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Lecture 6: Seismic Moment

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Lecture 6: Seismic Moment Earthquake source mechanics Lecture 6 Seismic moment GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Earthquake magnitude Richter magnitude scale M = log A(∆) - log A0(∆) where A is max trace amplitude at distance ∆ and A0 is at 100 km Surface wave magnitude MS MS = log A + α log ∆ + β where A is max amp of 20s period surface waves Magnitude and energy log Es = 11.8 + 1.5 Ms (ergs) GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic moment ß Seismic intensity measures relative strength of shaking Moment = FL F locally ß Instrumental earthquake magnitude provides measure of size on basis of wave Applying couple motion L F to fault ß Peak values used in magnitude determination do not reveal overall power of - two equal & opposite forces the source = force couple ß Seismic Moment: measure - size of couple = moment of quake rupture size related - numerical value = product of to leverage of forces value of one force times (couples) across area of fault distance between slip GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic Moment II Stress & ß Can be applied to strain seismogenic faults accumulation ß Elastic rebound along a rupturing fault can be considered in terms of F resulting from force couples along and across it Applying couple ß Seismic moment can be to fault determined from a fault slip dimensions measured in field or from aftershock distributions F a analysis of seismic wave properties (frequency Fault rupture spectrum analysis) and rebound GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD 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]] ß 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 log10 M0 = c M + d or Mw = 2/3 log10 M0 –6 (Moment-magnitude scale (Kanamori) GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic moment ß A few great fracturing events totally dominate the earthquake seismic moment released (moments more realistic than comparing magnitudes) ß The moment release, even at the major plate boundaries is distributed very unevenly ß About ¼ of the seismic moment released between 1904-86 was by the great Chilean earthquake of 1960 that ruptured 100km of the Seismic moment does not saturate subduction zone interface at e.g. Alaskan earthquake: M =8.4; the Peru-Chile trench s M =9.2 ß San Francisco 1906 doesn’t w even get a mention! GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic moment tensor The nine different force couples that make up the components of the moment tensor: ⎛ M M M ⎞ ⎜ 11 12 13 ⎟ M jk = ⎜ M 21 M 22 M 23 ⎟ ⎜ ⎟ ⎝ M 31 M 32 M 33 ⎠ GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic moment tensor Example of right lateral movement on a strike-slip fault in the x1 direction corresponds to: ⎛ 0 M 0⎞ ⎜ 0 ⎟ M = ⎜ M 0 0 0⎟ ⎜ ⎟ ⎝ 0 0 0⎠ Note Mij = Mji where Mo is defined as the scalar seismic moment: M0 = 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 GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Scalar seismic moment Define the scalar seismic moment (Aki) M0 = µ A s µ - rigidity l A - fault area s µ s - slip (vector) w Units: force x length (Nm or J) Aspect ratio: usually l/w ∼ 2, except for long strike-slip faults GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Far-field radiation pattern for double couple source P-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 S-waves 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 GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD 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. GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD 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. GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic moment from seismograms Define seismic moment M0 ∝ area under pulse Rupture length ∝ duration of pulse : l ∝τ Time domain - instrument corrected pulse 30 Pulse duration dM/dt τ Amplitude 0 Time GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic moment from seismograms Define seismic moment M0 ∝ A0 Rupture length ∝ 1/ frequency: l ∝ 1 / f0 Frequency domain Amplitude Frequency f0 GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Earthquake characteristics M0 = µ A s ∼µ2 l s by dimensional analysis slip is: 2 s = 2 M0 / µ l stress drop with earthquake: 2 ∆σ = 2 M0 / 2π w l Note can get ∆σ from seismogram as rupture length, l ∝τ , pulse duration and M0 is proportional to amplitude Stress drops in range 1-30 MPa (Kanamori) GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Stress drop in earthquakes ß Stress drop is typically a small fraction of total stresses in double couple earthquakes a Varies according to crustal properties, fault maturity ß Single-force earthquakes Fault length versus moment for large (landslides) have earthquakes (Scholz et al. 1986): larger stress much larger stress drop produces more seismic moment for a drops given rupture area GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Tectonics Infer seismic and tectonic slip rate slip rate = (sum of M0) / (µ l.w T) M0 - 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 GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Seismic moment - from fault area Scalar seismic moment (Aki) M0 = µ A s l s µ w Get area of fault plane from aftershocks Measure slip in the field GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Regional tectonics from seismotectonics ß Fault plane solutions a Type of faulting a Slip direction a Stress field orientation ß Quantitative seismotectonics a Seismic moment a Slip a Stress drop a Seismic and tectonic slip rate GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Moment tensor inversions 1. NEIC fast moment tensors - from teleseismic P waveforms http://gldss7.cr.usgs.gov/neis/FM/fast_moment.html 2. Harvard CMT solutions - Centroid momen-tensor (from long perdiod body waves) http://www.seismology.harvard.edu/projects/CMT/ 3. EMSC rapid source parameter determination - European- Mediterranean Seismological Centre - uses P & S waves – results in 24 hours http://www.emsc-csem.org/ 4. NEIC broadband depths and fault-plane solutions http://neic.usgs.gov/neis/nrg/bb_processing.html GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD .
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