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Earthquakes

Tectonic Plate Movement and Seismic Activity

If you drop a bucket of apples into a sink full of water, the apples will float around on the surface of the water, bouncing off of one another and swirling gently in the general direction of the movement of the water in the sink. Now imagine that these apples are large chunks of rock, fitted snugly together like

Tectonic Map of the World (image courtesy of USGS)

Tectonic Map of the World (image courtesy of USGS)

puzzle pieces, floating on a thick viscous layer of semi-solid rock, and we will have a situation very similar to that of the tectonic plates of the earth’s crust. These plates are in a sense drifting and bobbing on the uppermost layer of the earth’s mantle, the layer of the earth directly beneath the earth’s crust, which functions like a very thick liquid (much like pudding) causing the tectonic plates to swirl on its surface much like the apples in the sink. Over the course of millions of years, these incredibly slow movements are able to completely alter the configuration of our land masses and oceans here on Earth.

When the currents in our sink cause the apples to bump up against one another, they bump gently, and then drift apart. This is not the case, however, with the tectonic plates of the earth’s crust. Recall that these plates are fitted snugly against one another, and they have a considerable amount of force behind their movement due to their immense weight. For these reasons, when these plates bump or slide against one another, this often results in significant and measurable seismic activity.

Types of Faults

The junctions between plates of rock that are moving in different directions are known as “faults”. The junctions between the tectonic plates of the earth’s crust are major fault lines, where a great deal of significant seismic activity is centered. There are also many smaller fault planes on the earth’s surface where notable movement between plates of rock is occurring.

There are many different types of faults with a wide range of variations in their characteristics. All of these, however, fall into one of three larger categories: strike-skip faults, normal faults, and thrust faults.

San Andreas Fault (image courtesy of NASA)

San Andreas Fault (image courtesy of NASA)

  • A strike-slip fault involves sheets of rock on opposing sides of a fault sliding past each other. With this type of fault there is no vertical lifting or subduction component; the objects are moving in a side-by-side motion on the same plane. The San Andreas Fault in California is a good example of a strike-slip fault. This particular fault marks the boundary where the Pacific and North American plates meet. The San Andreas Fault is an area which is well known for having frequent and substantial seismic events.
  • A normal fault occurs where the rock on one side of the fault line is moving downward in relation to the

    Mid-Oceanic Ridge (image courtesy of USGS)

    Mid-Oceanic Ridge (image courtesy of USGS)

    rock on the other side. This differs from a strike-slip fault because we now have both horizontal and vertical components to our fault movement. The normal fault is typically associated with areas where the earth’s crust is extending; as the two sheets of rock slide away from one another, magma from the earth’s interior rises up to fill in the space that is left behind, forming new crust. Normal faults often occur along the mid-oceanic ridges. In these areas, the crust of the sea-floor is pulling apart, and the resulting void is filled in with magma from the earth’s mantle. These ridges are very active areas of crust formation; it is estimated that 2.5 km of new crust is being formed every year by this process.

  • A thrust fault operates in much the same way as a normal fault. The main difference is that on a thrust

    Rocky Mountains (image courtest of NASA)

    Rocky Mountains (image courtest of NASA)

    fault, the sheets of rock on opposing side of the fault are moving towards each other rather than away. The compressional force from this movement forces one of the sheets of rock to move up and over the top of the other. The Rocky Mountains have risen to their momentous stature as the result of thrust faulting. As the tectonic plates press against one another, the great compressional force that is generated causes the material on either side of the fault to be forced upward, resulting in mountains.

Rupture Along Fault Lines

The rocks on opposite sides of a fault have forces acting on them that are trying to move them in different directions from one another. The surfaces of these rocks are seldom smooth, and so a great deal of friction can build up between these surfaces. As this friction escalates visible signs on the surface can be seen. Objects that once followed a straight path across the fault, such as fences and roads, will begin to distort along with the rock following a slanted path across the fault line. Eventually, the rock surfaces along the fault line will reach a point where they can withstand no further distortion. Once this point is reached, the fault will rupture, or “slip”, at the weakest point along the fault line. Once this happens, this rupture spreads rapidly along the fault line and the rest of the fault will jerk suddenly into a position where it is under considerably less tension. This sudden slippage is known as elastic rebound, and this release of tension is accompanied by the release of a tremendous amount of energy.

Locating the Epicenter

Once this rupture, or “earthquake”, has occurred, seismologists begin the process of trying to pinpoint the location of the earthquake. There are seismology stations scattered across the globe, and soon after an earthquake happens these stations will start receiving information that can be used to discover exactly where the earthquake struck. The first method used is to compare the times at which P-waves begin to arrive at different stations in the general area of the rupture. If we were to compare the P-wave arrival times from 3 seismic stations in the area of a rupture, we can conclude that the

image courtesy of USGS

image courtesy of USGS

earthquake happened closest to the station where the first P-waves arrive the soonest, and furthest from the station where they arrive the slowest. The third will lie somewhere between these two. With this information we can get a rough idea of the area where we can expect to find evidence of a recent rupture. We cannot get a clear picture solely from this information, however, because time and distance are not directly proportional to one another, and because there is a good deal of variation in velocity within the earth.

It is possible to greatly improve the estimate of the location of an earthquake if both the P-wave and the S-wave arrival times are used. S-waves travel considerably slower than P-waves, so the lag between the first arrivals of these two types of waves at a particular station can tell a great deal more about the location of an earthquake. A longer lag will indicate that the earthquake is further away from the station, while a short lag will imply that the rupture was closer to the station where this was recorded. This estimate can be further improved by comparing the lag time between the P and S-waves to a standard P and S-wave travel time chart. The distance from the “epicenter”, the point on the surface of the earth that is directly above the source of seismic activity, can be read directly off of this chart. The time at which the rupture occurred can also be found from the same chart.

Once all of this information has been gathered, seismologists use what they have learned to draw an arc around each station corresponding with the location of the earthquake. They note the spot at which several of these arcs intersect; this spot is considered to be the epicenter of the earthquake.

Locating the Hypocenter

The depth of the hypocenter, the exact point below the surface of the earth where the displacement

3D Representation of Hypocenters Under a Fault Plane (image courtesy of USGS)

3D Representation of Hypocenters Under a Fault Plane (image courtesy of USGS)

occurred, can be found by comparing the rays that describe the behavior of the P-waves as they travel through the earth. If we compare the P-ray, the ray that travels directly from the hypocenter to the surface, with the pP- ray, which is generated as the P- wave bounces from the surface back into the interior of the planet, we can determine the depth of the hypocenter by noting the time difference between the arrivals of the waves associated with these rays. The exact depth can be read off of a standardized table, but in general it can be said that the deeper the hypocenter, the greater the time difference between the P and pP-wave arrivals.

Mapping Fault Plane Solutions

In addition to depth and location, it is also useful for seismologists to know the orientation of a fault and the direction in which the displacement is occurring. These two things can be determined by plotting a fault plane solution.

The orientation of a fault line can be determined by noting what direction the first P-waves arrived from. The greatest compressional force will be generated in a straight line that is directly extended from the fault plane. Thus we can conclude that the fault is lined up with the direction from which the greatest compressional force was recorded.

Discerning the displacement along a fault line is a little trickier, as the two sides of the rupture have moved in opposing directions. When a fault slips, the resulting wave pattern is symmetrical about the axis of the hypocenter. This means that we can record the wave pattern that is generated by an earthquake, and it will form a four-lobed radiation pattern around the hypocenter. Two of these lobes will line up with the displacement of the fault line, and the other two will be perpendicular to it. There is no way to tell from this information alone which lobes correspond to the real fault plane and which correspond the the plane perpendicular to it, also known as the axillary plane.

Much additional information can be used to determine the true direction of the displacement along a fault plane. It is possible that if the rupture was large enough a surface break will reveal the fault plane. Additionally, any aftershocks related to the rupture will occur along the true fault plane rather than the axillary plane. Seismologists can also infer that if several earthquakes have happened along a single line, that they all fall within the same fault plane.

It can be said that all faults are more or less on a plane, and displacement occurs within the plane that the fault lies on. Seismologists are able to describe the displacement and forces associated with a particular earthquake using a sphere. The sphere associated with an event will describe both the direction and the orientation of a fault. Since it is much easier to draw and understand the markings on a circle than a sphere, these fault-plane solutions are depicted in a circular graph known as a “beach ball”.

Fault Plane Soluton in 3D and the 2D projection ("beach ball")

Fault Plane Soluton in 3D and the 2D projection (“beach ball”)

Fault Plane Solutons (image courtesy of USGS)

Fault Plane Solutons (image courtesy of USGS)

In order to make the “beach ball” of a seismic event, seismologists note the location of the first P-wave arrivals from all of the seismic stations that received information from the event. These are projected back onto the fault plane in order to determine their take-off angle from a chart. The actual fault plane and the axillary plane are noted on the drawing, and each recording is projected into its proper place on the diagram, which has also been adjusted to indicate the orientation of the fault. If the first arrival was recorded as a compressional force, the circle denoting it is solid; if the associated force was dilatational, the circle is left open. Once this is accomplished, it is clear from the graph where all of the compressional and dilatational forces are centered. If the area was subject to compressional force, the entire area corresponding to it on the beach ball is shaded. If the force was dilatational, the area is left unshaded. After all of this has been done, the beach ball will clearly indicate, by the pattern of compression and dilatation, whether the fault in question is a normal, strike-slip, or thrust fault.

Mapping the Size and Displacement of a Rupture

After an earthquake has occurred, seismologists seek to determine both the length of the rupture and

INSAR satellite imagery can be used to determine the extent of a rupture (image courtesy of NASA)

INSAR satellite imagery can be used to determine the extent of a rupture (image courtesy of NASA)

the size of the displacement associated with the rupture. In the simplest of cases, seismologists can travel to the location and examine the fault break along the surface to gain this information. Often however, there is no surface break, or the fault lies beneath the ocean. In these cases, seismologists must resort to different means to discover this information. It has been noted that with earthquakes that do involve a surface break, the aftershocks nearly always occur along the original

visible displacement along a strike-slip fault (image courtesy of NASA)

visible displacement along a strike-slip fault (image courtesy of NASA)

rupture plane. It is assumed to be true that this is also the case with earthquakes that are not associated with a surface break. Therefore seismologists can map the locations of all of the aftershocks associated with a particular event, and this will yield an approximate map revealing the location of the fault plane along with the size of the rupture.

Information may also be gathered by comparing maps of an area before and after an earthquake. By pairing visual differences before and after the event with a few measurements along the rupture, seismologists can often get a good approximation of the size of the displacement that has occurred. More accurate information can be gathered by comparing satellite images taken before and after an event.

Measures of Earthquake Size

Intensity and Magnitude

The measurement of the size, or strength, of an earthquake can be done in several ways. The size of an earthquake can be a measurement of the effects at a certain locality or it can be the measurement of the disturbance at the source. These measurements are in the form of intensity or magnitude. Intensity is a subjective measurement of earthquake strength that assess how strongly an earthquake was felt and how severe was any damage caused at a locality. Such effects are perceptible shaking, small objects being shifted, structural damage… etc. This scale of measurement is called the Modified Mercalli Scale of 1931, which has twelve categories. This scale allows the intensity at each locality to be estimated after an earthquake by observing the damage and asking people what they felt and noticed. This data is collected and the observed intensities can be contoured as isoseismals. It is called an isoseismal map, as one draws contour lines to enclose locations having higher intensities.

Magnitude is an objective measurement of source strength of an earthquake. The first magnitude scale was designed by the acclaimed seismologist Charles Richter in partnership with Beno Gutenberg in 1935. The scale was originally intended to be used only in a particular study area in California, and on seismograms recorded on a particular instrument, the Wood-Anderson torsion seismometer. Though most commonly quoted in the media as the Richter magnitude scale, or Richter magnitude, many scientists and historians feel it should be known as the Richter-Gutenberg scale.

The Richter magnitude scale, or more correctly local magnitude ML scale, measures the amplitude in microns (millionths of a metre) of the largest oscillations (the surface waves) recorded by a seismometer, 100 km from the earthquake source. To make the long range of numbers more manageable, he took the logarithm (to base 10) of the values. This means an increase of one in magnitude is an amplitude 10 times as large.

ML= log10 (maximum amplitude of oscillation, in units of 10-16 m)

Corrections

There are some draw backs that need to be corrected for in Richter’s original formula. One such drawback is the fact that earthquakes are rarely 100 km from the seismometer. Also different types of seismometers give different amplitude seismograms. The formula that takes these two corrections into account is:

ML=log10(Ah)+ 3log10∆- 2.29

  • ML= local magnitude
  • Ah= maximum horizontal displacement
  • The second term in the equation is taking into account the 100 km from the epicenter.

Another correction to take into account is the fact that Richter’s seismometers were relatively close to the epicenter. At these smaller distances from the epicenter, S- waves have the largest amplitude, but beyond 600km surface waves have the largest amplitude and would create a different value. The equation that correct for this is:

MS= log10(A/τ)max+1.66log10(∆)+3.3+Corr(depth)

  • MS= surface wave magnitude
  • A= maximum vertical displacement (surface wave)
  • τ= period of the event
  • Corr(depth) is the correction made if the hypocenter is deeper than 50km.

Deep earthquakes are less effective in producing surface waves (largest amplitudes) than shallow earthquakes. This causes the measured amplitude to be an underestimate of the magnitude of deep earthquakes. To correct for this the largest body-wave amplitude is used. Because body waves would give a smaller magnitude than surface waves for shallow earthquakes, a constant is added to make up the difference. This formula is:

Mb= log10(Aρ/τ)+Q(∆,h)+ local correction

  • Mb= body wave magnitude
  • Aρ= Maximum vertical amplitude (P-waves)
  • τ = period( frequency=1/1second= 1Hz)
  • (∆,h) is the correction for both the distance from the epicenter and the depth ,h, from the hypocenter.

Because local geology of the station could cause the waves to be focused towards or deflected away ,as well as absorbed by underlying rock a station correction term, local corrections, is added to the formula.

Seismic moment

Though Richter magnitude is the most commonly quoted measure of earthquake size, it is not the most accurate. A better measure is seismic moment, Mo. Seismic moment occurs just before a fault ruptures, when the shear forces on either side of the fault create a couple, or torque, whose size/moment equals the product of the shear forces and the perpendicular forces between them.

  • Moment of couple= F×2b
  • F= μA × strain
  • μ= the rigidity of the rock around the source, linearly related to the size of the earthquake
  • A= surface area of the fault
  • Strain= d/2b
  • Moment of couple= μAd= Mo
  • d= offset of the fault (how much the fault slips)

    Figure 1,image inspired by Khan, M. Aftab and Alan E. Mussett. Looking Into the Earth: An Introduction to Geological Geophysics.New York: Cambridge, 2000.

    Figure 1,image inspired by Khan, M. Aftab and Alan E. Mussett. Looking Into the Earth: An Introduction to Geological Geophysics.New York: Cambridge, 2000.

It is safe to assume that the larger the earthquake the larger the rupture at the fault plane. A smaller earthquake does not penetrate all the way through the vertical extent of the fault plane, thus creating it’s smaller size. If an earthquake of some size does fully extend through the vertical extent of the fault plane it would then have to enlarge by traveling horizontally across the length of the fault(fig.2). This results in a difference in the seismic moment of rupture length for small and large earthquakes.

figure 2, inspired by Khan, M. Aftab and Alan E. Mussett. Looking Into the Earth: An Introduction to Geological Geophysics.New York: Cambridge, 2000.

figure 2, inspired by Khan, M. Aftab and Alan E. Mussett. Looking Into the Earth: An Introduction to Geological Geophysics.New York: Cambridge, 2000.

References