LECTURES 10 and 11 - Seismic Sources Hrvoje Tkalčić
*** N.B. The material presented in these lectures is from the principal textbooks, other books on similar subject, the research and lectures of my colleagues from various universities around the world, my own research, and finally, numerous web sites. I am grateful to E. Calais, E. Garnero and S. Ford for some material I used in this lecture. I am thankful to many others who make their research and teaching material available online; sometimes even a single figure or an idea about how to present a subject is a valuable resource. Please note that this PowerPoint presentation is not a complete lecture; it is most likely accompanied by an in-class presentation of main mathematical concepts (on transparencies or blackboard).*** Exercise 1: Locating a local earthquake Due next Tuesday, 10:10 AM in class
1. Measure time between P and S wave on seismogram 2. Use travel-time curves to get distance to epicenter 3. Draw circle on a map with radius of that distance 4. Three or more circles should intersect at EQ! What is an earthquake? eellaassttiicc rreebboouunndd - plates are continually moving & fault is stuck
- crust starts deforming (stores elastic energy)
- fault breaks, releases elastic energy
fault Seismic Sources Seismic Sources
These are, of course, fictitious forces. Seismic Moment Tensor Mij Seismic Sources Seismic Sources Seismic Sources
ε - the strength of CLVD component (from 0 to 0.5) Seismic moment tensors Model Source M Couples Focal Mechanism
Double-couple x Strike-slip (DC) y z
Compensated x linear vector dipole (CLVD) Ring Fault y z
Isotropic x Explosion y z Moment tensor decomposition
Full Isotropic DC CLVD Seismic Sources “Strike”, “Dip” and “Rake” angles Strike, Dip and Rake angles Aki & Richards (an advanced seismology book) definition of strike, dip, and rake
(adapted from page 106 of Aki & Richards (1980), Quantitative Seismology - Vol 1)
Strike - the fault-trace direction in decimal degrees (0 to 360, relative to North), defined so that the fault dips to the right side of the trace. That is, the fault always dips to the right when moving along the trace in the strike direction (from one point to the next). This means that the hanging-wall block is always to the right. This is important because rake (which gives the slip direction) is defined as the movement of the hanging wall relative to the footwall. For a vertical, strike slip fault (for which "hanging wall" has no physical meaning) we still call the right-side block the hanging wall to distinguish between right lateral and left lateral motion.
Dip - the angle of the fault in decimal degrees (0 to 90, relative to horizontal).
Rake - the direction the hanging wall moves during rupture, measured relative to the fault strike (between -180 and 180 decimal degrees). Rake=0 means the hanging wall, or the right side of a vertical fault, moved in the strike direction (left lateral motion); Rake = +/-180 means the hanging wall moved in the opposite direction (right lateral motion). Rake>0 means the hanging wall moved up (thrust or reverse fault). Rake<0 means the hanging wall moved down (normal fault).
Basic Examples:
Dip=90 & Rake=0 -----> left lateral strike slip Dip=90 & Rake=180 -----> right lateral strike slip Dip=45 & Rake=90 -----> reverse fault Dip=45 & Rake=-90 -----> normal fault Seismic Sources Seismic Sources Seismic Sources “Beach Balls” Types of focal mechanisms vs. boundaries Transform faults (e.g. San Andreas) Fault - crack in Earth where slip occurs Turkey Earthquake - slippage along a fault Aug 1999 M 7.4 Earthquake focus - fault slip location Subduction zones and ridges) Earthquake “belts”
95% of energy from earthquakes from thin zones (plate edges) Some are quite deep (subduction zones)
You are here: check out that unbeatable ray-path coverage for tomography Earthquake “belts”
95% of energy from earthquakes from thin zones (plate edges) Some are quite deep (subduction zones) Earthquake “belts”
notice the orientation of tectonic forces on this map
volcanoes - cliff from nearly vertical slip on fault
Hmm. How can we calculate the scalar seismic moment?
M =µAD 0
! Earthquake Intensity and magnitude
Mercalli intensity scale Intensity of shaking & damage at a specific location Depends on distance to earthquake & strength of earthquake
Magnitude A measure of the energy released in an earthquake Depends on size of fault that breaks Earthquake Intensity and magnitude Mercalli intensity scale Intensity of shaking & damage at Depends on distance to earthquake a specific location & strength of earthquake Magnitude A measure of the energy released in an earthquake Depends on size of fault that breaks Earthquake Intensity and magnitude Mercalli intensity scale Intensity of shaking & damage at Depends on distance to earthquake a specific location & strength of earthquake Magnitude A measure of the energy released in an earthquake Depends on size of fault that breaks
Regional moment tensor inversion
dn(x,t) = Mkj [ Gnk, j * s(t) ] d = seismic observations of displacement G = Green’s functions representing propagation effects M = moment tensor elements
If we assume a point source and now in matrix form d = Gm m = vector of 6 independent moment tensor elements m = (GTG)-1GTd Full waveform moment tensor inversion
Displacement u can be written:
where u is displacement, SS is vertical strike-slip, DS is vertical dip-slip, DD is 45º dip-slip, and EP is the explosion Green’s functions with Z, R, and T refering to vertical, radial and tangential components. Miso is (Mxx+Myy+Mzz)/3. Ai is given by Full waveform moment tensor inversion Now put the coefficients into the displacement equations and rearrange
# ZSS ZDD ZEP& # RSS RDD REP& uz = M xx% cos(2az) " + ( ur = M xx cos(2az) " + $ 2 6 3 ' $% 2 6 3 '( # ZSS ZDD ZEP& # RSS RDD REP& +M yy%" cos(2az) " + ( +M yy " cos(2az) " + $ 2 6 3 ' $% 2 6 3 '( # ZDD ZEP& # RDD REP& +M zz% + ( +M zz + $ 3 3 ' $% 3 3 '(
+M xy [ZSS sin(2az)] +M xy [RSS sin(2az)]
+M xz [ZDS cos(az)] +M xz [RDS cos(az)]
+M yz [ZDS sin(az)] +M yz [RDS sin(az)]