Travel Time Curve Activity.

Part of Planet X, Module 1,  The Earth’s Interior

Prepared by Gail Ballard as part of EAS 4900, Summer, 2001

 

INTRODUCTION

 

 

                                    The Earth is made up of three main layers, outer crust, mantle and the core.  Think of a boiled egg where the shell is the crust, the white of the egg is the mantle and the yolk is the core.  But how do we know that this model of the Earth is accurate?  The crust is very thin in comparison to the other layers of the Earth, ranging from 5km under the oceans to an average of 30km on the continents.  The deepest drill-hole into the Earth at 10km is still much less than this.  We haven’t even “cracked” the shell!  Scientist’s didn’t use Superman’s x-ray vision to see through the Earth, but they did use something else, Seismic data. 

                                   

 

Figure 1 Model of the interior of the Earth.

 

 

                                    Seismic data, or information from earthquakes, is one tool that scientists have used to develop the above model of the interior of the Earth.  Earthquakes generate waves much like the ripples from a stone thrown into water.  The time a seismic wave takes to travel to different locations around the Earth depends on its velocity.  If an earthquake location is known then the arrival time of the waves at various seismic stations around the world, can be used to create a Travel Time Curve.

 

                                    A Travel Time Curve is a plot of travel time versus location, (usually given as the geocentric angle Delta D.)  Scientists create an Earth model and use the data from Travel Time Curves to see if this model fits.  There are currently three recognized Earth models, each one very similar to the other.  Travel Time Curves, like the one pictured at the end of this exercise contain many lines.  Each line represents different seismic waves traveling at different velocities. There are many lines because the waves bend and reflect at the boundaries of the Earth’s layers.

 

                                    The three types of seismic waves are P- waves, S-waves and surface waves.  The P and S waves are called body waves because they travel through the Earth while the surface waves travel on you guessed it, the surface.  Think of three competitors starting a race: the P-wave sprints through the Earth to get to the finish; the S-wave jogs through the Earth, and the surface wave walks over the land and water.  Each one gets to the same place but at different times because of their different velocities.  This difference shows on seismograms as a characteristic wave pattern.  The velocity of a body wave is also affected by the medium through which it travels. S-waves will not travel through liquids and P-waves will slow down in a liquid medium.

 

Figure 2 Actual seismogram showing characteristic wave pattern.  P and S waves onset is marked.  Surface wave onset occurs at 18:37:47 and has the largest amplitude.  This seismogram was recorded at GNI.IU Station, 69 degrees from the Luzon, Philippine Islands earthquake of 12/11/99.  (IRIS)

 

                                    In this exercise you are a member of a team of Science Officers on Planet X., a colony planet very similar to Earth.  You will construct simple Travel Time Curves for two Planet models, one with a core and one without. Then using Planet X. seismograms you will choose the best model for this planet.  Next, you will use seismograms from an actual earthquake to determine if the Earth really does have a core.

               

 

PROCEDURE

 

 

1. Using a protractor and information in Table 1. mark the station locations On Planet Model 1.

                  2. With a metric ruler draw and measure linear ray-path (L) of body waves from epicenter source to each receiving station.  Use scale to convert to Km and record in Table 1.  (If models were not enlarged, 1 cm = 838 km.)  Check measurement with Equation 1. (L = 2Rsin(D/2)

 

Figure 3 Example of ray-path L from Seismic Wave Source to receiving station.

 (Modified from L. Braile.)

 

3. Use given velocities and Equation 2. (Time = distance ¸ velocity) to complete P, S and surface waves travel-time in Table 1.

 

 

EXAMPLE 1.  Calculating P-wave travel-time in minutes.

 

Station 1. (25 degrees)

 

L measured = 2,765 km         L calculated = 2,758 km (L = 2 x 6371km x sin 12.5 degrees)

Travel-time of P-wave in seconds         T = 2,758 km ¸ 11 km per second = 251 seconds

Travel-time of P-wave in minutes         T = 251 ¸ 60 = 4.2 minutes

 
 

 

 

 

 

 

 

 

 

 

Assumed velocities of Seismic Waves to be used in this exercise.

 

P-wave………………………...11km/sec.

P-wave liquid medium…………8km/sec.

S-wave….…………………….6.4km/sec.

Surface wave….………………5.7km/sec.

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 


4. Use data from Table 1. to draw travel time curves for P, S and surface waves on Graph 1.

5. Repeat step 1. and 2.for Planet Model 2.

6. Repeat step 3. for surface waves only and record in Table 2.

7. Assume that the core of Planet Model 2. is liquid. Shear or S-waves will not travel through a liquid medium while P-waves will slow down.  Mark the stations in the shadow of the core that will not record S-waves.  Compute S-wave travel time using step 3. for the remaining stations and record in Table 2.  (Stations in the shadow should be left blank.)

 

 

Figure 4 Model of the Earth showing location of P and S shadow of the Core.  Note the curved ray-path of actual Seismic Waves (Louie)

           

 

8. Complete P-wave travel times using step 3. for those stations not in the shadow and record in Table 2. 

 

 

9. The P-wave slows down in a liquid medium, so there are actually two velocities to consider if there is a solid mantle layer around the liquid core of Planet Model 2.  Consider only station 6 and 7.  Compute travel time of the P-wave for these stations by adding the travel times of each segment and record in Table 2. leaving other stations blank.

 

EXAMPLE 2.   Adding P-wave travel-time through Mantle and Core.

 

Station 6 (150 degrees)

 

L measured through Mantle = 6,285 km

L measured through Core    =  6,034 km

1.  Travel-time of P-wave in Mantle in Minutes = 6,285 km ¸11 km per second/60

2.  Travel-time of P-wave in Core in Minutes    = 6,034 km ¸  8 km per second/60

 

Add 1 and 2. for total travel-time in minutes. (Ans. 22.1 minutes.)

 
 

 

 

 

 

 

 

 

 

 

 

 

 


10. Use data from Table 2. to draw travel time curves for P, S and surface waves on Graph 2.

11. Use the seismic data from Planet X. to create a Planet X. travel time curve.

EXAMPLE 3.   Picking arrival times for P, S, and surface waves on      generated traces.

 

Trace 1 at location Delta = 30 degrees.

 

First large vertical deflection (P-wave)               5 minutes

Second large vertical deflection (S-wave)                      9 minutes

Third large vertical deflection (surface wave)     not shown

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 


12. Match Planet X curve to Graph 1. or 2.and choose best Planet Model for this new planet.

 

 

13. Using actual seismograms from an actual earthquake determine the P-wave arrival times for each station and enter into Table 3.  Plot this data onto Graph 2. (use contrasting color).

EXAMPLE 4.   Picking P-wave arrival times on actual seismograms.

 

Figure 8. Station LVC.IU seismogram at 7 degrees.

 

1. Event time UTC   20:33:14  (Universal Time Clock – hours:minutes:seconds)

 

2. First arrival UTC  20:34:42  (Use time of first vertical deflection.  Check the time intervals on each seismogram to determine the scale.  In this example, time is marked in intervals of 14 minutes.  Note the hours component of UTC is only marked at the beginning of the horizontal scale and is assumed at the other marked intervals.)

 

Subtract 1. from 2. to get P-wave travel-time. (In this example 20:34:42 – 20:33:14 = 1 minute and 28 seconds.)

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


14. Compare this simplified travel time curve with the Graph 2. and determine if Earth has a core. 

 

 

 

EQUATIONS

 

1. L = 2Rsin(D/2)   where R is the radius.  We will use R = 6,371 km.  D is the geocentric angle Delta, measured in degrees.

 

2. T = L/velocity    where T is the time in seconds, L is the distance in km and velocity is measured in km/sec.  To convert to minutes divide by 60.

 
 

 

 

 

 

 

 

 

 

 

 


Planet Model 1.

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


     Scale

 

 

 

Figure 5 Solid Planet Model

 
 

 

 

 

 

 

 


Planet Model 2.

                                               

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 6   Planet model with Core

 
 

 

 

 

 

 

 


Table 1.  Seismic Data for Planet Model 1.

 

 

Station #

Surface Distance, S

 

 

Angle Delta, D

 

 

 

Linear Distance, L

 

 

P-Wave Travel Time

 

 

S-Wave Travel Time

 

 

Surface Wave Travel Time

 

 

(Km)

(Degrees)

(Km)

(Minutes)

(Minutes)

(Minutes)

Meas.

Calc.

1.

2,780

25

2,765

2,758

4.2

 

 

2.

5,560

50

 

 

 

 

 

3.

9,452

85

 

 

 

 

 

4.

11,675

105

 

 

 

 

 

5.

14,455

130

 

 

 

 

 

6.

16,679

150

 

 

 

 

 

7.

20,015

180

 

 

 

 

 

 

 

 

Table 2.  Seismic Data for Planet Model 2.

 

 

Station #

Surface Distance, S

 

 

Angle Delta, D

 

 

 

Linear Distance, L

 

 

P-Wave Travel Time

 

 

S-Wave Travel Time

 

 

Surface Wave Travel Time

 

 

(Km)

(Degrees)

(Km)

(Minutes)

(Minutes)

(Minutes)

Meas.

Calc.

1.

2,780

25

2,765

2,758

4.2

 

 

2.

5,560

50

 

 

 

 

 

3.

9,452

85

 

 

 

 

 

4.

11,675

105

 

 

 

 

 

5.

14,455

130

 

 

 

 

 

6.

16,679

150

 

 

 

 

 

7.

20,015

180

 

 

 

 

 

  

 

 

 

 

Table 3. Actual Seismic Data

 

Station Name
Station Location

(Degrees)

First Arrival Time

(UTC  hr:min:sec)

Travel Time

(Minutes)

LVC.IU

7

 

 

TRQA.IU

24

 

 

HKT.IU

50

 

 

POHA.IU

88

 

 

KONO.IU

100

 

 

GNI.IU

121

 

 

GUMO.IU

143

 

 

TATO.IU

163

 

 

Graph 1 Travel Time Curve for a Solid Planet Model

 

 

 

 


Graph 2 Travel Time Curve for Constant Velocity Planet with a Fluid Core

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

GENERATED SEISMIC TRACES FOR PLANET X.

 

 

 

Figure 7 Six generated Planet X traces shown next to their corresponding geocentric location delta.  (Long)

 

 

 

ACTUAL SEISMIC DATA

 

The following seismograms are traces recorded at various worldwide stations of the 6/23/01 Peru earthquake which occurred at 20:33:14 UTC with a magnitude of 7.9.

 

 

Figure 8 Station LVC.IU at 7 degrees from source.  (IRIS)

 

 

 

 

 

Figure 9 Data from Station TRQA.IU at 24 degrees from source.  (IRIS)

 

 

 

 

 

 

 

Figure 10 Data from Station HKT.IU at 50 degrees from Source.  (IRIS)

 

 

 

 

 

Figure 11 Data from Station POHA.IU at 88 degrees from Source.  (IRIS)

 

 

 

 

 

 

 

Figure 12 Data from Station KONA.IU at 100 degrees from Source.  (IRIS)

 

 

 

 

 

Figure 13 Data from Station GNI.IU at 121 degrees from Source.  (IRIS)

 

 

 

 

 

 

 

 

 

Figure 14 Data from Station GUMO.IU at 143 degrees from Source.  (IRIS)

 

 

 

 

 

Figure 15 Data from Station TATO.IU at 163 degrees from Source.  (IRIS)

 

 

 

 

 

 

Figure 16 Copy of Travel Time Curve Poster available from IRIS showing reflected and diffracted seismic waves.