# The earthquake source

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1 Global seismology: The earthquake source Reading: Fowler p and Bolt Appendix G Earthquake location Earthquake focus: Latitude, longitude, depth Earthquake epicenter: Latitude, longitude Earthquakes occur on fault planes, energy is released from a volume of rock as is slips. However, from far away we consider an earthquake to be a point source: latitude, longitude, depth 1

2 Locating earthquakes For an earthquake at the surface there are three unknowns: latitude, longitude, origin time need observations of seismic arrival times at three stations Station at distance r 1 : P-wave arrives at: t 0 + r 1 / S-wave arrives at: t 0 + r 1 / Locating earthquakes With increasing station distance the S-P time increases: Given the S-P time we can calculate the epicentral distance r 1 2

3 Locating earthquakes Given the S-P time at 3 stations we can locate the earthquake Locating earthquakes Given the S-P time at 3 stations we can locate the earthquake Solve for latitude, longitude and origin time Complications The Earth is not flat and we can only estimate and There is an error associated with the arrival time measurement We also need to determine the focal depth Use arrival times at many stations around the globe 3

4 Earthquake depth To estimate depth we need: Seismic station above the earthquake Depth phases e.g. pp (not a good diagram!) Earthquake distribution indicates deformation at the Earth s surface 4

5 Earthquake depth distribution Indicate different patters of deformation ridges subduction Earthquake size damage How destructive is an earthquake? Earthquake size: magnitude and energy release Distance from populated regions Building standards intensity 5

6 Ground motion Kobe Earthquake, 1995 Ground motion Kobe Earthquake,

7 Loma Prieta Intensity: ShakeMap 1906 Intensity Darker means stronger shaking San Andreas soft bay mud The Lawson Report

8 1906 Intensity strongest shaking brown blue green pink yellow weaker shaking The Lawson Report 1908 Geology yellow man made land pink recent marine sands and alluvium dark color hard rock The Lawson Report

9 Intensity and soil/rock conditions strongest shaking weakest soils least shaking hard rock Richter magnitude Why magnitude? Intensity varies spatially for a given earthquake subjective measure depends on types of buildings need a measure of the size on an earthquake Magnitude single number for an earthquake initially, a measure of the amplitude of ground shaking with respect to a reference event: Richter magnitude: magnitude is log 10 of the maximum amplitude recorded on a Wood-Anderson seismometer at 100 km from the epicenter 9

10 Richter magnitude Wood-Anderson seismometer Torsion seismometer Frame twists around inertial mass (C) Light beam reflected off mirror writes on photographic paper Richter magnitude Nonogram 1. Measure S-P time. Provides distance 2. Measure amplitude in mm on Wood- Anderson seismometer 3. Draw line between the two points to obtain magnitude 10

11 Richter magnitude Nonogram How much smaller would the amplitude be if the earthquake was 1 mag unit smaller? factor of mm Richter magnitude Nonogram How much closer would you need to be to get an amplitude of 23 mm for a magnitude 4 earthquake? move from 210 km to 50 km 50 km 11

12 Richter magnitude Today Use different instruments and a distance correction factor: M L = log A - (Distance correction factor) M L = log A log A Obtain a magnitude estimate from every station waveform calculate average from all station for the final magnitude Other magnitude scales Body wave magnitude: m b Measured from P-wave amplitude of any waveform around the world m b = log A log T T A Alaskan earthquake recorded at Orville (see Bolt Appendix G) P-wave: A = 1.4 x 10-6 m T = 12 sec = 28 m b = =

13 Other magnitude scales Surface wave magnitude: M s Measured from surface-wave amplitude of any waveform around the world M s = log A log +2.0 A Alaskan earthquake recorded at Orville (see Bolt appendix G) P-wave: A = 1.4 x 10-6 m T = 12 sec = 28 m b = = 5.3 Rayleigh wave: A = 4.3 x 10-6 m M s = = 5.0 Are you surprised the magnitude estimates are different? Magnitude as a discriminator M s and m b estimates are usually different for a given earthquake m b measures the amplitude of the P-wave M s measures the amplitude of the surface wave Nuclear explosions Do not excite surface waves very well Use m b vs. M s to discriminate earthquakes How else can we discriminate? explosions 13

14 Magnitude-frequency relation Gutenburg-Richter relation: log N = a bm Global average for b is ~1 There are ten times as many magnitude 4 as there are magnitude 5 Magnitude and frequency 14

15 Earthquake energy To measure all the energy released in an earthquake we must integrate over space and time difficult! We can approximately relate magnitude to energy: log 10 E = M s (see Bolt Appendix G) A magnitude 5 earthquake releases about 30 times as much energy as a magnitude 4 Even when you add together the energy release from all the small earthquakes, it is small compared to the one big event Alaska earthquake at Orville (see Bolt appendix G) Rayleigh wave: A = 4.3 x 10-6 m M s = = 5.0 Estimate energy: log 10 E = M s E = 2.0 x ergs Some comparisons: US annual energy consumption: ergs Annual heat flow out of the Earth: ergs Total annual seismic energy: ergs 15

16 Best measure of earthquake size Seismic moment a measure of the total mechanical energy force couple: moment = FL F L F Seismic moment: Proportional to size of the fault times the slip Mo = μad Best measure of earthquake size Moment magnitude related to seismic moment: M w = 2 log M o Alaskan earthquake recorded at Orville M o = 4 x Nm therefore M w = 4.9 remember m b = 5.3 M s = 5.0 Fault length scales with Ms M s = log L therefore L = 3 km also from Bolt Appendix G 16

17 Other earthquakes Pakistan Oct 8, 2005 M b 6.7 * M s 7.7 M o 2.9 x dyne-cm M w 7.6 E 2.2 x ergs L 190 km 30,000 estimated dead * mb is not a good measure for large magnitude earthquake (M > 6) Other earthquakes Pakistan Oct 8, 2005 Loma Prieta Oct 17, 1989 M b 6.7 * M s 7.7 M o 2.9 x dyne-cm M w 7.6 M b 6.5 * M s 7.1 M w 6.9 E 2.2 x ergs L 190 km E 2.8 x ergs L 30 km * mb is not a good measure for large magnitude earthquake (M > 6) 17

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