# Earthquake source mechanics

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1 Earthquake source mechanics Lecture 6 Seismic moment

2 Earthquake magnitude Richter magnitude scale M = log A( ) - log A 0 ( ) where A is max trace amplitude at distance and A 0 is at 100 km Surface wave magnitude M S M S = log A + α log + β where A is max amp of 20s period surface waves Magnitude and energy log E s = M s (ergs)

3 Seismic moment Seismic intensity measures relative strength of shaking locally Instrumental earthquake magnitude provides measure of size on basis of wave motion Peak values used in magnitude determination do not reveal overall power of the source Seismic Moment: measure of quake rupture size related to leverage of forces (couples) across area of fault slip Moment = FL F L F - two equal & opposite forces = force couple - size of couple = moment - numerical value = product of value of one force times distance between Applying couple to fault

4 Seismic Moment II Applying couple to fault Stress & strain accumulation Fault rupture and rebound F F Can be applied to seismogenic faults Elastic rebound along a rupturing fault can be considered in terms of resulting from force couples along and across it Seismic moment can be determined from fault slip dimensions measured in field or from aftershock distributions analysis of seismic wave properties (frequency spectrum analysis)

5 Seismic moment Seismic moment = Area of fault plane x stress drop of earthquake x coseismic slip [NB: Area x stress = force force x distance = moment]] provides estimate of overall size of the seismic source Units: units of moment = newton-metres = Nm = = joule = J = unit of energy So seismic moment is also a measure of the energy of the earthquake Empirical relation between moment and magnitude is log 10 M 0 = c M + d or M w = 2/3 log 10 M 0 6 (Moment-magnitude scale (Kanamori)

6 A few great fracturing events totally dominate the earthquake seismic moment released (moments more realistic than comparing magnitudes) The moment release, even at the major plate boundaries is distributed very unevenly About ¼ of the seismic moment released between was by the great Chilean earthquake of 1960 that ruptured 100km of the subduction zone interface at the Peru-Chile trench San Francisco 1906 doesn t even get a mention! Seismic moment Seismic moment does not saturate e.g. Alaskan earthquake: M s =8.4; M w =9.2

7 Seismic moment tensor The nine different force couples that make up the components of the moment tensor: M jk M = M M M M M M M M

8 Seismic moment tensor Example of right lateral movement on a strike-slip fault in the x 1 direction corresponds to: M 0 = M 0 0 M Note M ij = M ji where M o is defined as the scalar seismic moment: M 0 = µ A s where µ is the rigidity modulus, A is the area of the fault and s is the slip or displacement of the fault

9 Scalar seismic moment Define the scalar seismic moment (Aki) M 0 = µ A s µ - rigidity A - fault area s - slip (vector) Units: force x length (Nm or J) s l µ w Aspect ratio: usually l/w 2, except for long strike-slip faults

10 Far-field radiation pattern for double couple source P-waves S-waves The orientation of the small arrows shows the direction of first motion; their length is proportional to the wave amplitude. The P-wave first motions are outward in the compressional quadrant and inward in the dilatational quadrant, with nodal lines in between. S-wave first motions are generally away from the pressure axis and toward the tension axis; there are 6 nodal points and no nodal lines in S

11 Example of focal spheres Example of focal spheres and their corresponding fault geometries. The lower half of the focal sphere is plotted to the left, with compressional quadrants shaded. The block diagrams show th two fault geometries (the primary and auxillary fault planes) that could have produced the observed radiation pattern.

12 Far-field pulse shapes The near-field displacements caused by an earthquake will be permanent. M(t) would look like this In the far field there is a displacement pulse. dm/dt is proportional to the far-field dynamic response, such as observed with P-wave arrivals. Note most seismometers measure velocity or acceleration rather than displacement.

13 Seismic moment from seismograms Define seismic moment M 0 area under pulse Rupture length duration of pulse : l τ Time domain - instrument corrected pulse 30 Amplitude dm/dt Pulse duration τ 0 Time

14 Seismic moment from seismograms Define seismic moment M 0 A 0 Rupture length 1/ frequency: l 1 / f 0 Frequency domain Amplitude Frequency f 0

15 Earthquake characteristics M 0 = µ A s µ2 l s by dimensional analysis slip is: s = 2 M 0 / µ l 2 stress drop with earthquake: σ = 2 M 0 / 2π w 2 l Note can get σ from seismogram as rupture length, l τ, pulse duration and M 0 is proportional to amplitude Stress drops in range 1-30 MPa (Kanamori)

16 Stress drop in earthquakes Stress drop is typically a small fraction of total stresses in double couple earthquakes Varies according to crustal properties, fault maturity Single-force earthquakes (landslides) have much larger stress drops Fault length versus moment for large earthquakes (Scholz et al. 1986): larger stress drop produces more seismic moment for a given rupture area

17 Tectonics Infer seismic and tectonic slip rate slip rate = (sum of M 0 ) / (µ l.w T) M 0 - summing and earthquake catalogue l.w - overall tectonic setting T - duration of earthquake catalogue Find active slip rate (SAF) is 3 cm/yr Aseismic (creep) rate is 3 cm/yr Compare with satellite data, GPS

18 Seismic moment - from fault area Scalar seismic moment (Aki) M 0 = µ A s l s µ w Get area of fault plane from aftershocks Measure slip in the field

19 Regional tectonics from seismotectonics Fault plane solutions Type of faulting Slip direction Stress field orientation Quantitative seismotectonics Seismic moment Slip Stress drop Seismic and tectonic slip rate

20 Moment tensor inversions 1. NEIC fast moment tensors - from teleseismic P waveforms 2. Harvard CMT solutions - Centroid momen-tensor (from long perdiod body waves) 3. EMSC rapid source parameter determination - European- Mediterranean Seismological Centre - uses P & S waves results in 24 hours 4. NEIC broadband depths and fault-plane solutions

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