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!
elastic rebound What is an earthquake? - 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 Strike-slip Double-couple (DC) y z x Ring Fault Compensated linear vector dipole (CLVD) y z x 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 Earthquake - slippage along a fault Earthquake focus - fault slip location Turkey Aug 1999 M 7.4
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 0 =µad
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 Depends on distance to earthquake & strength of earthquake Magnitude Intensity of shaking & damage at a specific location A measure of the energy released in an earthquake Depends on size of fault that breaks
Earthquake Intensity and magnitude Mercalli intensity scale Depends on distance to earthquake & strength of earthquake Magnitude Intensity of shaking & damage at a specific location A measure of the energy released in an earthquake Depends on size of fault that breaks
Regional moment tensor inversion d n (x,t) = M kj [ G nk, 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 = (G T G) -1 G T d
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. M iso is (M xx +M yy +M zz )/3. A i is given by
Full waveform moment tensor inversion Now put the coefficients into the displacement equations and rearrange # u z = M xx $ % ZSS 2 # +M yy " ZSS $ % 2 cos(2az) " ZDD 6 # ZDD +M zz 3 + ZEP & $ % 3 ' ( [ ] [ ] [ ] +M xy ZSS sin(2az) +M xz ZDS cos(az) +M yz ZDS sin(az) cos(2az) " ZDD 6 + ZEP 3 & ' ( + ZEP 3 & ' ( # u r = M xx $ % RSS 2 # +M yy " RSS $ % 2 # RDD +M zz $ % 3 cos(2az) " RDD 6 cos(2az) " RDD 6 + REP 3 +M xy RSS sin(2az) & ' ( [ ] [ ] [ ] +M xz RDS cos(az) +M yz RDS sin(az) + REP 3 & ' ( + REP 3 & ' ( " TSS u t = M xx $ # 2 sin(2az) % ' & " + M yy $ ( TSS # 2 sin(2az) % ' & [ ] [ ] [ ] + M xy (TSS cos(2az) + M xz TDS sin(az) + M yz (TDS cos(az)
d = Gm Green s functions computed for a 1-D model Data and synthetics are filtered between 10 and 50 s M W < 4 20 and 50 s 4 < M W < 5
BDSN regional MT solutions (1997-1998) The Long Valley Caldera (CA - NV border) If you ever In my opinion, visually the most spectacular part of California (east of HW 395, going south from Mono Lake to Death Valley) I determined most of the beach balls shown here as a graduate student at UC Berkeley (some of them in the middle of the night, immediately after earthquakes occurred) San Francisco Bay Area To Las Vegas
Anomalous Non-Double Couple Earthquakes in the Long Valley Caldera Percentages of DC, CLVD, ISO (ISO is Set to 0 restrained ) significant ISO, when MT is fully decomposed Dreger et al., Science, 2000 " M 1 0 0 % $ ' $ 0 M 2 0 ' = 1 " tr(m) 0 0 % " 0 0 0 % "(M 3 0 0 % $ ' $ ' $ ' 0 tr(m) 0 3$ ' + (1( 2)) $ 0 (M 3 0 ' + ) $ 0 (M 3 0 ' # $ 0 0 M 3 &' # $ 0 0 tr(m) &' # $ 0 0 M 3 &' # $ 0 0 2M 3 &' The presence of significant volumetric component Indicates A direct involvement of magmatic processes (e.g. pressurised liquid opening Cracks)
The puzzle of the Bárðarbunga earthquake: constraints from kinematic modelling? An example of a research project in volcano seismology - similar problems can be tackled at RSES, ANU
Bárðarbunga Photo taken by Oddur Sigurdsson, Iceland Geological Survey
Gjalp Subglacial Eruption (3 October 1996)
Gjalp Fissure (October 1996) Photo taken by Oddur Sigurdsson, Iceland Geological Survey
The Earthquake and Stations Location Azimuthal coverage excellent!
Time Domain MT Inversion Results Insignificant volumetric component!!! (unexpected) Tkalčić et al., 2007
Solution Stability The importance of having enough stations in the inversion is illustrated here
Faulting mechanism hypothesis Nettles and Ekström, 1998
Finite source simulations using finite differences method to produce synthetic data Tkalčić et al., 2007
Constraints on geometry of the caldera
Constraints on geometry of the caldera Tkalčić et al., 2007
Finite Source: Full-Circumference Not a good solution (opposite sense of CLVD from the observed)
Finite Source: Instantaneous Caldera Drop Not a good solution; tangential component of displacement very small in comparison to the observed
Finite Source: Quarter-Circumference Not a good solution, DC dominates the moment tensor (CLVD too small) in comparison to the observed
Finite Source: Half-Circumference This is a good solution, similar to the observed focal mechanism
Finite Source: Bilateral Rupture This is also a good solution, similar to the observed focal mechanism
Possible Rupture Speed
Cone sheets and ring dikes From Mull and Iona by David Stephenson Under which circumstances can these sheets rejuvenate to produce conical walls Observed, but with steep angles of dipping not exactly at 45 degrees, as in our models
Mass-exchange mechanism? Modelling: Horizontal tension crack at 2 km depth and compensating isotropic source at 3 km depth (below the crack) (this is done to simulate two magma chambers exchanging some volume of magma, which would be an alternative mechanism to the tectonic one) Retrieves a similar focal mechanism, but in most cases a large isotropic component, that was not observed (however, this can not be excluded as a plausible physical mechanism responsible for the puzzling focal mechanism)
Mass-exchange mechanism?
Conclusions The mechanism for the Bárðarbunga earthquake appears to be strongly NDC without a large isotropic component. We were able to simulate the observed mechanism using a finite rupture on a conical surface. Although our models are simplified in the sense of fault geometry, slip distribution (assumed uniform) and rupture velocity (assumed constant), they bracket the range of possible parameters in the finite-source process. A range of rupture speeds results in the observed mechanism, however the observed H/V ratio is better fit with super-shear rupture velocity. An alternative model with two offset sources with similar but opposite volume changes cannot be ruled out, however our modeling indicates that such scenarios often produce isotropic components.