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How do Earthquakes occur?

Earthquakes are primarily caused by the rupture of rocks in the earth's crust along faults. Most earthquakes typically take place along faults located in plate boundaries. As discussed previously, tectonic plates are always slowing moving, but sometimes they get stuck at their edges due to frictional forces. Eventually the forces and stresses caused by the movement of plates will build up and overcome the frictional forces felt along their edges. When this happens, an earthquake occurs and releases energy in the form of seismic waves.

Structure of an Earthquake
The hypocenter or focus of an earthquake is the point within the earth where the initial rupture starts. The epicenter is the point on the surface of the earth that is directly above the hypocenter.

Earthquake block diagram

Fig 6. Gamesby, Rob. "Background to Earthquakes." Coolgeography.co.uk.
N.p., n.d. Web. 11 Apr. 2015. <http://www.coolgeography.co.uk/GCSE/AQA/Restless
%20Earth/Earthquakes/Earthquakes%20background.htm>.

Seismic Waves

A seismic wave is a type of elastic wave caused by an impulse such as an explosion or earthquake. Seismic waves generated during an earthquake can be broken down into body waves and surface waves.

Body Waves
Body Waves travel from an earthquakes hypocenter through the interior of the earth. Seismic body waves are divided into primary waves (P waves) and secondary waves (S waves).

body wave joke

Fig 7. Body wave... (?) Thompson, Jeff. "Science of "The Wave"" Jeff Thompson.
N.p., 09 May 2011. Web. 11 Apr. 2015. <http://www.jeffreythompson.org/blog/
2011/05/09/science-of-the-wave/>.

Primary Waves (P Waves)

P waves are considered longitudinal or compressional waves because alternating compressions and expansions travel through the surrounding materials. P waves move parallel to the direction of wave movement. P waves are the fastest moving seismic waves and they are the first to arrive at seismograph stations.

Velocity of P waves (α) in m/s α = ((κ + 4/3μ) ρ)^1/2

κ = bulk modulus of the rock (resistance to volume change)
μ = modulus of rigidity (resistance to change in shape)

ρ = density (g/cm³)

Secondary Waves (S Waves)

S waves are also known as shear or transverse waves. In contrast to P waves, the movement of S waves is perpendicular to the direction of wave movement. S waves cannot be transmitted through a liquid because liquids have no resistances to shear stresses. This fact is why scientists believe that part of the earth's core is liquid. S waves travel at about 60% the speed of P waves. They are typically more damaging because they have a higher amplitude.

Velocity of S waves (β) in m/s β = (μ/ρ)^1/2

μ = modulus of rigidity (resistance to change in shape)
μ = 0 in liquids, thus velocity of S waves in liquids is zero

ρ = density (g/cm³)

S and P waves

Fig 8. "219G - Faulting and Earthquakes." 219G - Faulting and Earthquakes. N.p., n.d. Web. 11 Apr. 2015. Fig 9. "Properties of Waves and Wave Cycles. Scalar, Transverse, Energy and More.
<http://www.aeic.alaska.edu/input/west/guides/amato_faulting/ASRA_index.html>. - The Light Coalition." The Light Coalition. N.p., 20 Jan. 2015. Web. 11 Apr. 2015.

<http://lightcoalition.org/properties-waves-wave-cycles-scalar-transverse-energy/>.

slinky example of s and p waves

Fig 10. "Categories of Waves." The Physics Classroom. N.p., n.d. Web. 11 Apr. 2015.
<http://www.physicsclassroom.com/class/waves/Lesson-1/Categories-of-Waves>.

Surface waves - Rayleigh and Love

Surface waves move along the earth's surface from the epicenter of the earthquake. Surface waves are characterized by longer periods (10 – 20 seconds) and wavelengths of 20 to 80 km and they arrive at seismograph stations after both P and S waves. There are two types of surface waves, Rayleigh waves and Love waves. Rayleigh waves produce a movement similar to that of ocean waves where most of the displacement occurring is in the vertical direction. Rayleigh waves travel at approximately 90% the speed of S waves. Love waves originate from S waves that have reached the surface of the earth at the location of the epicenter. Love waves only produce horizontal side to side ground motion.

love and rayleigh waves

Fig 11. "219G - Faulting and Earthquakes." 219G - Faulting and Earthquakes. N.p., n.d. Web.
11 Apr. 2015. <http://www.aeic.alaska.edu/input/west/guides/amato_faulting/ASRA_index.html>.

How Does a Seismograph Work?
A seismograph is the primary tool used to detect and record the motions of earthquakes. During an earthquake the motion of the earth is measured by comparing its movements to an object that remains completely independent of the grounds motion. A basic seismograph consists of two parts, one part is the seismometer and the other is the seismic recording device. The seismometer is a mass suspended from a base by springs. While the base of a seismograph will move during an earthquake, the seismometer mass is the object that remains still and independent of the earth's motion. In modern data collection, it is common for the movement of the base with respect to the mass be converted into an electrical voltage. This voltage is then recorded by the seismic recording device onto paper, magnetic tape or digitally.

Simply put, seismographs work by using the knowledge of Newton's First Law (Law of Inertia) that states: objects in motion will stay in motion, while objects at rest will stay at rest.

Fig 12. "Lab 10 - Earthquake Epicenter Location." Lab 10 - Earthquake Epicenter Location. N.p., n.d. Fig 13. "Why So Many Earthquakes Recently? It's Physics." Science 2.0. N.p., 14 Apr. 2010. Web. 10 Apr. 2015
Web. 10 Apr. 2015. <http://www.oakton.edu/user/4/billtong/eas100lab/lab10quake.htm>. <http://www.science20.com/news_articles/why_so_many_earthquakes_recently_its_physics-66846>.

Fig 14. "Earthquakes, Richter Scale, and Logarithms." Continuous Everywhere but Differentiable Nowhere. N.p., 29 July 2008.
Web. 11 Apr. 2015. <http://samjshah.com/2008/07/30/earthquakes-richter-scale-and-logarithms/>.

Using the Time-Distance Relationship between S and P waves to Locate the Epicenter of an Earthquake

V = dx/dt (vector – has direction) V = d/t (scalar – does not have direction)

V = velocity                                                   V = velocity
dx = change of displacement                           d = distance
dt = change in time    t = time

The velocity difference between P and S waves means that the time interval between the first P waves and S waves increases with distance from the earthquake. (Remember, P waves are faster than S waves) With this relationship, the time interval between P and S wave arrivals measured at seismograph stations is actually an indication of the distance that the station is located from the epicenter. In order to locate the epicenter of an earthquake, there must be at least three seismograph stations, otherwise this specific method will not work. The P and S wave time difference is used as the radius of a circle around each station. When there are three stations, three separate circles can be plot. Where these three circles intersect is the location of the epicenter.

time distance relationship between s and p waves

Fig 15. P and S wave time vs. distance Fig 16. Location of epicenter is where the 3 circles intersect

Fig 15. and Fig 16. Reference
Kehew, Alan E. Geology for Engineers and Environmental Scientists. 3rd ed. Upper Saddle River, NJ: Prentice Hall, 2006. Print.

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