Surface Wave Propagation Around the Earth -
A Problem Solving Exercise
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#### L. Braile, Professor

Purdue University

January, 2001  Background:

Examine the seismograms shown in Figure 1.  The display is called a seismic record section.  Each trace is a seismogram recorded at a seismograph station.  Most of the station locations (letter code adjacent to each trace) can be found on the seismograph network maps shown in Figures 2 and 3.  On the record section (Figure 1), the seismograms are plotted according to the distance (in degrees, geocentric angle) from the earthquake location and time from the earthquake origin.  The traces are of the vertical component of ground motion, and have been filtered to include only periods longer than 125 seconds.  The prominent arrivals (often called phases) that “angle across” the record section and are labeled R1, R2 and R3 are long-period Rayleigh (surface) waves that travel along the surface of the Earth.  Surface waves penetrate (have particle motion) to depths of tens to hundreds of km (depending on the type of wave and the period of oscillation of the phase) but travel approximately parallel to the Earth’s surface.

Questions:

1.   What explains the unusual pattern of the R1, R2 and R3 phases across the record section?  (That is, what are the surface wave propagation paths for R1, R2 and R3 that explain this pattern?).  Hint:  For our purposes we can assume that all of the stations are located in a line (actually a great circle) around the Earth.  The cross section diagram in Figure 4 illustrates this situation.  A few of the seismograph stations are shown at the appropriate distance from the earthquake.  (The actual locations of the stations are shown in Figures 2 and 3 and are not arranged in a line or great circle path through the epicenter of the Loma Prieta Earthquake.  However, because the surface waves propagate in all directions from the source, the arrival times are approximately the same as if the stations were all located along a great circle path from the epicenter.)

2.   What is the approximate velocity of propagation of the long period Rayleigh waves illustrated in Figure 1?  Hint:  the velocity along the surface (often called the apparent velocity, which for the surface waves is the actual propagation velocity because they are propagating parallel to the surface) can be determined from the slope (velocity = 1/slope) of the arrivals for the R1, R2 and R3 phases on the record section.  What is the velocity in degrees/minute?  For the spherical Earth of approximate radius 6371 km, one degree of geocentric angle corresponds to a distance along the surface of approximately 111.19 km.  Using this information, what is the approximate velocity of the long-period Rayleigh waves in units of kilometers/second?  (The conversion to km/s is useful because these units are commonly used to describe the velocity of propagation of seismic waves through Earth materials.)

3.   Using the velocity found in question 2 (in degrees/minute or km/s), how long does it take for the long period Rayleigh wave to propagate completely around the Earth (360 degrees)?

Reference (and source of Figures 1, 2 and 3, pp. 14, 189, 190):

Lay, Thorne, and Terry C. Wallace, Modern Global Seismology, Academic Press, San Diego, California, 521 pp., 1995. Figure 1.  Seismograms of the 1989 Loma Prieta (central California) earthquake in record section form showing the long period Rayleigh wave (largest amplitudes) labeled R1, R2, R3.  The seismograms are vertical component records and have been filtered to include only periods longer than 125 seconds.  Seismograph stations that recorded the seismograms, in order of distance, are:  AMNO, COL, KIP, HRV, SJG, PPT, RPN, AFI, CAY, MDJ, HIA, TOL, BDF, WMQ, TAM, KMY, CAN, TWO, HYB, BCAO, NWAO, SLR, RER.  Locations of most of these stations are shown on the maps in Figures 2 and 3.  (Modified from Lay and Wallace, 1995). 180o Figure 2.  Locations of modern, digital, broadband seismograph stations of the IRIS/USGS-GSN and IRIS-IDA networks.  (Modified from Lay and Wallace, 1995).

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# TOL o Figure 3.  Locations of modern, digital, broadband seismograph stations of the Project GEOSCOPE network.  Dots and triangles are GEOSCOPE stations.  Open circles are other digital stations recording seismograms shown on the record section in Figure 1.  (Modified from Lay and Wallace, 1995). Figure 4.  Schematic diagram illustrating a cross section through the Earth and the locations of seismograph stations.  Distance from the earthquake epicenter to a station can be measured in kilometers along the surface or by the geocentric angle (D) in degrees.

ÓCopyright 2001.  L. Braile.  Permission granted for reproduction for non-commercial uses.