How to Use the Earthquake Travel Time Graph (Page 11of the Earth Science Reference Tables).

The graph on page 11 can be used to find several different variables. Let’sstart with:

TRAVEL TIME or DISTANCE from EPICENTER (Given one, find the other)

Sample Problem: A seismic station is 3000 kilometers from the epicenter of anearthquake. How long will it take P waves from this earthquake to reach theseismic station?

You must always ask yourself two questions:

1) What information do I have?

2) What information am I looking for? If you don’t know what you’re looking for it’s very unlikely that you’ll find it!

3000 kilometers from the epicenter

How long (time)

We know the distance (3000km)We’re trying to find the time it willtake P waves to travel this distance.Find 3 (really 3000km) on the bottomaxis and, using a straight edge(a ruler) draw a line up to meet theP wave line.Now, using the ruler, draw a line overto the left axis and read the traveltime: 5 minutes and 40 seconds.Notice that each small box is worth20 seconds.Now try the same problem in reverse:It takes P waves 5 minutes and 40seconds to travel from an epicenterto a seismic station. How far is theseismic station from the epicenter?

We know the P wave travel time:5 minutes and 40 seconds.We are trying to find the distancebetween the epicenter and theseismic station.Using a ruler, draw a line from thetime (5:40) to the P wave line.Now draw a line straight down tothe bottom axis and read the distance.............

3000 kilometers!All of these problems are the same.Given the time, find the distance.Given the distance, find the time.And it doesn’t matter whether youare given P or S wave travel timeas long as you are careful to usethe correct line and, most important:

TAKE THE TIME TO BE CAREFUL AND ACCURATE!

Let’s take this one step further. A seismic station is 3000 km from the epicenter of an earthquake. If P waves from that quake arrive at the station at 4:25:40 PM (4 hours, 25 minutes and 40 seconds), at what time did the earthquake occur? We do exactly the same thing wedid before, we find the travel time which is 5:40 (5 minutes, 40 sec.)Now some math. If the waves arrived at 4:25:40 and they’ve been traveling for 5:40, when did they start out?

Subtract: 4:25:40 5:40 ------------ 4:20:00

The quake occurred at 4:20:00 PM

OK, let’s try another type of problem involving both P and S waves. Here’san example...........................

It takes P waves 7:20 (7 minutes and 20 seconds) to travel from an earthquakeepicenter to a seismic station. How long will it take S waves from the sameearthquake to reach the seismic station?What do we know? We know P wave travel time is 7:20

What are we trying to find? We want to find S wave travel time.

Do we have enough information to do the problem? NO!

We have to divide the problem into 2 parts. First, we do just what we did inthe previous problem. We use the P wave travel time to find the distanceto the seismic station and then.................................

We use the distance to the seismic station to find how long it took S wavesto travel that same distance.

Let’s see how it’s done....................................

We know P wave travel time is 7:20so, using a ruler, draw a line from7:20 over to the P wave line.Now draw a line straight down to findthe distance from the epicenter.........The distance is 4200 km. Notice thateach small box on the bottom axis is200 km.Now we can get on with the secondhalf of the problem. If the seismicstation is 4200 km from the quakeepicenter, how long (time) did it takethe S waves to travel that samedistance?Draw a line from 4200 km straight upto the S wave line.

Now draw a line over to the verticalaxis and read the time..........

13 minutes exactly (13:00)

And now for something completely different.......................

Another type of question involves the“difference in travel time between Pwaves and S waves”.

Whenever you are given the differencein arrival times OR you are given bothtimes so that you can subtract and findthe difference, you should immediatelyrealize that you will be dealing with theshaded area (yellow) between the twolines.

Here’s a sample problem:P waves arrive at a seismic station 4:30 (4 minutes, 30 seconds) beforethe arrival of S waves from the sameearthquake. How far from the epicenteris the seismic station?

Here’s what you know: P & S wavesarrive at a seismic station 4 minutes and30 seconds (4:30) apart. You are askedto find the distance to the epicenter.Here’s how:1) Take a sheet of paper and line up the left edge with the vertical axis (time). Be sure that most of the paper is hanging down below the graph. This is important.2) Make a small, thin, and accurate mark on the paper at 0 time. Make another small, thin, and accurate, mark at 4:30 (4 minutes, 30 seconds).

Your 2 marks are now 4:30 apart!

Now slide your paper to the rightuntil one of your marks is exactlyon the S wave line and the otheris exactly on the P wave line. It isvery important to be sure yourpaper is straight (vertical).

Now look to see where the bottomof your paper crosses the lower(epicenter distance) axis. In thiscase it crosses at exactly 3000 kmwhich is the answer.

When P & S waves arrive 4 minutesand 30 seconds apart it means thatthe seismic station is exactly 3000km from the epicenter of the quake.

Of course we can do the sameproblem in reverse!

A seismic station is 3000 km fromthe epicenter of an earthquake.How long after P waves arrive willS waves from the same earthquakearrive at the station?

This time place your paper on the3000 km mark taking care to keepthe paper straight and to coverboth the P and S wave lines.

Make small, thin, and accuratemarks where your paper crossesthe P line and the S line.

Then..............................

Slide your paper to the left so that yourlower mark is on time 0.

Now just read the time indicated by yourtop most mark: 4:30 (4 minutes and30 seconds) which is the answer.

This kind of question may also be phrased this way:“P waves arrive at a seismic station at12:32:00. S waves from the same earthquake arrive at 12:36:30. How farfrom the epicenter is the seismic station?

All you need to do is subtract in orderto get the difference in arrival times. 12:36:30- 12:32:00---------------- 00:04:30 0 hours, 4 minutes, and 30 seconds.

Just remember, if you’re given 2 times, just subtractto get the difference.

One last kind of problem to become familiar with. Sometimes, instead of giving youthe difference in arrival times, you will be given a seismogram (a record made by aseismograph) instead.Using this seismogramfind when the P wavesand the S waves arrive.

Do this by carefully making a mark at theP wave and S wavearrival times.

Now count the number ofminutes between thearrival of P and S waves atthe station.

From this point on it’s just like the previous problem: If the difference in arrival timesbetween P and S waves is 6 minutes, how far is the seismic station from the epicenter of the earthquake?

Using the seismogram (on the previouspage) you determined that P & S wavesarrived at a seismic station 6 minutesapart.

Place your paper along the vertical axis(time) and make small and accuratemarks at time 0 and time 6. Rememberto keep most of the paper hanging downbelow the graph.

Now slide your paper until onemark is on the S wave line and theother is on the P wave line. Beabsolutely sure that your paperis straight (vertical).

Read the distance at the pointwhere the edge of the papercrosses the bottom (distance)axis.

Remember that each small box is200 km. The answer is............

4400 km!

That all there is to it. But doingthis once or twice won’t help. TheONLY way to get good at anythingis to practice, practice and thenpractice some more!

One last type of problem: Find the‘time of origin of the earthquake’.In other words, use the informationgiven to find out when the quakeoccurred.Here’s a sample problem: A seismic station is 4000km from the epicenterof an earthquake. P waves arriveat the station at 2:48:00 PM. At whattime did the earthquake occur?First, use the distance to find the P wave travel time.OK, the P waves took 7 minutes totravel the 4000km distance.If they arrived at 2:48:00 and thetrip took 7 minutes, they must havestarted out 7 minutes before 2:48 PMSo subtract. 2:48:00 - 7:00 ---------------Origin time: 2:41:00 PM

Let’s try another one: P waves arriveat a seismic station at 4:22:10 AM. S waves from the same earthquakearrive at 4:28:50 AM. What is the timeof origin of the earthquake?

First subtract to get the difference inarrival times:

4:28:50 - 4:22:10 --------------difference = 6:40 (6 min, 40 sec)

Now, as we did before, get a pieceof paper and carefully andaccurately make marks at time 0and time 6:40

Slide the paper until one markis on the P wave line and theother is on the S wave line.Now read the distance fromthe epicenter on the bottom:4000 km. Now that we know the distanceto the epicenter we can easilytell how long it took P wavesto travel that distance.P waves took 7 minutes totravel the 4000 km and sincethey arrived at 4:22:10 wecan subtract to find out whenthey started. 4:22:10 - 7:00 --------------Origin time: 4:15:10

Best advice:

Many students read a question and immediately realize that they donot know what to do. They feel they are completely lost. In that casethere’s one important thing to remember:DO SOMETHING! Just don’t sit there! Do something with the informationyou have. For instance, if the question mentions P waves and gives adistance, use that to find a travel time.

If the question gives a travel time for S waves use that to find adistance to the epicenter.

Now you have a little more information than you had before. Re-readthe question. Be sure you know what you’re looking for and see ifyou now have enough information to get the answer.

Never give up. Never let yourself sit there doing nothing!