Earthquake Notes

What is an earthquake?
An earthquake is the vibration of the earth produced by the quick release of energy. Most often, earthquakes are caused by movement along large fractures in the earth’s crust. Such fractures are called faults. The energy that is released radiates in all directions from its origin in the form of waves. These waves are similar to the waves that occur when you drop a stone into water. Just as the stone sets the water in motion, the energy released in an earthquake produces seismic waves that move through the earth. Frequency range of seismic waves is large, from as high as the audible range (greater than 20 hertz) to as low as the frequencies of the free oscillations of the whole Earth (2 and 7 millihertz). Attenuation of the waves in rock imposes high-frequency limits, and in small to moderate earthquakes the dominant frequencies extend in surface waves from about 1 to 0.1 hertz. The amplitude range of seismic waves is also great in most earthquakes. In the greatest earthquakes the ground amplitude of the predominant P waves may be several centimeters at periods of two to five seconds. Very close to the seismic sources of great earthquakes, investigators have measured large wave amplitudes with accelerations of the ground exceeding that of gravity (9.8 meters, or 32.2 feet, per second squared) at high frequencies and ground displacements of 1 meter at low frequencies.

Earthquake Magnitude and Energy Release Equivalence

What is the mechanism that produces earthquakes?
Earth is not a static planet: in the earth’s crust, tectonic forces are constantly at work pushing rocks on both sides of a fault in different directions. In this process, the material is deformed. As rocks don’t slide past each other very easily, strain is built up, just as if you bend a stick. At a certain level, the rocks can no longer resist the strain and slip past each other into their original shape. This “springing back” of the rock is called elastic rebound. It is this quick movement that we feel as an earthquake. The elastic rebound usually happens a few kilometres deep in the crust. This location is called the focus of the earthquake. The place on the surface directly over the focus is called the epicentre.

Reid’s Elastic Rebound Theory
From an examination of the displacement of the ground surface which accompanied the 1906 earthquake, Henry Fielding Reid, Professor of Geology at Johns Hopkins University, concluded that the earthquake must have involved an “elastic rebound” of previously stored elastic stress. If a stretched rubber band is broken or cut, elastic energy stored in the rubber band during the stretching will suddenly be released. Similarly, the crust of the earth can gradually store elastic stress that is released suddenly during an earthquake.

This gradual accumulation and release of stress and strain is now referred to as the “elastic rebound theory” of earthquakes. Most earthquakes are the result of the sudden elastic rebound of previously stored energy. The following diagram illustrates the process. Start at the bottom. A straight fence is built across the San Andreas fault. As the Pacific plate moves northwest, it gradually distorts the fence. Just before an earthquake, the fence has an “S” shape. When the earthquake occurs the distortion is released and the two parts of the fence are again straight; but now there is an offset.

Slow, Quiet and Silent Earthquakes
• When we think of an earthquake source, we think of a crack that propagates through the crust close to the shear-wave speed, which is generally several kilometers per second. Fault rupture is sudden, accompanied by violent shaking of the ground. But, creep events (on the San Andreas fault) during which propagation along a fault occurs at rates of millimeters per year. Earth deformation occurs at rates that differ widely. From fast ruptures that suddenly release stored elastic-strain energy • • • • • • • Ordinary earthquakes to Slow earthquakes (speed of hundreds of meters per second). Silent earthquakes (speed of tens of meters per sec.) Creep events, and finally strain migration episodes with speeds in centimeters or millimeters per second.

Slow earthquakes include episodes of rupture propagation that produce an ordinary seismogram of high-frequency body waves. However, slow earthquakes take an unusually long time to rupture in comparison to ordinary earthquakes of similar moment magnitude. Oceanic transform faults have produced several slow earthquakes, such as the 1960 Chilean transform fault earthquake that ruptured for about an hour as a series of small events. Silent earthquakes are not accompanied by high-speed rupture propagation events. Thus they do not generate high-frequency waves that are recorded teleseismically. Conventional seismographs do not record these events. Strain metes document creep events on the San Andreas fault system (10mm/sec). Silent earthquakes may offer promise as precursors to ordinary earthquakes.

How can the energy of an earthquake be felt?
The energy that is released in an earthquake travels in waves through the materials of the earth. Two types of waves can be distinguished. 1. Some travel along the earth’s outer layer and are called surface waves. 2. Others travel through the earth’s interior and are called body waves. Body waves are further divided into Primary waves (P waves) Secondary waves (S waves).

P waves (primary waves) P waves are “push-pull” waves—they push (compress) and pull (expand) rocks in the direction the wave is travelling. Imagine holding someone by their shoulders and shaking them. This push-pull movement is how P waves move through the earth. Solids, liquids and gases resist a change in volume when compressed and will elastically spring back once the force is removed. Therefore, P waves can travel through all these materials. Highest velocity (6 km/sec in the crust).

S waves (secondary waves)
S waves, on the other hand, “shake” the particles at right angles to their direction of travel. This can be illustrated by holding one end of a rope steady and shaking the other end (see illustration below). In contrast to P waves, which for a moment change the volume of the material, S waves change the shape of the material they travel through. Because liquids and gases do not respond elastically to changes in shape, they will not transmit S waves. An S wave is slower than a P wave and can only move through solid rock. (3.6 km/sec in the crust)

Damage nature due to body waves

Surface Waves
Travel just below or along the ground’s surface Slower than body waves; rolling (Rayleigh) and side-to-side (Love) movement Especially damaging to buildings

Love Waves
After A.E.H. Love and suggested in early twentieth century. L-wave can be thought of as the constructive interference of multiple reflected S-waves whose particle motion is horizontal. Travel just below or along the ground’s surface with side-to-side particle velocity. Speed is slower than body waves. This wave is especially damaging to buildings. Typical velocity: Depends on earth structure (dispersive), but less than velocity of S waves. Typical velocity: Depends on earth structure (dispersive), but less than velocity of S waves. Behavior: Causes shearing motion (horizontal) similar to S waves. Arrival: They usually arrive after the S wave and before the Rayleigh wave.

Love waves are dispersive, that is, different periods travel at different velocities, generally with low frequencies propagating at higher velocity. Depth of penetration of the Love waves is also dependent on frequency, with lower frequencies penetrating to greater depth. V L ~ 2.0 – 4.5 km/s in the Earth depending on frequency of the propagating wave

Rayleigh Waves

After Lord Rayleigh who predicted existence in 1887. These waves are analogous to waves travelling across the ocean. A floating object is not only pitched up and down, but also to and fro as wave passes. The actual movement of the object describes an ellipse. The motion of

waves dies out quickly with depth, and this is also the case with Rayleigh waves. Rayleigh wave can be thought of as arising from the constructive interference of multiple reflected P and S waves travelling in vertical plane. Typical velocity: ~ 0.9 that of the S wave Behavior: Causes vertical (rolling anticlockwise) together with back-and-forth horizontal motion. Motion is similar to that of being in a boat in the ocean when a swell moves past. Most of the shaking felt from an earthquake is due to the Rayleigh wave, which can be much larger than the other waves.ch can be much Arrival: They usually arrive last on a seismogram.

larger than the

Rayleigh waves are also dispersive and the amplitudes generally decrease with depth in the Earth. Appearance and particle motion are similar to water waves. Depth of penetration of the Rayleigh waves is also dependent on frequency, with lower frequencies penetrating to greater depth. Generally, Rayleigh waves travel slightly slower than Love waves. VR ~ 2.0 – 4.5 km/s in the Earth depending on frequency of the propagating wave

Damage pattern due to surface waves

What is a seismograph and how does it work?
A seismograph is an instrument that records earthquake waves (also called seismic waves). The principle : A weight is freely suspended from a support that is attached to bedrock. When waves from an earthquake reach the instrument, the inertia of the weight keeps it stationary, while the earth and the support vibrate. The movement of the earth in relation to the stationary weight is recorded on a rotating drum. What is recorded on the rotating drum is called a seismogram.

Seismograms show that there are two types of seismic waves generated by the
movement of a mass of rock.

Example of an earthquake record.

Locating an Earthquake’s Epicenter
P waves arrive first, then S waves, then L and R After an earthquake, the difference in arrival times at a seismograph station can be used to calculate the distance from the seismograph to the earthquake source (D). If average speeds for all these waves are known, use the S-P (S minus P) time formula: a method to compute the distance (D) between a recording station and an event. Distance Time = Velocity P wave has a velocity VP and S wave has a velocity VS ; VS is less than VP Both originate at the same place – the hypocenter They travel same distance, but the S wave takes more time than the P wave. D Time for the S wave to travel a distance DTS = Vs D Time for the P wave to travel a distance DTP = Vp The time difference (TS – TP) = D D =D Vs Vp

 1 1    Vs – Vp  = D   

 Vp – Vs    Vp Vs    

Now solve for the Distance D

 Vp Vs  D=   Vp – Vs  * (TS – TP)   

Epicenter of an earthquake can be obtained by surface projection of earthquake source. Travel-times for location

Measure time between P and S wave on seismogram Use travel-time graph to get distance to epicenter

The epicenter is located using three or more seismograph

Earthquake depths
 Earthquakes originate at depths ranging from 5 to nearly 700 kilometers  Earthquake foci classified as  Shallow (surface to 70 kilometers)  Intermediate (70 to 300 kilometers)  Deep (over 300 kilometers)

Seismic Wave Speeds and Rock Properties
Variations in the speed at which seismic waves propagate through the Earth can cause variations in seismic waves recorded at the Earth’s surface

Vp =

4   µ + k 3 

ρ

Vs =

µ ρ

It can be shown that in homogeneous, isotropic media the velocities of P and S waves through the media are given by the expressions as above. Where Vp and Vs are the P and S wave velocities of the medium, ρ is the density of the medium, and µ and k are referred to as the shear and bulk moduli of the media. Taken together, µ and k are also known as elastic parameters. The elastic parameters quantitatively describe the following physical characteristics of the medium. •

Bulk Modulus – Is also known as the incompressibility of the medium. The bulk modulus describes the ratio of the pressure applied to the cube to the amount of volume change that the cube undergoes. If k is very large, then the material is very stiff, meaning that it doesn’t compress very much even under large pressures. If k is small, then a small pressure can compress the material by large amounts. For example, gases have very small incompressibilities. Solids and liquids have large incompressibilities. Shear Modulus – The shear modulus describes how difficult it is to deform a cube of the material under an applied shearing force. For example, imagine you have a cube of material firmly cemented to a table top. Now, push on one of the top edges of the material parallel to the table top. If the material has a small shear modulus, you will be able to deform the cube in the direction you are pushing it so that the cube will take on the shape of a parallelogram. If the material has a large shear modulus, it will take a large force applied in this direction to deform the cube. Gases and fluids can not support shear forces. That is, they have shear moduli of zero. From the equations given above, notice that this implies that fluids and gases do not allow the propagation of S waves.

Any change in rock or soil property that causes ρ, µ, or k to change will cause seismic wave speed to change. For example, going from an unsaturated soil to a saturated soil will cause both the density and the bulk modulus to change. The bulk modulus changes because air-filled pores become filled with water. Water is much more difficult to compress than air. In fact, bulk modulus changes dominate this example. Thus, the P wave velocity changes a lot across water table while S wave velocities change very little.

Wave Propagation Through Earth Media
 Any change in rock or soil property that causes ρ, µ, or k to change will cause seismic wave speed to change.  For example, going from an unsaturated soil to a saturated soil will cause both the density and the bulk modulus to change.  When seismic waves travel from one layer to another, ray gets bent away from or toward the normal depending on layer density.  Propagation of seismic waves in media is governed by Snell’s Law Snell’s Law describes the relationship between the angles and the velocities of the waves. Snell’s law equates the ratio of material velocities V1 and V2 to the ratio of the sine’s of incident and refracted angles, as shown in the following equation.

sin θ1 sin θ2 = VL1 VL 2
Where: VL1 is the longitudinal wave velocity in material 1. VL2 is the longitudinal wave velocity in material 2.

Shows P and S wave shadow zones that forms on other side of the earth due to the occurrence of an earthquake in opposite side.

P – P wave only in the mantle PP, PPP, SS, SSS – P or S wave reflected once or twice off earth’s surface so there are two or more P or S wave segments in the mantle. PKP – P wave that has two segments in the mantle separated by a segment in the core. PcP – P wave reflected from outer core & mantle boundary. PKiKP – P wave reflected from outer core & inner core boundary. PKIKP – P wave that traverse inner core is denoted by I. PKJKP – Phases with an S leg in the inner core is denoted by J. PPS, PSP, PSS – P wave twice reflected from the Earth’s surface. S denotes converted wave.

ScP – S wave reflected from outer core-mantle boundary and converted into P type wave. ScS – S wave reflected from outer core & mantle boundary. SKS – S wave traversing the outer core as P and converted back into S when again entering the mantle.

Earth’s Major Boundaries

The crust – Continental » Less dense » 20-70 km thick – Oceanic » more dense » 5-10 km thick

The (Moho) Mohorovicic discontinuity
Discovered in 1909 by Andriaja Mohorovicic Separates crustal materials from underlying mantle Identified by a change in the velocity of P waves

• The core-mantle boundary
• • Discovered in 1914 by Beno Gutenberg Based on the observation that P waves die out at 105 degrees from the earthquake and reappear at about 140 degrees • 35 degree wide belt is named the P-wave shadow zone

• Discovery of the inner core
• • Predicted by Inge Lehmann in 1936 P-wave shadow zone is not a perfect shadow – there are weak Pwaves arriving, and Lehmann suggested that these P-waves were bounced from a solid inner core.

Foreshocks and Aftershocks
Faults are believed to consist of stronger and weaker parts whose ability to rupture during an earthquake varies. These stronger parts are called barriers or asperities. These two terms assign different roles to the stronger patches in the earthquake rupture process.

The left side of the above figure shows the condition of a fault just before an earthquake while the right side shows its condition after an earthquake. The upper part of the figure is based on the barrier hypothesis, while the lower part is based on the asperity hypothesis. The shaded portion indicates a stressed portion of the fault while the unshaded is the slipped or unstressed portion. According to the barrier hypothesis, the fault is in a state of uniform stress (upper left) before the earthquake. During the earthquake the rupture propagates leaving unbroken stronger patches (upper right). These patches or barriers are the location of numerous aftershocks which represent the release of stress through static fatigue. According to the asperity hypothesis, just prior to the earthquake (main shock) the fault is not in a state of uniform stress but rather there has been some release of stress over part of the fault through foreshocks leaving behind strong patches or asperities which are broken resulting in a smoothly slipped fault (lower right). The existence of both aftershocks and foreshocks indicate that some strong patches behave as barriers while others behave as asperities. Barriers and asperities are significant to earthquake ground motion because they represent locations of concentrated stress release and localized stopping and starting of the rupturing fault.

Measuring the size of earthquakes
Two measurements that describe the size of an earthquake are • • • Intensity – a measure of the degree of earthquake shaking at a given locale based on the amount of damage Magnitude – estimates the amount of energy released at the source of the earthquake The drawback of intensity scales is that destruction may not be a true measure of the earthquakes actual severity

The Modified Mercalli (MM) Scale of Earthquake Intensity (Developed in 1931 by the American seismologists Harry Wood and Frank Neuman) Intensity I II III IV Felt / Damage People do not feel any Earth movement. A few people might notice movement if they are at rest and/or on the upper floors of tall buildings. Many people indoors feel movement. Hanging objects swing back and forth. People outdoors might not realize that an earthquake is occurring. Most people indoors feel movement. Hanging objects swing. Dishes, windows, and doors rattle. The earthquake feels like a heavy truck hitting the walls. A few people outdoors may feel movement. Parked cars rock. Almost everyone feels movement. Sleeping people are awakened. Doors swing open or close. Dishes are broken. Pictures on the wall move. Small objects move or are turned over. Trees might shake. Liquids might spill out of open containers. Everyone feels movement. People have trouble walking. Objects fall from shelves. Pictures fall off walls. Furniture moves. Plaster in walls might crack. Trees and bushes shake. Damage is slight in poorly built buildings. No structural damage. People have difficulty standing. Drivers feel their cars shaking. Some furniture breaks. Loose bricks fall from buildings.

Damage is slight to moderate in well-built buildings; considerable in poorly built buildings. Drivers have trouble steering. Houses that are not bolted down might shift on their foundations. Tall structures such as towers and chimneys might twist and fall. Well-built buildings suffer slight damage. Poorly built structures suffer severe damage. Tree branches break. Hillsides might crack if the ground is wet. Water levels in wells might change. Well-built buildings suffer considerable damage. Houses that are not bolted down move off their foundations. Some underground pipes are broken. The ground cracks. Reservoirs suffer serious damage. Most buildings and their foundations are destroyed. Some bridges are destroyed. Dams are seriously damaged. Large landslides occur. Water is thrown on the banks of canals, rivers, lakes. The ground cracks in large areas. Railroad tracks are bent slightly. Most buildings collapse. Some bridges are destroyed. Large cracks appear in the ground. Underground pipelines are destroyed. Railroad tracks are badly bent. Almost everything is destroyed. Objects are thrown into the air. The ground moves in waves or ripples. Large amounts of rock may move.

Magnitude
Magnitude of earthquake is a measure of energy and based on the amplitude of the waves recorded on a seismogram. Concept: the wave amplitude reflects the earthquake size once the amplitudes are corrected for the decrease with distance due to geometric spreading and attenuation. Magnitude scales have the general form:

where A: amplitude of the signal T: its dominant period f : correction for the variation of amplitude with the earthquake’s depth h and distance ∆ from the seismometer C: regional scale factor

Richter Magnitude
Charles Richter developed the first magnitude scale in 1935. Richter’s magnitude is the logarithm to the base 10 of the maximum seismic wave amplitude, in thousandths of a millimeter, recorded on a special type of seismograph (Wood-Anderson seismograph) at a distance of 100 km from the earthquake epicenter. Wood-Anderson seismograph has a natural oscillation period of about 0.8 seconds, and waves of longer period are increasingly diminished on the records even if they are present in the ground.

ML = log10A(mm) + (Distance correction factor)
Here A is the amplitude, in millimeters, measured directly from the photographic paper record of the Wood-Anderson seismometer, a special type of instrument. He proposed zero magnitude for an earthquake that would produce a record with amplitude of 1.0 micro meter at a distance of 100 km from the epicenter on WoodAnderson seismograph with time period 0.8 sec (1.25 Hz natural frequency), damping h 0.8 and 2800 magnification factor. He calibrated his scale of magnitudes using measured maximum amplitudes of shear waves recorded in southern California. The logarithmic form of Richter magnitude scale (ML) for 100 km epicentral distance is as given below.

ML = log10A – log10A0
Where, A0 is the amplitude for zero magnitude earthquakes. Thus, an earthquake trace with amplitude 10 micro meter of seismograph at an epicentral distance of 100 km has magnitude 1.0

The distance factor by Richter

The diagram below demonstrates how to use Richter’s original method to measure a seismogram for a magnitude estimate in Southern California:

The scales in the diagram above form a nomogram that allows you to do the mathematical computation quickly by eye.

Body-wave magnitude is

Mb = log(A/T) + Q(D,h)
where A is the ground motion (in microns), T is the wave’s period (in seconds), and Q(D,h) is a correction factor that depends on distance to the quake’s epicenter D (in degrees) and focal depth h (in kilometers). Mb uses relatively short seismic waves with a 1-second period, so to it every quake source that is larger than a few wavelengths looks the same. Mb saturates around magnitude above 6.

Surface-wave magnitude is

Ms = log(A/T) + 1.66 logD + 3.30
Ms uses 20-second waves and can handle larger sources, but it too saturates around magnitude 8. That’s OK for most purposes because magnitude-8 or great events happen only about once a year on average for the whole planet. But within their limits, these two scales are a reliable gauge of the actual energy that earthquakes release. Limitations: Magnitude saturation It’s a general phenomenon for Mb above about 6.2 and Ms above about 8.3.

A simple solution that has been found by Kanamori: defining a magnitude scale based on the seismic moment. Moment Magnitude, Mw, is not based on seismometer readings at all but on the total energy released in a quake, the seismic moment Mo (in dyne-centimeters):

Mw = 2/3 log(Mo) – 10.7
This scale therefore does not saturate. Moment magnitude can match anything the Earth can throw at us. Still, Kanamori inserted an adjustment in his formula such that below magnitude 8 Mw matches Ms and below magnitude 6 matches Mb, which is close enough to Richter’s old ML. So keep calling it the Richter scale if you like—it’s the scale Richter would have made if he could. Seismic Moment (Mo) = The seismic moment is a measure of the size of an earthquake based on the area of fault rupture, the average amount of slip, and the force that was required to overcome the friction sticking the rocks together that were offset by faulting.

Moment = µ A D µ = shear modulus; A = LW = area D = average displacement during rupture

Ground Motion Acceleration Measurement
Peak ground acceleration (PGA) is a measure of earthquake acceleration. Unlike the Richter magnitude scale, it is not a measure of the total size of the earthquake, but rather how hard the earth shakes in a given geographic area. It is measured by instruments, not from personal reports, although it generally correlates well with the Mercalli scale.

Peak ground acceleration can be measured in g (the acceleration due to gravity) or m/s². The peak horizontal acceleration (PHA) is the most
commonly used type of ground acceleration in engineering applications. Other ground motion parameters used to characterize earthquake motion include peak velocity and peak displacement.

Strong Motion Sensors
Most strong motion sensors are designed to measure the large amplitude, high frequency seismic waves typical of large local earthquakes. These seismic waves result in the strong ground motion we feel during a large earthquake. Strong ground motion is often to blame for the structural damage that occurs during an earthquake. The data seismologists record with strong motion sensors is used to improve the design of earthquake resistant buildings and to understand earthquake-induced geologic hazards like liquefaction and landslides. The range of motions of interest for strong motion applications includes accelerations from 0.001 to 2 g and frequencies from 0 to 100 Hz.

Why We Need Strong Motion Sensors
Before the wide use of strong motion instruments, scientists attempted to estimate the shaking from strong earthquakes by extrapolating (scaling up) the observed effects of smaller earthquakes (magnitude 2.5-5.0). This method works well for many applications and has improved with the use of data from strong motion instruments. However, this approach is not applicable in every situation. Some geologic materials and structures do not respond to strong shaking in a simple, predictable manner that can be accurately scaled upward. In these situations, scientists need actual data generated by strong ground motion to better understand the processes at work. Strong motion sensors have been installed in different areas of geologic interest throughout the Pacific Northwest to provide this type of data. Using strong motion data, earth scientists hope to gain a better understanding of: 1) ground response near fault ruptures of large earthquakes 2) effects of severe shaking on different subsurface structures and geologic materials. 3) ground response in areas that undergo liquefaction.