**Earthquakes as Seismic Sources** Lupei Zhu

**Topics** • Earthquakes as seismic sources • How do earthquakes happen? • Rupture on faults; stress buildup • Locating earthquakes • Hypocenter, epicenter; how to locate? • Earthquake magnitudes • Richter’s local magnitude • Body wave magnitude and surface wave magnitude • Moment magnitude • How often do earthquake happen? • Gutenburg-Richter Law EASA-130 Seismology and Nuclear Explosions

**Seismic Sources** • Any radiator of seismic waves • Earthquakes • Explosions • Landslides • Parameters to describe a seismic source • Location • Occurrence time • Source dimension • Time duration • Strength EASA-130 Seismology and Nuclear Explosions

**How Earthquakes happen** • Earthquakes happen when rocks somewhere underground break along a surface called fault and the two sides pass each other in a sudden and violent motion. See Faults. • The cause of this sudden faulting is due to a gradual buildup of stress by the long-term plate-tectonics process inside the Earth. This explains why earthquakes are concentrated at plate boundaries. • Faults that were ruptured previously are weak zones and therefore are likely to be broken again in the future (Earthquake cycle). The time interval between earthquakes, however, is very irregular. • New faults can also be produced (so no one is 100% safe) EASA-130 Seismology and Nuclear Explosions

**Locating Earthquakes** • The starting point of an earthquake rupture is called the earthquake hypocenter, which is given by the latitude and longitude of its projection on the surface (called epicenter) and depth. • Seismologists use arrival times of P and S waves at different seismic stations to locate an earthquake and determine its occurrence time. • At least three stations are needed to determine the epicenter and occurrence time (three unknowns). One more station is needed if the depth is included. • Earthquake depth trades off with its occurrence time and is more difficult to get accurately. • Modern Seismic Networks usually use hundreds of stations. EASA-130 Seismology and Nuclear Explosions

**Travel Time** • Travel time, T, is defined as T = distance / velocity • Since P-waves travel faster than S-wave, the time separation between the two is larger at greater distances. EASA-130 Seismology and Nuclear Explosions

**A “Rule of Thumb”** • Because of the structure of Earth, for distance ranges between about 50 and 500 km, we can use a formula to estimate the distance from the observed S-arrival time minus the P-arrival time: distance = 8 (S-P arrival time) EASA-130 Seismology and Nuclear Explosions

**Example** • If the arrival time of an S wave is 09:30:15.0 (GMT) and the arrival time of a P wave is 09:29:45.0 (GMT), then the time difference is 30 s. Thus, the earthquake is located about 240 km away from the seismometer. • But in which direction ??? EASA-130 Seismology and Nuclear Explosions

**Distances and Circles** • In this case, if you know the distance the earthquake is from the seismometer, you know the earthquake must be located on a circle centered on the seismometer, with a radius equal to the distance. EASA-130 Seismology and Nuclear Explosions

**Triangulation** • With three or more stations, you can locate the earthquake using triangulation. EASA-130 Seismology and Nuclear Explosions

**Richter’s Local Magnitude** • Another important parameter is the magnitude of an earthquake. It is a measure of the energy it released in the form of seismic wave. • Charles Richter in 1935 first developed a magnitude scale based on the peak amplitude A of the seismogram recorded by a particular type of seismometer km away from the epicenter ML = Log A + 2.76 Log - 2.48 • Richter’s scale is a logarithmic scale. Earthquakes of 1 magnitude difference produce 10 times amplitude difference. • Since the Richter Scale is defined for a old type of seismometer, it is rarely used today. But it is still widely and mistakenly quoted in news press. EASA-130 Seismology and Nuclear Explosions

**Other Magnitude Scales** • The two most common modern magnitude scales are: • MS, Surface-wave magnitude (Rayleigh Wave) • mb, Body-wave magnitude (P-wave) EASA-130 Seismology and Nuclear Explosions

**Problem with Ms and mb** • It was found that these two magnitudes saturate when earthquakes are large than certain levels (6 for mb and 7-8 for Ms). EASA-130 Seismology and Nuclear Explosions

**What Causes Saturation?** • The rupture process. Large earthquakes rupture large areas and are relatively depleted in high frequency (short wavelength) seismic signals which the Ms and mb are measured with. EASA-130 Seismology and Nuclear Explosions

**The Best Magnitude** • The best magnitude should be based on the actual ruptured area and the amount of slip. This is how theseismic momentM0 is defined:Mo = (rigidity)(rupture area)(slip)The rigidity is a measure of how strong the rock is. Rock rigidity is ~30 GPa. Water’s rigidity is zero.M0 has units of force*distance (Nm) • The moment magnitude Mw is defined asMW = 2/3 log M0 - 6.0to tie it to the surface magnitude. It will never saturate. EASA-130 Seismology and Nuclear Explosions

**Some Magnitude Examples** • For an earthquakes like the 1991 Landers, California, Earthquake that ruptures a fault of 100 by 10 km2 with an offset of 3 m, the Mw is 7.3. • The hypothetical largest earthquake on Earth would to rupture the upper 100 km of the Earth around the globe, which corresponds to a magnitude of ~11-12. • An example of magnitude zero earthquake would be a 3 cm slip on a one square meter area. • So there are earthquakes of negative magnitudes (such as tearing a piece of paper, ~ -6). EASA-130 Seismology and Nuclear Explosions

**Seismic Energy and Magnitude** • Seismic energy E is the energy released from the source in the form seismic waves. • It is only a small portion of the total energy released during the earthquake. A large portion (more than 90%) is spent on breaking rocks and producing permanent deformation in the source region. • It is directly related to magnitude log E (in joule) = 1.5 M + 4.8 • The seismic energy for a magnitude 6 earthquake is 1014 J (20 kt TNT, a Hiroshima type nuclear bomb), which is 101.5 = 32 times greater than from a magnitude 5 earthquake. EASA-130 Seismology and Nuclear Explosions

**Magnitude-Frequency Law** • Gutenberg and Richter did statistics on number of earthquakes of different magnitudes in a given time. They found a universal law ( the Gutenberg-Richter Law) log N = a - M or N = N0 10-M • Globally, every year there are about two magnitude 8 earthquakes, 20 magnitude 7’s, 200 magnitude 6’s, … • The largest earthquake ever recorded is the 1960 Chile Earthquake of magnitude 9.8. According to the Gutenberg-Richter law, earthquake of this size happens every 50 years (we are almost there). • The parameter N0 varies from region to region, depending on local geology and stress environment. EASA-130 Seismology and Nuclear Explosions

**EASA-130 Seismology and Nuclear Explosions**