CSU, Long Beach -- Geography 458/558 -- Hazards and Risk Assessment

This laboratory exercise will familiarize you with the general idea behind the process by which earthquake epicenters are determined.

The method is based on the fact that there are different types of seismic waves and that each type tends to move at different velocities. The fastest wave is the primary wave, or compressional wave, which is followed in time by the slower secondary wave, or shear wave. Even slower are the various surface waves (e.g., Love waves and Rayleigh waves).

Now each wave can travel somewhat faster through dense, uniform, and rigid materials and somewhat slower (with greater amplitude) in less dense, less uniform, and less consolidated material. Even so, they are affected similarly by the materials they cross. As a result, there are relatively constant ratios between the velocities of different pairs of seismic wave types, no matter what kind of material they're passing through.

Given this constancy of ratio, then, we can use the difference between the arrival times of different pairs of wave types at a seismic recording station to figure out the distance from the focus to the station. By triangulating among at least three such stations, it is possible to define the probable epicentral area, at least generally.

In more detail, P waves generally travel between 5.95 and 6.75 kilometers per second in the crust, depending on compressibility, rigidity, uniformity, and density of the materials traversed. S waves tend to move at velocities between 2.9 and 4.0 km/sec in the crust. Rayleigh waves travel somewhere between 2.7 and 3.7 km/sec. Expressed as ratios, these are:

V_p:V_s = 1:1.73 or V_s:V_p = 1:0.58

V_s:V_r = 1:1.09 or V_r:V_s = 1:0.92

Directions for Estimating a Station's Distance from the Epicenter

Time and distance can be graphed for each of the wave types. What you need are the arrival times for any two pairs (P and S, S and R, or P and R) of seismic waves. You subtract the arrival time of the faster wave from that of the slower wave to get the difference in arrival times. Then, take a card and align it on the Y axis (difference in time) of the graph and mark the difference in time on the card. Now, move the card into the body of the graph, until the tick marks on your card are perfectly aligned with the two curves matching the two wave types involved. Make sure your card is exactly perpendicular with the X axis (distance), so the card is straight up and down where it crosses the two curves. Now, read down to see the distance on the X axis. This is the approximate distance between the earthquake's focus and your seismometer. Give your answer rounded to the nearest 250 km.

Mapping Distances to Epicenter

To use these distances to create a map of the probable epicenter on Figure 2, using a ruler or the edge of a card and a compass. For each of the three stations, convert the distance from the station to the epicenter into the units of measure provided as a bar scale on the map. Then, stretch your compass just that distance. Now, center the metal point of the compass on the station and draw a circle centered on each station, which represents its distance from the epicenter. When you've done all three, you will notice that the three circles come together in one area: That is the probable epicenter (the point on the earth's surface lying directly above the earthquake's focus).

In the real world, readings from all stations around the world recording the seismic event will be used to estimate the epicenter and the magnitude of the event. More local stations will help locate the focus.

That is why reports on the epicenter and the magnitude will shift around in the weeks after a major quake, reflecting the integration of data from more and more sources. For example, the January 17 1994 earthquake in L.A. was first reported as a 6.6, then a 6.8 (as some really high and anomalous readings came in from Scandinavia), and finally a 6.7. The epicenter at first was reported as in San Fernando and then a few hours later "somewhere near Northridge" and was eventually (about a week later) pinpointed in Reseda (but the media by then had dubbed it the "Northridge" earthquake).

Epicenter Triangulation Problems

Station A records the first arrival of P waves at 14:05 GMT. The S waves arrive at 14:09.

What is the difference in time between their arrival? ______________
About how far away was the earthquake, in kilometers? ______________
Draw a circle on the map around Station A with that radius.

Station B records the S waves at 14:10 GMT and the R waves at 14:16:30.

What is the difference in time between their arrival? ______________
About how far away was the focus, in kilometers? ______________
Draw a circle on the map around Station B with that radius.

Station C records the P waves at 14:01 and the R waves at 14:03:30.

What is the difference in time between their arrival? ______________
About how far was the focus, in kilometers? ______________
Draw a circle on the map around Station C with that radius.

Now, label the area where the three circles come together as "probable epicenter."

The Nomogram

A rather handy graph lets you estimate the local (Richter) magnitude of an earthquake if you know both the maximum amplitude of the ground motion, measured in millimeters as traced on a particular kind of seismograph (Woods-Anderson) and the difference in time between the first record of the primary wave and the first record of the secondary wave on the seismograph. In Figure 3, you see the use of the nomogram for an earthquake producing a 23 mm maximum amplitude trace and a 24 second lag between the primary and secondary waves' arrival. The difference in arrival times corresponds to a distance of just over 200 km and a magnitude of 5.0.

So, what would be the magnitude of an earthquake with the following characteristics?