Earth Sciences 80A - Lecture 12

Earthquakes: Recordings, Locating, Size and Destruction

The 1994 Northridge California caused about $30-40 billion damage and took over 60 lives. It was a magnitude 6.7 event. 2000 houses were destroyed or badly damaged, 40 apartment buildings collapsed, 500 apartment building had moderate to severe damage. The response of the U.S. government to this disaster was to cut funding for the earthquake monitoring and analysis efforts of the U.S. Geological Survey.....

Earthquakes release stored elastic energy in strained rock, a fraction of which spreads outward into the surrounding rock masses as elastic waves. These waves are then responsible for distant shaking by the earthquake, which may be catastrophic in its effects on human structures. Specialists in the design of structures to withstand the shaking induced by earthquakes are called earthquake engineers (former UCSC Chancellor Karl Pister is one). Engineers recognize that structures all have some intrinsic mechanical flexibility, and thus they can be analyzed as vibrating mechanical systems. In fact, every structure has distinct natural harmonic periods at which they will undergo stable resonating vibrations, if the building is shook. The period of harmonic vibration depends on the building design, so engineers can influence it. The main problem is that if the ground shakes at the natural harmonic period of the building, the oscillations of the building are maximized. This tends to cause rapid damage to the structure. Basically the period is proportional to the square root of the mass and inversely proportional to the square root of the building stiffness. By making a building stiffer, the period is reduced (or the resonant frequency is increased). By increasing the mass, the period is increased (frequency reduced). We'll demonstrate this with a model.

Building damage is a result of ground shaking induced by earthquake occurrence, but it does not directly tell us about the earthquake process. In order to study earthquakes we need to somehow record them. One approach is to describe the felt shaking and damage from an earthquake. This reveals the general location of the faulting, to the extent that there are any nearby human observers or structural effects. It also suggests something about how much energy was released in the degree of damage. But there are many factors which influence the damage that have nothing to do with the faulting. For example, variations in construction standards around the world enhance catastrophic building collapses and loss of life in some areas. Our understanding of the earthquake process itself must be independent of such human-induced variations.

About 100 years ago, scientists interested in studying earthquakes realized that what was needed was accurate recordings of how the ground actually shook at different places on the Earth, rather than how building responded to that shaking. This led to the invention of instruments called seismometers, which record the ground shaking at a given location as a function of time. Most seismometers work on an Inertial Pendulum System of one type or another. This involves some arrangement with a mass suspended on a spring. The spring is connected to the Earth, and when the Earth moves, the spring stretches instantly due to the inertia of the mass (inertia is the resistance to a change in motion). The stretching of the spring eventually causes the mass to move, but it is slightly delayed and shifted relative to the motions of the Earth, and it is that relative motion that we record onto a recording (either on paper or on magnetic tape) called a seismogram. Why is this all necessary? Remember, if you are trying to measure how the ground moves, you have to deal with the fact that the instrument you want to use to record the motion will move with the ground. You need to have some way of separating the recording sensor from the ground. You have seen film footage of earthquake shaking, often recorded at TV studios or on security cameras. The ground shaking is visible because the wall holding up the camera acts as a spring, delaying the motion of the camera relative to the ground.

Seismologists have developed very sensitive seismometers, capable of detecting very tiny ground motions that are imperceptible to humans. By continuously operating these seismometers at locations around the world, we have the ability to record shaking motions anywhere on the planet. The fact that seismic waves travel outward in all directions from the earthquake (or explosion) source allows the disturbance to be detected at many seismic recording stations. Each station keeps accurate time records, so that we know the time at which the ground at a particular location vibrated. Accurate recordings of the vibrations allow us to study earthquakes quantitatively.

The types of vibrations that are recorded involve the P and S waves radiated outward from the source by the release of elastic strain energy in the rock as a fault slides. P and S waves are called body waves, because they travel through the Earth's interior. Because the Earth has layers, as well as a free surface, the P and S waves can bounce around inside the earth, analogous to echoing sound in a canyon. This gives rise to many paths by which P and S wave energy can travel from the source to each point on the Earth's surface. Thus, the ground motion recordings from earthquakes tend to be rather complex, with a sequence of arrivals that are mainly controlled by the Earth structure, not by the source. The earthquake faulting may last only a few seconds, while the ground shaking will be more prolonged because the P and S waves travel with different velocities and there are many paths with different total travel times for the energy to get to the station.

The surface of the Earth causes P and S waves to interact with each other and with the layering of the crust and mantle to produce patterns of vibrations that we call surface waves. There are two main types of surface waves: Love waves and Rayleigh waves. Love waves travel faster than Rayleigh waves, but slower than S waves. Love waves involve only horizontal motions of the Earth, perpendicular to the direction in which the wave is propagating. They are trapped, reverberating S waves near the surface of the Earth. Rayleigh waves involve shaking in the vertical direction (up and down), as well as back and forth in the direction of propagation of the wave. They are a mix of P and S wave energy reverberating near the surface. These waves propagate along the surface, rather than through the body of the planet, thus, their energy is spread out on an expanding ring on the surface rather than over a spherical shell. This makes surface wave amplitudes larger than body wave amplitudes, and thus most damage from earthquake shaking is caused by Love or Rayleigh waves.

Because the P, S, Love and Rayleigh waves all involve different shaking motions, seismometers are designed to record all possible directions of shaking at the surface. This is achieved by having 3 instruments at each site, one recording vertical motions, and two recording perpendicular horizontal motions (usually North-South and East-West). Any motion of the surface can be described as time varying vector (with direction and amplitude), which has components on the three orthogonal axes recorded by the seismometer.

Thus, if we record the ground shaking at a site, and there is a nearby earthquake we will see a sequence of seismic waves pass by the site. First will come the P wave, then the S wave, then the Love wave and finally the Rayleigh wave. The velocity with which each wave type travels determines the time at which the corresponding energy passes by the site and shakes the seismometer, leaving a record of the amplitude, direction, and arrival time of various vibrations. This provides a quantitative record of the ground shaking that can be used to study the source or the layered Earth.

Typically, the first thing we want to do is to determine the origin time and location of the source of the seismic waves. Remember, we do not initially know when or where an earthquake has occurred. What we have are recordings of the times at which the ground began to shake at different places, along with the sense of motion of the shaking. Since the P wave is expected to be the first shaking, from several stations we can identify the arrival time of the P wave at each position. The time at which the wave arrived depends on when the source released the initial energy, and how far it was from each station. In order to determine those unknown quantities, we must know the velocity at which P waves travel through the rock. From a bunch of P wave arrival times, and knowing the P velocity appropriate for the region, one can estimate (by guessing or by more formal mathematical procedures called inversion) where and when the source had to be located in order to account for the observed arrival times at different locations. This is a form of triangulation, done in three dimensions, since the earthquake may be deep in the crust.

We can also use the arrival times of S waves at each station, as long as we know the S wave velocity. Since the S wave travels slower than the P wave, the time separation between their arrivals at a station increases with the distance from the source. Thus, the S-P difference in arrival time is proportional to the distance. Given some knowledge of the S and P velocities of rocks, we can take the S-P time at each station and draw a circle around it with a radius corresponding to the distance to the event. Intersections of the circles from multiple stations identify the unique common position for the source. Once the location is determined, the origin time is set by the absolute P arrival times.

The arrival times of waves are used to locate the event, and once it is known where the event was, we can use the amplitudes at different distances to determine how Big the event was. The basic fact that helps in this effort is that the amplitudes of the waves get progressively smaller with distance, and knowing the distance, we can correct for that effect to tell how big the motions were right at the fault. This gives an estimate of the total energy put into the ground, which is proportional to how big the area of fault slip is and how much slip occurred.

There are several measures of earthquake size that reflect the ground shaking amplitudes. The first is a qualitative measure called Intensity. This is actually a damage scale, in which the level of shaking felt or damage caused is categorized into ten or twelve categories. Intensities tend to give higher damage, and higher intensity values near the source. This does not use seismograms at all, but is very useful for historical events for which there are no seismic recordings. Intensities are also practical, in the sense of reflecting human effects rather than scientific measures of the source.

Seismograms give seismic wave amplitudes that are used to determine earthquake Magnitudes. These are based on the distance corrected amplitudes of seismic waves, but often have a mix of quantitative and empirical procedures. Magnitude scales are all logarithmic, meaning that they are based on powers of ten. For each increase in the magnitude value by one unit, the ground motions were 10 times larger. The energy required to produce 10 times larger motions is about 30 times larger. Thus, a magnitude 5.0 earthquake produces ground shaking at some given distances, say 10 km, that is ten times larger than a magnitude 4.0 event recorded at the same distance.

The earthquake magnitude that is determined depends on which seismic wave is measured, and there are different magnitude scales for P waves, for Rayleigh waves, and for different periods of motion. The Richter scale is just one of many magnitude scales, and really involves only events recorded in Southern California on a particular type of seismic instrument (sensitive to high frequency body wave shaking), corrected for distance by the special formulas appropriate for Southern California. While much more general magnitude scales are applied to events around the world, using a variety of seismic instruments, the media tends to call them all Richter magnitude.

The most quantitative measure of earthquake size determined by seismograms is called the Seismic Moment. This is an energy based measure that accounts for the actual geometry of the faulting (magnitudes do not, despite the fact that seismic wave radiation is affected by whether the fault is strike-slip, normal, or thrust faulting). The seismic moment is a quantity proportional to the permanent displacement on the fault. It is given by the product of the rigidity, the fault area that ruptured and the amount of slip. This quantity is determined by making a computer model of the faulting that matches the observed amplitudes of the complete seismogram, accounting for any differences in excitation (strength of radiation) of the P, S, Love and Rayleigh waves caused by fault depth, geometry, and slip process. A magnitude scale called the Moment Magnitude scale was determined to provide familiar logarithmic numbers. While all other magnitude scales only work for a limited range of events, the Moment Magnitude scale is good for all events. The largest earthquake that has been recorded this century was the 1960 Chile earthquake, which had a moment magnitude of 9.5! Richter magnitudes tend to saturate around magnitude 8.2-8.5, meaning that even if the event is bigger, you get the same Richter magnitude. Thus, the Moment Magnitude is particularly useful for very large events.

Earthquake Catastrophes Through Time

Some of the World's Worst Earthquakes (in lives lost)

Year	Magnitude	Place	Estimated Deaths
856		Corinth, Greece	45,000
1038		Shansi, China	23,000
1057		Chihil, China	25,000
1170		Sicily	15,000
1268		Silicia, Asia Minor	60,000
1290		Chihil, China	100,000
1293		Kamakura, Japan	30,000
1456		Naples, Italy	60,000
1531		Lisbon, Portuga	l30,000
1556		Shensi, China	830,000
1667		Shemaka, Caucasia	80,000
1693		Catania, Italy	60,000
1731		Peking, China	100,000
1737		Calcutta, India	300,000
1755		Northern Persia	40,000
1755		Lisbon, Portuga	l70,000
1783		Calabria, Italy	50,000
1797		Quito, Ecuador	40,000
1811		New Madrid, MO	several
1812		New Madrid, MO	several
1819		Kutch, India1,	543
1822		Aleppo, Asia Minor	22,000
1828		Echigo, Japan	30,000
1847		Zenkoji, Japan	34,000
1868		Peru/Ecuador	25,000
1868		Ecuador/Colombia	70,000
1872		Owens Valley, CA	50
1875		Venezuela/Colombia	16,000
1886		Charleston, SC	60
1891		Mino-Owari, Japan	7,000
1896		Sanriku, Japan	22,000
1897	8.7	Assam, India	1,500
1899	8.6	Yakutat Bay, Alaska
1906	8.2	San Francisco, CA	700
1908	7.5	Messina, Italy1	20,000
1915	7.0	Avezzano, Italy	30,000
1920	8.5	Kansu, China	180,000
1923	8.2	Kwanto, Japan	143,000
1932	7.6	Kansu, China	70,000
1935	7.5	Quetta, India	60,000
1939	7.75	Chillan, Chile	30,000
1939	8.0	Ezrican, Turkey	23,000
1948		Fukui, Japan	5,131
1949	6.9	Pelileo, Ecuador	6,000
1949		Khait, USSR	12,000
1950	8.6	Assam, India	1,526
1957		Northern Iran	2,500
1960	9.5	Southern Chile	5,700
1960	5.9	Agadir, Morocco	14,000
1962	7.3	Northern Iran	14,000
1963	6.0	Skopje, Yugoslavia	1,200
1964	9.4	Alaska	131
1968	7.4	Iran	11,600
1970	7.8	Peru	66,000
1971	6.5	San Fernando, CA	65
1972	6.2	Managua, Nicaragua	5,000
1976	7.9	Guatemala	22,000
1976	7.6	Tangshan, China	250,000
1976		Philippines	3,100
1980	7.7	El Asnam, Algeria	3,500
1980	7.2	S. Italy	3,000
1981	6.9	S. Iran	3,000
1981	7.3	S. Iran	1,500
1982	6.0	Yemen	2,800
1983	6.9	Turkey	1,342
1985	7.9	Michoacan, Mexico	9,500
1986	5.4	El Salvador	1,000
1987	7.0	Colombia	1,000-5,000
1988	6.6	Nepal-India Border	1,450
1988	7.0	Spitak, Armenia	25,000
1989	6.9	Santa Cruz, CA	63
1990	7.7	Iran	40,000
1990	7.8	Luzon, Philippines	1,700
1992	7.3	Landers, CA	1
1994	6.5	Northridge, CA	65
1995	6.5	Kobe, Japan	5,000

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