path the wave takes beneath the surface.
Defining the Secondary Wave (S-Wave)
The S-wave is one of the two main types of body waves, meaning it travels through the Earth’s interior rather than along the surface. This wave is named “secondary” because it arrives at seismographs after the faster primary (P) wave. S-waves are a type of shear or transverse wave, characterized by the motion of rock particles perpendicular to the direction the wave is propagating. This side-to-side or up-and-down shaking is largely responsible for the destructive ground motion experienced during an earthquake.
A defining characteristic of the S-wave is its inability to pass through liquids and gases, as these fluids cannot sustain the necessary shearing motion. This property is a powerful tool for seismologists, as the absence of S-waves in certain areas, such as the Earth’s outer core, provides definitive evidence that those regions are molten.
Factors That Determine S-Wave Speed
There is no single speed for an S-wave; its velocity is determined by the properties of the material it is passing through. The primary factors controlling S-wave speed are the density and the rigidity of the rock. S-waves travel faster in materials that are denser and more rigid, which is why their speed increases with depth within the Earth.
In the shallow crust, where rocks are less compressed and may contain fractures, S-wave velocities are relatively slow, starting around 2.0 to 3.5 kilometers per second (km/s). As the wave descends into the mantle, the immense pressure and greater rigidity cause the speed to increase significantly. In the deeper, more solid parts of the mantle, the S-wave velocity can reach up to 7.2 km/s. This variability means that two S-waves generated simultaneously may cover vastly different distances depending on their path.
Calculating the Travel Distance in 10 Minutes
The distance an S-wave travels can be determined using the formula: Distance equals Speed multiplied by Time. Since the time is fixed at 10 minutes, or 600 seconds, the distance depends on the average speed of the wave along its specific path. Because the wave path is complex and the speed is constantly changing, we must use a realistic range of average velocities. This range accounts for waves traveling predominantly through the slower crust or primarily through the faster, deeper mantle.
For a wave traveling mainly through the shallower crust at a slower average speed of 2.5 km/s, the distance covered in 600 seconds is 1,500 kilometers (2.5 km/s x 600 s). Conversely, a wave propagating through the faster, deeper mantle layers at an average speed of 6.0 km/s would travel 3,600 kilometers in the same ten-minute period (6.0 km/s x 600 s). Therefore, the realistic range of travel distance for an S-wave in 10 minutes is between 1,500 km and 3,600 km.
The Significance of S-Wave Travel Time
Understanding the travel time of S-waves is important in seismology, particularly for locating earthquakes. The key application is the S-P interval, which is the time difference between the arrival of the faster P-wave and the slower S-wave at a seismograph station. Because the time interval between the two waves increases with distance from the earthquake source, seismologists use this lag to calculate the exact distance to the earthquake’s epicenter.
By combining distance calculations from three different seismograph stations, a process known as triangulation, the precise location of the earthquake’s epicenter can be determined. Furthermore, the difference in travel time is utilized in modern earthquake early warning systems. The detection of the P-wave provides a short but valuable warning period before the slower, more destructive S-wave arrives at a given location, potentially giving people a few seconds to seek cover.