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Geology 452 – Introduction to Geophysics (ATH) XIII. PHYSICS OF EARTHQUAKES Locating Earthquakes Determination of earthquake locations is a triangulation process. Two steps are involved. (1) Determine the distance of earthquakes from seismograms based on the difference in P and S arrival times using a J-B diagram. (2) Use the station location as a center and the distance determined in (1) as a radius, draw a circle. You need at least three stations. The intersections of the three circles form a triangulated area where the earthquake occurred. The following diagrams illustrate the principle of this triangulation procedure. Consider three seismic stations A, B, and C. According to the seismograms obtained in each station, the arrival time difference between the P and the S waves can be measured. Using these measurements, the distance of the earthquake to each station (i.e., x a , x b , and x c ) can be obtained from a J- B diagram as illustrated in the following diagram. Once the distances are determined, location of an earthquake can be triangulated on a map as illustrated in the following schematic diagram. x c x a C A B earthquake epicenter x b Note that in theory, these three circles should intersect at a single point where the earthquake occurred if everything works out perfectly. In practice, however, every measurement involves errors and uncertainties. Thus, it is almost impossible to have three circles to intersect at a single point. As a result, one needs as many stations as one can get to determine the location of an earthquake accurately. The more stations one uses to locate the earthquake, the more accurate the location will be. Origin Time To determine the time when an earthquake occurs, one only needs information from one station, at least in principle. The distance between the source and a station x can be expressed by the following equation. t C S B A ( ) ( ) 0 p p S S 0 x V t t V t t = = (13.1) P x where V p and V S are the seismic velocities, and t p and t s are the arrival times, of P- and S- waves, respectively; t o is the origin time. Re-arranging this equation, the origin time can be calculated by the following. x c x a x b University of Illinois at Urbana-Champaign copyright © 2004 hsui, all rights reserved 1

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Page 1: HYSICS OF EARTHQUAKES map as illustrated in the following ...pages.uoregon.edu/drt/Tectonics/attachments/earthquakes.pdf · Locating Earthquakes Determination of earthquake locations

Geology 452 – Introduction to Geophysics (ATH)

XIII. PHYSICS OF EARTHQUAKES Locating Earthquakes Determination of earthquake locations is a triangulation process. Two steps are involved. (1) Determine the distance of earthquakes

from seismograms based on the difference in P and S arrival times using a J-B diagram.

(2) Use the station location as a center and the distance determined in (1) as a radius, draw a circle.

You need at least three stations. The intersections of the three circles form a triangulated area where the earthquake occurred. The following diagrams illustrate the principle of this triangulation procedure. Consider three seismic stations A, B, and C. According to the seismograms obtained in each station, the arrival time difference between the P and the S waves can be measured. Using these measurements, the distance of the earthquake to each station (i.e., xa, xb, and xc) can be obtained from a J-B diagram as illustrated in the following diagram. Once the distances are determined, location of an earthquake can be triangulated on a

map as illustrated in the following schematic diagram. xc xa

C A B

earthquake epicenter

xb

Note that in theory, these three circles should intersect at a single point where the earthquake occurred if everything works out perfectly. In practice, however, every measurement involves errors and uncertainties. Thus, it is almost impossible to have three circles to intersect at a single point. As a result, one needs as many stations as one can get to determine the location of an earthquake accurately. The more stations one uses to locate the earthquake, the more accurate the location will be. Origin Time To determine the time when an earthquake occurs, one only needs information from one station, at least in principle. The distance between the source and a station x can be expressed by the following equation.

t

C S B

A ( ) ( )0p p S S 0x V t t V t t= − = − (13.1) P

x where Vp and VS are the seismic velocities,

and tp and ts are the arrival times, of P- and S- waves, respectively; to is the origin time. Re-arranging this equation, the origin time can be calculated by the following.

xc xa xb

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Geology 452 – Introduction to Geophysics (ATH)

0p p S S

p S

V t V tt

V V−

=−

(13.2)

Thus, based on measurements of the P- and S- waves arrival times, the origin time of an earthquake can be obtained.

Once we learn how to locate earthquakes, a map of the global distribution of earthquakes can be constructed. Following is such a map constructed during the 1970’s. Although a lot more earthquakes have occurred since this time, the main feature of the map has not changed much.

It is immediately apparent that earthquakes do not occur everywhere on the globe. Instead, they are confined to within narrow bands. The most prominent are those associated with the mid-ocean ridges, and the ocean trenches. Nevertheless, areas of diffused seismicities can be found in Central

Asia and western United States. Most of these earthquakes are relatively shallow (i.e., < 100 km depth). If all shallow earthquakes are removed from the above map, a distribution map of deep seismicities can be obtained and it is given below.

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Geology 452 – Introduction to Geophysics (ATH)

It is clear that deep earthquakes are located along trench axes. From the surface, they appear to cover a broad area over several hundred km wide. A cross-sectional cut into the interior of the Earth shows that again the deep earthquakes again are confined to narrow bands of no more than 50 km wide, except now, they are dipping into the interior as illustrated in the following examples. The first example represents deep earthquakes beneath the Tonga Trench in South Pacific. It is obvious that these deep events are confined within a band dipping at about 45o with respect to the surface. It is also interesting to note that the dip angle seems to change from the northern to the southern Tonga Trench.

Another example is beneath the Mariana Trench. It is illustrated in the diagram below.

Again, deep earthquakes in this area are confined to a narrow band. In this case, the dip is almost vertical with respect to the surface. The following diagram summarizes the distribution of earthquakes on the surface of the Earth. All earthquakes along mid-ocean ridges are shallow earthquakes. Surrounding the Pacific, deep earthquakes seems to happen beneath the deep sea trenches.

It is of interest to show that the Central United States is not free of earthquakes. The following map shows the historic earthquakes during the past 70 years of the New Madrid seismic zone.

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Geology 452 – Introduction to Geophysics (ATH)

It is clear that abundant earthquakes exist in southern Illinois. Earthquake Magnitudes Intensity : Earthquake intensity is measured in terms of the number of buildings destroyed and the number of lives lost. It is not an objective scientific scale. It is biased towards population centers. The Richter Scale : The Richter scale is a more scientific measure of earthquake magnitude based on seismograms. The equation used is given by the following.

( )10log ,aM f hT⎛ ⎞= + ∆⎜ ⎟⎝ ⎠

C+ (13.3)

where a is the amplitude of the ground motion for a particular type of wave (say, surface Rayleigh wave); T is the dominant period; ∆is the epicenter distance and h is the depth of the hypocenter. In general, f is a function that takes into account the effects of geometric spreading and anelastic attenuation of the earth. C is a parameter for local station corrections. If an earthquake is measured using surface waves, it is called a surface wave magnitude MS. Typically, equation (13.1) is modified to have the following form.

10 10max

log 1.66 log 3.3SaMT⎛ ⎞= + ∆⎜ ⎟⎝ ⎠

+ (13.4)

If an earthquake magnitude is measured using body waves, it is a body wave magnitude Mb. Body wave magnitudes usually follow the expression below.

(10max

log ,ba )M f hT⎛ ⎞= +⎜ ⎟⎝ ⎠

S

(13.5)

MS and Mb are related through the following relationship.

2.94 0.55bM M= + (13.6) Seismic energy released is also related to seismic magnitude through the following relationship.

10log 5.24 1.44 SE M= + (13.7) where E is the seismic energy given in joules. Seismic Moment : Earthquakes do not always occur instantaneously. When they occur over a finite period of time, their magnitudes are better described in terms of seismic moments. Seismic moments are calculated according to the following equation.

average slip break areaM µ= × × (13.8) In equation (13.6), µ is the shear modulus of the medium. Thus, seismic moment takes into consideration the rate of fault slip as well as the size of fault breaks. It is a term used only in specialized technical or scientific investigations. EARTHQUAKE SOURCE AND FOCAL MECHANISMS Faults are rock fractures. Earthquakes simply represent rock-fracturing processes. Depending on the orientation and sense of motion at the surface, faults can be classified into three groups. They are (1) normal faults, (2) thrust faults and (3) strike-slip faults.

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Geology 452 – Introduction to Geophysics (ATH)

X

TopView

SideView

Normal Fault Thrust Fault St rike-Slip Fault

How do stresses relate to rupture directions? Consider the following experimental setup. According to laboratory uni-axial loading experiments, it appears that rocks usually rupture at an angle between 30 to 50 degrees with respect to the loading direction. Hence, for analytical convenience, it is assumed that ruptures typically occur at 45 degrees with respect to the applied stress direction. For ease of analysis, one can always define a coordinate system such that the fault plane lies on the x-y plane. Thus, slip vectors will run parallel to the fault plane as shown below.

auxiliary plane applied uniaxial stress II I fault

plane x fracture rock sample III IV fracture According to the sense of slip, quadrangles II and IV are under compression, whereas I and III are under dilatation (or tension). Stresses needed to produce the slip are indicated by the heavy arrows in the diagram. RADIATION PATTERNS For seismic stations surrounding an earthquake (i.e., the rupture source), amplitudes of P and S wave arrivals can be plotted to form the following radiation patterns.

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Geology 452 – Introduction to Geophysics (ATH)

The earthquake mode described above is known as the single couple mechanism. The mechanism applies no net force on the fault plane. However, it does exert a net torque (or a net couple). The existence of a net torque on the fault is inconsistent with the equilibrium condition prior to an earthquake. Therefore, a new mechanism is proposed. A DOUBLE COUPLE MECHANISM A double couple mechanism assumes that slip occurs on both the fault plane and the auxiliary plane. As a result, the following radiation patterns are obtained.

While the two mechanisms yield an identical P-wave radiation pattern, the resultant S-wave radiation patterns are distinctly different. However, S-wave radiation patterns are more difficult to construct in practice because it is more difficult to pick out S arrivals from a seismogram. Therefore, even though the double couple mechanism is preferable from a theoretical standpoint, it has not yet been verified that all earthquakes are double couple earthquakes. SUMMARY OF THE INTERPRETATION OF FOCAL SPHERES Focal sphere reconstruction enables us to evaluate the nature of the fault planes corresponding to each earthquake. Ideally, the three types of faults will yield the

P-wave P-wave

+ +− −

− −+ +

S-wave S-wave

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Geology 452 – Introduction to Geophysics (ATH)

following three surface projections of the corresponding earthquake focal spheres.

X

normal fault t hrust fault st rike-slip fault

TopView

SideView

SideView

Of course, actual focal spheres obtained from earthquake observations are never this ideal. A large number of earthquakes contain a combination of two mechanisms. Generally, they are dominated by either normal faulting or thrust faulting with some strike-slip components. Only along strike-

slip faults, a purely strike-slip focal sphere can be observed. Question : Is it possible to have normal faulting and thrust faulting at the same time?

Construction of Focal Spheres Construction of focal spheres is based on a stereonet. A stereonet is a projection of coordinates on a hemispheric surface onto a two-dimensional plane. Let us first examine how longitudes and latitudes are projected onto a stereonet. The following illustrations demonstrate the principle of the projection.

In this diagram, the great circle formed by the intersection between a dipping plane and the lower hemisphere is illustrated. To project this great circle onto the equatorial plane, a procedure illustrated in the following diagram is used.

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Geology 452 – Introduction to Geophysics (ATH)

One can draw a line connecting the northpole with every point on the great circle. The intersections between these lines and the equatorial plane form a trajectory, which represents the projection of this dipping plane on a 2D stereonet. Following

a similar procedure, the small circles (i.e., latitudes) can also be projected onto this equatorial plane. The following diagram illustrates this point.

Finally, a stereonet is given in the following diagram.

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Geology 452 – Introduction to Geophysics (ATH)

Notice that in this stereonet, the straight line connecting the two poles represents a vertically dipping plane. The curves connecting these two poles represent dipping planes with increasingly shallower dip angles as one moves from the center to the edges of the stereonet. The two semi-circles at the outermost edge of the stereonet are planes with zero dip angles. Plotting Earthquakes on a Stereonet Note that the center of a stereonet represents the location of a seismic event. Orientation of a stereonet is such that one pole is

pointing towards the north. Given a seismic station anywhere in the world and knowing the seismic velocity structure of the Earth, one can perform a ray tracing and determine the angle of incidence of the seismic ray path between the earthquake and the station. Thus, the direction and the dip angle of the seismic ray can be evaluated. I hope that you are convinced that such a determination procedure can be carried out in principle, although the details are beyond the scope of this course. Once the direction and the angle of incidence are known, location of the station can be plotted on the stereonet.

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Geology 452 – Introduction to Geophysics (ATH)

The next thing that we need to know is whether the earthquake arrived at the station as a compressional or extensional event. That can be identified by examining the first

motion of the seismogram associated with the earthquake as illustrated in the following diagram.

A common practice is such that a compressional event will be denoted by a black circle, whereas an extensional event will be denoted by an open circle. Based on a collection of seismograms from a large number of seismic stations from all direction of the seismic event, a plot of the distribution of compressional and extensional arrivals can be generated on a stereonet. What needs to be done next is to separate these arrivals into quadrangles as discussed earlier. There is a cookbook approach to achieve this task.

(1) Copy the arrival data from the various stations and the outline of the stereonet onto a trace paper.

(2) Lay the trace paper on top of another

clean stereonet of the same size with their centers fall on top of each other.

(3) Rotate the bottom stereonet until one

of the great circles that separates a

group of compressional events from another group of tensional events. This great circle represents one of the fault planes associated with the earthquake.

(4) Because the auxiliary fault plane

must be at 90 degree angle with respect to this fault plane by definition, one needs to count a 90 degrees distance along a straight line that bisects all the great circles. Mark that point on the trace paper as point A.

(5) The auxiliary fault plane must then

pass this point A and separate another group of compressional events from the tensional events (or vice versa). Thus, one just rotate the stereonet underneath until such a great circle is identified.

(6) Once these two fault planes are

identified, construction of the focal sphere of the earthquake is complete.

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Geology 452 – Introduction to Geophysics (ATH)

Following are some examples of earthquake focal mechanisms at different tectonic provinces. The first diagram shows some earthquakes at the mid-ocean ridge of the Atlantic.

As you can see, all these three events are normal faulting events. In other words, the mid-ocean ridge of the Atlantic is under east-west horizontal tension. The next diagram represents earthquakes near the coast of Central America.

It is clear the on shore earthquakes are compressional events, whereas those at the Pacific ocean floor are strike-slip events. They are related to the plate subduction at the Central American Trench and the fracture zones of the Pacific, respectively. Their stress directions have strong implications about the plate motions at this area. It is of interest to note that not all deep earthquakes are compressional events as you may have guess. Many of the deep earthquakes are extensional events. Following is a diagram that summarizes some of the current knowledge about deep earthquake focal mechanism.

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Geology 452 – Introduction to Geophysics (ATH)

As one can see that only shallow dipping earthquakes show compressional characteristics. When earthquakes occur at a depth that exceeds about 300 km, they tend to show an extensional mechanism. Can you hypothesize what is happening down there? The methods that we discussed for earthquake location and focal sphere construction are classical methods. They are very useful to illustrate the principle of these procedures. However, they are not good methods to follow if one wishes to automate

these processes. It is mainly because it is difficult to teach a computer to pick P and S arrivals, to determine the polarity of a P arrival, and to rotate a stereonet to find a fault plane. What a computer can do well is to carry out a large amount of computations very quickly. Thus, it is more common to use synthetic seismograms to match the full wave forms obtained from all the seismic stations to locate earthquakes and to determine their focal mechanisms automatically. It is only when the results obtained by the computer do not appear

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Geology 452 – Introduction to Geophysics (ATH)

reasonable, manual approaches will then be used to double check the results. Seismic Tomography Up to this point, we try to reveal the interior of the Earth as onion-like spherical shells. With the advent of computing power, one can actually construct a three-dimensional seismic velocity structure within the interior of the Earth. Such a three-dimensional structure is known as a seismic tomography. Following is an example of a hemispheric cut of the Earth along a great circle that passes through North America.

The top box shows the surface map of the Earth. The straight line in the middle represents the great circle cut. This great circle cuts through North America, Central Asia, and Antarctica. The middle diagram shows the vertical cut of the top 700 km

shell. The spherical shell has been stretched out and mapped into a rectangle. The bottom diagram is the same as the middle diagram except it is for the lower mantle (i.e., from 700 km – 3000 km depth). Dark areas in the picture represent areas with higher seismic velocities. Generally, one can correlate colder materials with higher seismic velocities. Thus, the interpretation is that materials beneath continents are generally colder, whereas it is warmer beneath the oceans within the upper mantle. There is less correlation between deep mantle structure and the distribution of continents on the surface, however. Nowadays, the same results are usually presented in color as given below. Again, this is a cut of the Earth across the North American continent in the E-W direction.

Notice the strong high velocity anomaly beneath the western North America that represents the subducted Farallon Plate. The cold continental root beneath Iran is also visible. The large low velocity anomaly beneath Iran is interesting but puzzling.

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