earthquakes (2): waveform modeling, moment tensors, & source parameters kikuchi and kanamori,...
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SOMETIMES FIRST MOTIONS DON’T
CONSTRAIN FOCAL MECHANISM Especially likely when
- Few nearby stations, as in the oceans, so arrivals are near center of focal sphere
- Mechanism has significant dip-slip components, so planes don’t cross near
center of focal sphere
Additional information is obtained by comparing the observed body and surface waves to theoretical, or synthetic waveforms computed for various source parameters, and finding a model that best fits the data, either by forward modeling or inversion.
Waveform analysis also gives information about earthquake depths and rupture processes that can’t be extracted from first motions.
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Regard ground motion recorded on seismogram as a combination offactors:
- earthquake source
- earth structure through which the waves propagated
- seismometer
Create synthetic seismogram as Fourier domain convolution of these effects
SYNTHETIC SEISMOGRAM AS CONVOLUTION
SOURCE TIME FUNCTION DURATION PROPORTIONAL TO FAULT LENGTH L AND THUS CONSTRAINS IT
Also depends on seismic velocity V and rupture velocity Vr
SOURCE TIME FUNCTION DURATION ALSO VARIES WITH STATION AZIMUTH FROM FAULT, AND THUS CAN CONSTRAIN WHICH
NODAL PLANE IS THE FAULT PLANE
Analogous effect: thunder igenerated by sudden heating of air along a lightning channel in the atmosphere. Observers in positions perpendicular to the channel hear a brief, loud, thunder clap, whereas observers in the channel direction hear a prolonged rumble.
Directivity similar to Doppler Shift, but differs in requiring finite source dimension Stein & Wysession,
2003
BODY WAVE MODELING FOR
SHALLOW EARTHQUAKE
Initial portion of seismogram includes
direct P wave and surface reflections pP and sP
Hence result depends crucially on earthquake
depth and thus delay times
Powerful for depth determination
Stein & Wysession, 2003
SYNTHETIC BODY WAVE
SEISMOGRAMS
Focal depth determines the time separation between arrivals
Mechanism determines relative amplitudes ofthe arrivals
Source time function determinespulse shape & duration
IMPULSES
WITH SEISMOMETER AND ATTENUATION
Okal, 1992
BODY WAVE MODELING FOR DEPTH DETERMINATION
Earthquake mechanism reasonably well constrained by first motions.
To check mechanism and estimate depth, synthetic seismograms computed for various depths.
Data fit well by depth ~30 km.
Depths from body modeling often better than from location programs using arrival times
International Seismological Center gave depth of 0 ± 17 km: Modeling shows this is too shallow
Depth constrains thermomechanical structure of lithosphere
Stein and Wiens, 1986
High frequencies determining pulse shape preferentially removed by attenuation.
Seismogram smoothed by both attenuation and seismometer.
Pulses at teleseismic distances can look similar for different source time functions of similar duration.
Best resolution for details of source time functions from strong motion records close to earthquake.
EARTH & SEISMOMETER
FILTER OUT HIGH FREQUENCY
DETAILS
Stein and Kroeger, 1980
MODEL COMPLEX EVENT BY SUMMING
SUBEVENTS
1976 Guatemala Earthquake
Ms 7.5 on Motagua fault, transform segment of Caribbean- North American plate boundary
Caused enormous damage and22,000 deaths
Kikuchi and Kanamori, 1991
Amplitude radiation patterns for Love and Rayleigh waves corresponding to several focal mechanisms, all with a fault plane striking North.
Show amplitude of surface waves indifferent directions
Can be generated for any fault geometry and compared to observations to find the bestfitting source geometry
SURFACE WAVE AMPLITUDE
RADIATION PATTERNS
Stein & Wysession, 2003
SURFACE WAVE MECHANISM CONSTRAINT
Normal faulting earthquake in diffuse plate boundary zone of Indian Ocean
First motions constrain only E-W striking, north-dipping, nodal plane
Second plane derived by matching theoretical surfacewave amplitude radiation patterns (smooth line) to equalized data. Stein, 1978
SURFACE WAVE CONSTRAINT ON DEPTH
How well waves of different periods are generated depends on depth
DEPTH (km)
Tsai & Aki, 1970
SURFACE WAVE
DIRECTIVITY CONSTRAINT
1964 Mw 9.1 Alaska earthquake
7m slip
include finite fault area (500 km long) directivity to match surface wave radiation pattern
Pacific subducts beneath North America Kanamori, 1970
SEISMIC MOMENT TENSOR
Represents other types of seismic sources as well as slip on a fault
Gives additional insight into the rupture process
Simplifies inverting (rather than forward modeling ) seismograms to estimate source parameters
Used to produce global data set of great value for tectonics
FORCES REPRESENTING SEISMIC SOURCES
SINGLE FORCE - Landslide (Grand Banks slump) or Explosion (Mt. St. Helens)
SINGLE COUPLE - add 3 for isotropic explosion
DOUBLE COUPLE - slip on fault
Stein & Wysession, 2003
SEISMIC MOMENT TENSOR
General representation of seismic source using 9 force couples
Stein & Wysession, 2003
REPRESENTING EARTHQUAKE WITH MOMENT TENSOR
Simple representation yields seismic waves produced by a complex rupture involving displacements varying in space and time on irregular fault
First, approximate rupture with a constant average displacement D over a rectangular fault
Approximate further as a set of force couples.
Approximations are surprisingly successful at matching observed seismograms.
Stein & Wysession, 2003
MOMENT TENSOR ADVANTAGES FOR SOURCE STUDIES:
Analyze seismograms without assuming that they result from slip on a fault. In some applications, such as deep earthquakes or volcanic earthquakes, we would like to identify possible isotropic or CLVD components.
Makes it easier to invert seismograms to find source parameters, because seismograms are linear functions of components of the moment tensor, but are complicated products of trigonometric functions of the fault strike, dip, and slip angles. This is not a problem in forward modeling, but makes it hard to invert the seismograms to find the fault angles.
MOMENT TENSOR DATA FOR TECTONIC STUDIES
Globally-distributed broadband digital seismometers permit reliable focal mechanisms to be generated within minutes after most earthquakes with Ms > 5.5 and made available through the Internet.
Several organizations carry out this service, including the Harvard CMT (centroid moment tensor) project.
CMT inversion yields both a moment tensor and a centroid time and location. This location often differs from that in earthquake bulletins, such as that of the International Seismological Centre (ISC), because the two locations tell different things. Bulletins based upon arrival times of body wave phases like P and S give the hypocenter: the point in space and time where rupture began. CMT solutions, using full waveforms, give the centroid or average location in space and time of the seismic energy release.
The availability of large numbers of high-quality mechanisms (Harvard project has produced over 17,000 solutions since 1976) is of great value in many applications, especially tectonic studies.
SEISMOLOGY GIVES FOCAL MECHANISMS, SEISMIC MOMENTS, SOME INFORMATION ABOUT FAULT DIMENSIONS
Our goal is to use these to understand tectonics
Loma Prieta
1989
Ms 7.1Davidson et al., 2002
THREE EARTHQUAKES IN NORTH AMERICA - PACIFIC PLATE BOUNDARY ZONE
Tectonic setting affectsearthquake size
San Fernando earthquake on buried thrust fault in the Los Angeles area, similar to Northridge earthquake. Short faults are part of an oblique trend in the boundary zone, so fault areas are roughly rectangular. The down-dip width seems controlled by the fact that rocks deeper than ~20 km are weak and undergo stable sliding rather than accumulate strain for future earthquakes.
San Francisco earthquake ruptured a long segment of the San Andreas with significantly larger slip, but because the fault is vertical, still had a narrow width. This earthquake illustrates approximately the maximum size of continental transform earthquakes.
Alaska earthquake had much larger rupture area because it occurred on shallow-dipping subduction thrust interface. The larger fault dimensions give rise to greater slip, so the combined effects of larger fault area and more slip cause largest earthquakes to occur at subduction zones rather than transforms.Stein & Wysession, 2003
EARTHQUAKE SOURCE PARAMETER ESTIMATES HAVE CONSIDERABLE UNCERTAINTIES FOR SEVERAL REASONS:
- Uncertainties due to earth's variability and deviations from the mathematical simplifications used. Even with high-quality modern data, seismic moment estimates for the Loma Prieta earthquake vary by about 25%, and Ms valuesvary by about 0.2 units.
- Uncertainties for historic earthquakes are large. Fault length estimates for the San Francisco earthquake vary from 300-500 km, Ms was estimated at 8.3 but now thought to be ~7.8, and fault width is essentially unknown and inferred from the depths of more recent earthquakes and geodetic data.
- Different techniques (body waves, surface waves, geodesy, geology) can yielddifferent estimates.
- Fault dimensions and dislocations shown are average values for quantities that can vary significantly along the fault
Hence different studies yield varying and sometimes inconsistent values. Even so, data are sufficient to show effects of interest.
LARGER EARTHQUAKES GENERALLY HAVE LONGER FAULTS AND LARGER SLIP
M7, ~ 100 km long, 1 m slip; M6, ~ 10 km long, ~ 20 cm slip Important for tectonics, earthquake source physics, hazard estimation
Wells and Coppersmith, 1994
IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY CONSTANT
LONGER FAULTS (L LARGER) HAVE LARGER SLIP D
IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY CONSTANT
LINEAR DIMENSION3 OR FAULT AREA3/2 INCREASES WITH MOMENT M0
EARTHQUAKE STRESS DROPS TYPICALLY 10s TO 100s OF BARS
Estimate from fault area if known
Kanamori, 1970
ESTIMATING STRESS DROP FROM BODY WAVE MODELING -- HARDER
Stein and Kroeger, 1980
Inferring source dimension from time function requiresassuming rupture velocity & fault geometry
Estimated stress drop ~1 / L3 , so uncertainty in faultdimension causes large uncertainty in ∆
Small differences in time function duration correspondto larger differences in stress drop, even for assumedrupture velocity & fault geometry
ESTIMATE STRESS DROP FROM SOURCE SPECTRA
Infer corner frequency reflecting fault dimensions
Challenging
Results depend on assumed fault geometry & rupture velocity
WHY?
- Only a small fraction of stress released ?
- Lab values apply to contact area, only a fraction of total fault surface ?
-Lab values don’t scale correctly ?
DIFFERENT MAGNITUDES REFLECT ENERGY RELEASE AT DIFFERENT PERIODS
1 s - Body wave magnitude mb
20 s - Surface wave magnitude Ms
Long period - moment magnitude Mw derived from moment M0
Geller, 1976
Compared to ridge earthquakes, transform earthquakes often have large Ms relative to mb and large Mw relative to Ms suggesting that seismic wave energy is relatively greater at longer periods.
Earthquakes that preferentially radiate at longer periods are called "slow" earthquakes.
Underlying physics unclear
SLOW EARTHQUAKES
Stein and Pelayo, 1991
SUMMARY
Body & surface waveform modeling improve estimates of focal mechanism & depth
CMT data provides large mechanism dataset
Some generalizations can be made about earthquake source parameters
Results facilitate tectonic studies of plate motions, plate boundary zone and intraplate deformation, and thermo-mechanical structure of the lithosphere