1. 8: EARTHQUAKE SOURCE PARAMETERS
Magnitude, fault area, fault slip, stress drop, energy release
“the big one”

2. EARTHQUAKE MAGNITUDE Earliest measure of earthquake size
Dimensionless number measured various ways, including
ML local magnitude
mb body wave magnitude
Ms surface wave magnitude
Mw moment magnitude
Easy to measure
Empirical - except for Mw, no direct tie to physics of faulting
Note; not dimensionally correct

7. COMPARE EARTHQUAKES USING SEISMIC MOMENT M0
Magnitudes, moments (dyn-cm), fault areas, and fault slips for several earthquakes
Alaska & San Francisco differ much more than Ms implies
M0 more useful measure
Units: dyne-cm or Nt-M
Directly tied to fault physics
Doesn’t saturate
Stein & Wysession, 2003

8. 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 values
vary by about 0.2 units.
- Uncertainties for historic earthquakes are large. Fault length estimates for the San Francisco earthquake vary from 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 yield
different 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.

9. Moment magnitude Mw Magnitudes saturate:
No matter how big the earthquake
mb never exceeds ~6.4
Ms never exceeds ~8.4
Mw defined from moment so never saturates

10. SOURCE PULSE FROM EARTHQUAKE
TIME DURATION = rupture time T R needed to propagate along fault * rise time TD for full slip at any point
TR = fault length / rupture velocity

11. SPECTRUM OF SOURCE TIME FUNCTION

12. Decays below corner frequency
SOURCE SPECTRUM is flat and equal to seismic moment at periods longer than corner frequency 2/TR
Decays below corner frequency
Corner frequency shifts to left (lower frequency) for larger earthquakes with longer faults
Seismic moment
LOW
HIGH

13. 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

14. DIFFERENT MAGNITUDE SCALES REFLECT AMPLITUDE AT DIFFERENT PERIODS
Body & surface wave magnitudes saturate - remain constant once earthquake exceeds a certain size - because added energy release in very large earthquakes is at periods > 20 s
20 s
1 s
No matter how big an
earthquake is, body and surface wave magnitudes do not exceed ~ 6.5 and 8.4,
respectively.
For very large earthquakes
only low period moment magnitude
reflects earthquake’s size.
This issue is crucial for tsunami warning
because long periods excite tsunami, but are harder to study in real time

15. E. Okal

16. SCALING RELATIONS BETWEEN SOURCE PARAMETERS

18. THREE EARTHQUAKES IN NORTH AMERICA - PACIFIC PLATE BOUNDARY ZONE
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.
THREE EARTHQUAKES IN NORTH AMERICA - PACIFIC PLATE BOUNDARY ZONE
Tectonic setting affects
earthquake size
Stein & Wysession, 2003

19. STRAIN & STRESS CHANGES

20. EARTHQUAKE STRESS DROPS TYPICALLY 10s TO 100s OF BARS
Estimate from fault area if known
Kanamori, 1970

21. SPECTRAL CORNER FREQUENCY APPROACH

22. Problem: for shallow earthquakes P, pP, and sP often overlap, yielding a combined spectrum quite different from the source pulse.
Spectra differ between stations due to the variation in amplitude between direct and reflected arrivals, and cannot be used to corner frequencies or seismic moment.
Difficulty can be addressed by modeling the body waves, including the free surface reflections,
and estimating the source time function duration by matching the
observed waveforms. Given a duration estimate and an assumed
fault geometry, the fault length and stress drop are estimated as in corner frequency analysis.

23. ESTIMATING STRESS DROP FROM BODY WAVE MODELING -- HARDER
Inferring source dimension from time function requires
assuming rupture velocity & fault geometry
Estimated stress drop ~1 / L3 , so uncertainty in fault
dimension causes large uncertainty in ∆
Small differences in time function duration correspond
to larger differences in stress drop, even for assumed
rupture velocity & fault geometry
Stein and Kroeger, 1980

24. INTRAPLATE EARTHQUAKES THOUGHT TO HAVE HIGHER STRESS DROP (?)
(the slope is 3/2)
4.6-11

25. IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY CONSTANT
LONGER FAULTS (L LARGER) HAVE LARGER SLIP D

26. IF STRESS DROP IN EARTHQUAKES IS APPROX IMATELY CONSTANT
LINEAR DIMENSION3 OR FAULT AREA3/2 INCREASES WITH MOMENT M0

27. LARGER EARTHQUAKES GENERALLY HAVE LONGER FAULTS AND LARGER SLIP
Wells and Coppersmith, 1994
M7, ~ 100 km long, 1 m slip; M6, ~ 10 km long, ~ 20 cm slip Important for tectonics, earthquake source physics, hazard estimation

28. Underlying physics unclear
SLOW EARTHQUAKES
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
Stein and Pelayo, 1991

29. For a given moment and fault shape, lower stress drop corresponds to larger fault dimensions, and hence longer time functions and smaller corner frequencies.
Given two earthquakes with the same rupture velocity, one with lower stress drop will have less high frequency radiation, and thus lower Ms and mb.
Similar effects can result from a slower rupture
velocity, which also gives a longer time function for a given fault dimension.

30. ENERGY RADIATED BY EARTHQUAKE

31. ENERGY & MAGNITUDE 5

32. 1906 SF – 4 m of slip on 450-km long fault  3 x 10
1906 SF – 4 m of slip on 450-km long fault  3 x 10**16 Joules of elastic energy – equivalent to a 7 Megaton bomb (Hiroshima was Mt)
1960 Chile – 21 m of slip on a 800 km long fault  10**19 J of elastic energy (more than a 2000 Mt bomb – larger than all nuclear bombs ever exploded – largest was a Soviet atmospheric test of 58 Mt)
Earthquakes of a given magnitude are ~10 times less frequent than those one magnitude smaller. An M7 earthquake occurs approximately monthly, and an earthquake of M> 6 about every three days. Hence although earthquake predictor I. Browning claimed to have predicted the 1989 Loma Prieta earthquake, he said that near a date there would be an M6 earthquake somewhere, a prediction virtually guaranteed to be true.
Magnitude is proportional to the logarithm of the energy released, so most energy released seismically is in the largest earthquakes. An M 8.5 event releases more energy than all other earthquakes in a year combined. Hence the hazard from earthquakes is due primarily to large (typically magnitude > 6.5) earthquakes.

33. Only a small fraction of stress released ?
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 ?