EARTHQUAKES AND THE EARTH’S INTERIOR

OBJECTIVES

• Be familiar with the layers of the Earth
• Recognize the two main classifications of Seismic waves
• Determine the distance from an earthquake using P and S wave lag time
• Triangulate three epicenters to determine the location of an earthquake
• Understand the Intensity and Magnitude scales for measuring earthquakes

SUPPLIES

• Pencil
• Ruler
• Drafting Compass
• Calculator

INTRODUCTION TO THE EARTH’S INTERIOR

What is inside the Earth has been a question throughout the ages.  Studying the Earth’s interior poses a significant challenge due to the lack of direct evidence.  Scientists use direct (physical samples such as the ultra-mafic igneous rock - peridotite and lab created materials) and indirect (computer and mathematical models) lines of evidence to answer this complex question.  Seismic data generated from earthquake waves is the primary source of data into the Earth (figure 1). Exploration of the Earth’s interior through seismic waves has led to the discovery of the solid metal inner core, liquid metal outer core, the complex and dynamic core-mantle boundary and convective heat flow within the solid rocky mantle.   The convective heat flow within the mantle is the energy that drives the movement of surface tectonic plates. The movement is the primary cause of earthquakes. In order to understand the variety of surface features, such as volcanoes and earthquakes we must know what lies beneath.

Figure 1. A simplified version of the Earth’s inner layers with thickness units in kilometers. Image:bgs.ac.uk/discovering   Geology/hazards/earthquakes  /structureOfEarth.  CC BY SA license

LET’S TAKE A LOOK AT REPRESENTING THE LAYERS OF THE EARTH IF IT WERE THE SIZE OF A BASKETBALL

The Earth’s crusts are very thin – 5 km for the ocean crust and 35 km on average for continental crust – though this varies greatly from as thin as less than a kilometer at rift zones to as thick as several 100 km at mountain ranges.  If the earth were the size of an apple the relative thickness of the apple skin is thicker than the relative thickness of the crust to the earth. So, let’s compare the Earth to a basketball and determine the proportions.  A ruler, calculator and pencil are needed. The Earth consists of four main compositional layers: inner core, outer core, mantle and crust. On top of the oceanic crust is the ocean (part of the hydrosphere) and on top of that is the atmosphere.

The Earth has a radius of approximately 6,371 km.  Using the grid below and the radius of the image of a basketball determine a mm to km ratio, then determine the thickness of each layer by multiplying the ratio (mm/km) by the thickness of each layer.  Draw in the layers starting with the inner core, then add the outer core layers on top.  Follow this with each layer placed on top of the previous layer.

1. First measure the radius of the basketball image in millimeters.
2. Divide the basketball radius in mm by the radius of the Earth – 6371km. You will then multiply this mm/km ratio by the thickness of each layer, starting with the inner core.

EARTHQUAKES AND SEISMIC WAVES

An earthquake occurs when the land ruptures and releases the built-up stresses from the moving tectonic plates (figure 2).  Much like slowly bending a stick can result in the stick snapping suddenly. As an earthquake occurs, two main types of energy waves are produced:

        Body waves travel fast and move through the entire body of the Earth. There are two types.

                Primary (P) waves are compressional waves and move back and forth, similar to a slinky                         (figures 3 & 4).  As P waves move through the earth the compression is parallel to the direction                         of wave propagation.  P waves can travel through all materials, as all materials can be                                 compressed to some degree.  They are also the fastest moving waves.  If you are some distance                         away from the earthquake the first wave that you will feel is a P-wave.  

                Secondary (S) waves are shear waves that move in a perpendicular direction to the direction of                 travel.  S-waves motion is similar to the motion generated by flicking a rope up and down or a                         stadium of fans doing ‘the wave’ (figures 3 & 4).  S-waves can only travel through solid                                 materials and         move slower than P-waves.

        Surface waves travel along the Earth’s surface. Surface waves are slower than body waves.         Surface waves do not travel as far from the         earthquake as Body waves. Body waves occur in two         types:         

                Rayleigh (R) and Love (L) waves. Their motion is similar to the rolling sensation of a boat at sea                         (figure         5).  Since surface waves move more slowly than Body waves their amplitude tends to be                 higher causing more damage to buildings near the earthquake.  

Figure 2. Over time stresses in the Earth build up (causes by slow movements of the plates – a few inches a year) At some point the stresses become so great that the crust ruptures.  The built-up stresses are releases as energy waves and this is felt as an Earthquake. Not all the stress may be releases. Image: bgs.ac.uk/discoveringGeology/ CC BY SA license

Figure 3.  Body waves which consists of Primary (P waves) are compressional and Secondary (S waves) which shear. Image USGS.gov public domain. https://earthquake.usgs.gov/ - https://earthquake.usgs.gov/learn/glossary/images/PSWAVES.JPG

Figure 4. Slinky representation of compression (P-waves) and a rope flick representation of Shear waves (bottom). Image CC BY-Sa S Earle opentextbookbc.ca/geology

Figure 5. Surface waves: Rayleigh (R) and Love (L). Image CC BY SA S Earle. Opentextbookbc.ca/geology.

Scientists such as Beno Gutenberg, Inge Lehmann and many others in the early 1900’s, discovered the unique layers within the earth and that seismic waves bend and refract when they travel between layers of different densities and phases (liquid or solid).  Seismic waves travel at various speeds depending on the density and phase of the materials (figure 6).  This variation causes waves to travel along curved paths and to bend and refract when the change in density is very sudden.  This bending and distortion of seismic waves produces shadow zones. Shadow zones are regions on the Earth’s surface that do not receive P or S waves due to the bending or absorbing of earthquake waves (figure 7). S-wave shadow zones are produced by the absorption of S-waves by the liquid outer core.  P-wave shadow zones are more complex and are produced by the bending and refracting of P-waves as they travel between several layers of different densities (figure 6).

Figure 6. Speeds of S and P waves as they travel through the earth’s different layers.  P-waves travel much faster than S-waves. S-waves cannot penetrate the liquid outer core and thus the blue line marked S stops at the boundary. Image CC BY SA S Earle. Opentextbookbc.ca/geology

Figure 7. S-wave absorption and modification as a result of the liquid outer core results in a large S-wave shadow zone extending from 1030 around. P-wave shadow zones result from multiple refractions of waves and extend from 1030 to 1500 on the surface. Image: public Domain IRIS Incorporated research institutions for seismology NSF. From S. Earle CC BY https://geo.libretexts.org/Bookshelves/Geology/Book%3A_Physical_Geology_(Earle)/09%3A_Earths_Interior/9.01%3A_Understanding_Earth_Through_Seismology

PLATE BOUNDARIES AND EARTHQUAKES

Prior to our understanding of plate tectonics, the location, intensity and recurrence of often deadly earthquakes were a mystery until scientists such as Harry Hess, Bruce Heezen, Marie Tharp and many others connected earthquake occurrence with plate boundaries.  Figures 8-11 are representations of the three main plate tectonic boundaries.

Figure 8. Divergent plate boundary creating new basaltic ocean. Image CC BY SA bgs.ac.uk/discoveringGeology

Figure 9. A convergent boundary showing the subduction of an oceanic plate. Image: CC BU SA bgs.ac.uk/discoveringGeology/

Figure 10. A convergent plate boundary showing mountain formation as continental crust collides with continental crust as in the Himalayan mountain range. Image: CC BY SA bgs.ac.uk/discoveringGeology/

Figure 11. A transform boundary where two plates slide past one another.  This produces strike-slip faults such as the San Andreas fault system. Image CC BY SA bgs.ac.uk/discoveringGeology/

Earthquakes are most frequent along active tectonic plate boundaries.  They can be sudden and very deadly.  Earthquakes originate at a point beneath the earth’s surface called the focus (plural foci).  From this point below the earth’s surface energy travels outward in all directions as seismic energy waves.  The point on the earth’s surface directly above the focus is the epicenter (figure 12).  Earthquake foci may be shallow (less than 70 km) to deep (greater than 300 km) (figures 13 & 14).  Shallow and intermediate foci earthquakes are the most common.  The depth is directly related to the type of plate boundary (figure 15).  

Figure 12. An illustration depicting the focus (below the surface point of rupture) and the epicenter (point on the surface directly above the focus). Image Wikimedia CC BY-SA 1.0 S. Hocevar. https://en.wikipedia.org/wiki/Epicenter#/media/File:Epicenter_Diagram.svg AnsateSam Hocevar (original author; this is a derivative work)User:TFerenczy create SVG version; cs translationUser:NikNaks es translationUser:Lies Van Rompaey nl translationUser:Rostik252004 ru translationUser:Ата uk translation, CC BY-SA 1.0 <https://creativecommons.org/licenses/by-sa/1.0>, via Wikimedia Commons

Figure 13. A seismicity cross-section along the subducting ocean to ocean convergent boundary at Kuril Islands northeast of Japan.  Note the earthquake foci are located along the descending slab. The star at the surface represents the epicenter of the November 15, 2006 8.3 magnitude earthquake. Image USGS (2006) public domain USGS, Public domain, via Wikimedia Commons. http://plateboundary.rice.edu by Dale Sawyer Rice University after S.Earle Opentextbookbc.ca/geology.

Figure 14. Distribution of earthquakes in the area of the mid-Atlantic ridge near the equator.  Orange color circles represent 0-33 km depth of foci. Blue circles represent instrument intensity scale of IV and V on the USGS shake map. Data from Google Earth USGS August 2016. Image USGS Public Domain

There is a direct relationship between earthquake locations, depth and the different plate tectonic boundary types (figure 15). Looking at a specific boundary with greater detail seismologists can closely correlate the boundary type with the depth of the earthquake. For greater detail and specific maps showing historic or recent global earthquakes please visit the USGS.gov National Earthquake Information Center (NEIC) website or IRIS the Incorporated Research Institutions for Seismology.

Use the plate tectonics map below to compare the different plate boundary types with the depth distribution of earthquake foci.

• Identify the location of shallow versus deep earthquakes
• Connect shallow earthquakes to specific plate boundary
• Connect deep earthquakes to their plate boundary type
• Determine the direction of plate motion for the deep earthquake boundaries.

Figure 15.  Plate tectonics map showing plate boundaries and the different earthquake depths that occur at the various boundaries using color.  Image nsf.gov credit Lisa Christiansen, Caltech Tectonics Observatory public domain. https://www.nsf.gov/news/mmg/mmg_disp.jsp?med_id=64691

SEISMOLOGY - Earthquake Intensity and Magnitude

Prior to our understanding of Plate tectonics, the causes of earthquakes were unknown, with many cultures developing creative legends to explain this natural phenomenon.  The study of earthquakes is called seismology.  A seismograph is the instrument used to measure the vibrational waves that move through the earth (figure 16). The record of the earthquake produced is called a seismogram.

Earthquake measurements are divided into two types of measurements: Qualitative measures of the damages inflicted by an earthquake are referred to as Intensity.  Quantitative measures of the energy released by an earthquake are termed Magnitude measures.  Both measures are meaningful data for interpreting the relative importance of an earthquake.

Figure 16 A seismograph and the seismogram record that it produces. The rotating drum creates a paper recording of the earthquake event. Image CC BY-SA 3.0 Yamaguchi. https://commons.wikimedia.org/wiki/File:Kinemetrics_seismograph.jpg

Intensity takes into account both the damage incurred by the earthquake and the way people respond to it.  The Modified Mercalli Scale (figure 17) is the most widely used scale to measure earthquake intensities.  The scale ranges from Roman numerals I-XII and was originally created by the Italian volcanologist Giuseppe Mercalli in 1883 and altered in 1902.  Intensity maps or commonly called shake maps are generated from the information collected after an earthquake by the USGS to provide near-real-time maps of ground motion and shaking intensity. Colors are used to create a visual representation of the highest damage areas around the earthquake’s epicenter (figure 18). This Instrumental Intensity makes it easier to relate ground motion to what you expect to feel. You can access current information about shake maps at http://pubs.usgs.gov/tm/205/12A01. Or view and interact with actual shake maps at https://earthquake.usgs.gov/data/shakemap/.

Figure 17. An abbreviated table of the Modified Mercalli Intensity Scale. Image CC BY-SA 3.0 R. Harris. Oer.galileo.usg.edu/geo-textbook/1

Figure 18. An intensity or shake map of the Virginia August 2011 earthquake. The star represents the epicenter. Image USGS.gov public Domain via Wikimedia Commons. https://en.wikipedia.org/wiki/2011_Virginia_earthquake. https://earthquake.usgs.gov/earthquakes/shakemap/global/shake/082311a/

Another way to classify an earthquake is by the amount of energy released during the event.  This is referred to as Magnitude.  Charles Richter first developed this scale in the 1930’s.  Most of you are familiar with the Richter scale.  Richter numbers (0-10) are actually magnitudes on a new scale that is more commonly used for describing magnitudes.  Over time there was an increase in the measurement of earthquakes, and it was determined that the Richter magnitude did not accurately measure all earthquake types.  The new scale is called the Moment Magnitude scale.  The Moment Magnitude scale is very similar to the Richter scale and for small earthquakes the numbers are nearly identical.  The moment magnitude scale estimates the total energy released by an earthquake and is based on the seismic moment which is a product of the distance a fault moved, and the force required to move it.  Both the Richter and the Moment Magnitude scale are logarithmic scales, which means that for each whole number that you increase on the scale the energy increases by a factor of ten.  For example, a Richter 4 is ten times the size of a Richter 3. A Richter 4 is 100 times a Richter 2 (10 x10). Each unit on the Moment Magnitude scale represents an increase of energy of 101.5 or 32 times the energy.  So, a Moment Magnitude 4 earthquake represents 32 times more energy released than a 3 earthquake. A Moment Magnitude 4 releases 1,024 times more energy than a Moment Magnitude 2 (32 x 32) (figure 19).

Figure 19. Earthquake magnitudes and frequency relative to energy equivalents. Image: Public Domain. Iris.edu image gallery Rick Callender. https://www.usgs.gov/media/images/graph-showing-earthquake-magnitudes-and-equivalent-energy-release

Let’s compare logarithmic scales.

• If a Richter 1 is represented with a circle the diameter of 1 mm, about the size of a pinhead, CREATE a scale showing the diameter of items that increase by a factor of 10. For example, a Richer 2 represents the diameter of 10 mm or 1 centimeter. The width of a standard yellow #2 pencil.
• THEN, try to redo a portion of this scale representing the energy release Moment Magnitude scale of 32 times energy. Just try 3 or 4 items.
• Compare how quickly the scales sizes differ.

LOCATING EARTHQUAKES

During an earthquake, seismic waves travel all over the globe. Though they may weaken with distance, seismographs are sensitive enough to still detect the waves. The seismogram data from seismographs can give us information including the distance between the earthquake and the seismograph station.  Figure 20 shows an example of a seismogram from a station where a small earthquake has occurred. Notice the fastest moving P wave arrive first, followed by the slower and higher amplitude S wave.

Figure 20. P and S-waves from a small Magnitude 4 earthquake near Vancouver Island in 1997. Image CC BY SA S Earle. Opentextbc.ca/geology

Seismologists use characteristics of the earthquake waves recorded on the seismogram to calculate the times when the P and S waves arrived at the seismograph station. Figure 21 shows a set of seismograms from a station recording a single earthquake event. This data can be used to calculate the distance from a seismograph station to the earthquake epicenter. Let’s walk through the process of identifying P and S wave arrival times at a seismograph station using the seismograms in figure 21.

First, identify the positions of the P and S wave arrivals, reading from left to right on the seismogram. The arrival of seismic waves will be recognized by an increase in amplitude – look for a pattern change as the lines get taller and more closely spaced. The P-wave arrival is easy to identify, it is the first point where the amplitude of the line (also known as the trace) on the seismogram moves above the flat line. Read the arrival time (usually in seconds) for the P-wave on the x-axis beneath the point where the P-wave arrive (note that there aren’t numbers on the x-axis of Figure 21 so for the purposes of this example let’s call the timepoint “0”).

Second, the S-wave arrival is a bit trickier to identify, here, it is an increase in the amplitude of the trace that occurs after the P-wave amplitudes start to decrease. All three traces in Figure 21 are from the same seismograph station. Note that the arrival times of the P and S waves are virtually identical for all three traces but there are some differences in the wave amplitudes depending on the direction of shaking recorded in the trace.

Figure 21. An example seismogram with the arrival of P (red line) and S waves (green line) included. The X-axis represent time. The Y-axis represents the shaking. Image CC BY SA bgs.ac.uk. Wikicommons Public Domain by Pekachu

Third, determine how far away the earthquake occurred from the seismograph.  Calculate the time interval between the arrival of the P-wave and the arrival of the S-wave. In the example in Figure 20, the time between the P- and S-wave arrival times is about 10 s.

Fourth, use a travel-time curve, (figure 22) which is a graph of P and S wave arrival times, to determine the distance of the earthquake from the seismograph station. In the example from figure 19, if the P-S arrival difference is 10 seconds, the earthquake occurred approximately 100 km from the seismograph. A longer time interval between the P and S wave indicates the earthquake is a longer distance from the station.

Last, though the distance to the earthquake epicenter can be determined using a travel-time graph, this single seismogram cannot tell us exactly where the earthquake occurred. The earthquake could lie at any location, in all directions along that distance from the earthquake. Data from at least three seismographs locations are needed to pinpoint the earthquake epicenter (figure 23). Sometimes it takes more than three seismograms to pinpoint the epicenter, depending on the geometry of the station locations. Ideally the stations are located in a triangle around the earthquake epicenter but this is not always the case.

Figure 22. A travel-time graph that includes the arrival of P-waves and S-waves. Note that these curves plot distance versus time and take into consideration that the Earth is spherical. Curves vary with the depth of earthquake because waves behave differently (i.e. their velocities change) with depth and changes in the material properties of the Earth. This curve is used for shallow earthquakes (<20 km deep) with stations within 800 km of the earthquake epicenter. The S-P curve refers to the difference in time between the arrival of the P-wave and S-wave. If you noted on your seismogram that the P-wave arrived at 10 seconds, and the S-wave arrived at 30 seconds, the difference between arrival times would be 20 seconds. You would read the 20 seconds off the y-axis above to the S-P line, then drop down to determine the distance to the epicenter. In this case, it would be approximately 200 kilometers. Image: Original work by Randa Harris (2015) CC BY-SA 3.0. oergalileo.usg.edu/geo-textbooks. Part of Geology Commons

Figure 23. In order to locate this earthquake epicenter, seismologists used seismograms from Portland, Salt Lake City, and Los Angeles. The time between P and S wave arrivals was calculated for each station, and travel timetables gave a distance. Circles were drawn from the stations for the calculated distances. The one resulting overlap point, at San Francisco, was the earthquake epicenter. Image: Original work by Randa Harris (2015) CC BY-SA 3.0. oergalileo.usg.edu/geo-textbooks. Part of Geology Commons.

EXERCISE – LOCATING AN EPICENTER (this activity is a modification from oer.galileo.usg.edu Randa Harris CC BY-SA 3.0)

SIMPLE DISTANCE

Imagine that a strong earthquake takes place in Philadelphia, PA. Assuming that the crustal average P-wave velocity is 5 km/s, how long will it take for the first seismic waves (P-waves) to reach you in the following places (distances from the epicenter are shown)?

TRIANGULATION – Locating the epicenter

You will determine the location of an earthquake epicenter using seismograms from Carrier, Oklahoma, Smith Ranch in Marlow, Oklahoma, and Bolivar, Missouri (figures 1-3). These are actual seismograms that you will be reading, from an actual earthquake event. For each seismogram, three different readouts are given, because the seismograph measures movement along three different axes simultaneously. You can use any of the three readouts for each station in your calculations, because each of the readouts will have the same arrival time for the different components of each wave.

First, determine the time when the P and S waves first arrived for each station. To identify the P and S waves. Look for a pattern change as the amplitude of the lines gets bigger; this indicates the arrival of each of the waves. Mark both the arrival of the P-wave and S-wave on the seismogram and record that information in the table.

Second, using the time scale in seconds on each of the three figures, determine the time difference between the P and S wave first arrivals. Write these times in the Table below for each of the three seismograms.

Figure 1. Seismogram readings from Carrier, Oklahoma.
Source: USGS (2015) public domain, source webpage: https://earthquake.usgs.gov/

Figure 2. Seismogram readings from Smith Ranch, Marlow, Oklahoma.
Source: USGS (2015) public domain, source webpage: https://earthquake.usgs.gov/

Figure 3. Seismogram readings from Bolivar, Missouri. 
Source: USGS (2015) public domain, source webpage: https://earthquake.usgs.gov/

Third, the difference between the P and S wave first arrival times will be used to determine the distances to the epicenter from each station in Figure 4. Make sure that you use the curve for the difference between the S and P wave first arrival times (S-P). Find the difference between the S and P first arrival times in seconds on the y-axis, draw a line over to the S-P curve at the same time, then draw a line down to the x- axis to determine the distance. Add the values to Table 1.

Figure 4. A travel-time graph that includes the arrival of P-waves and S-waves. Note that these curves plot distance versus time and are calculated based on the fact that the Earth is a sphere. Curves vary with the depth of earthquake because waves behave differently (i.e. their velocities change) with depth and change in material. This particular curve is used for shallow earthquakes (<20 km deep) with stations within 800 km. The S-P curve refers to the difference in time between the arrival of the P-wave and S-wave. If you noted on your seismogram that the P-wave arrived at 10 seconds, and the S-wave arrived at 30 seconds, the difference between arrival times would be 20 seconds. You would read the 20 seconds off the y-axis above to the S-P line, then drop down to determine the distance to the epicenter. In this case, it would be approximately 200 kilometers. Source: Randa Harris (2015) CC BY-SA 3.0.

Last, figure 5 shows the locations of the three stations. You will draw circles on this map to represent the distance of the earthquake epicenter from each station. Use a drafting compass to draw the circles. This map includes a legend in kilometers. For each station, note the distance to the epicenter. Measure the scale on the map in centimeters and convert your distances in kilometers to centimeters (e.g., if the map’s scale of 100 km = 2.1 cm on your ruler, and you had a measured distance from one station of 400 km, that would equal 8.4 cm on your ruler). For this fictional example, you would use a drafting compass to make a circle around the station that is 8.4 cm in radius (from the center to the edge). Create a circle for each of the three stations, using their different distances to the epicenter. They should overlap (or nearly overlap) in one location. The location where they overlap is the approximate epicenter of the earthquake.

Figure 5.  Map depicting three seismograph stations (Carrier, Smith Ranch, and Bolivar) located in Oklahoma and Missouri, USA. Source: Joyce McBeth (2018) CC BY 4.0, after Randa Harris (2015).