# EARTHQUAKE MAGNITUDE

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1 EARTHQUAKE MAGNITUDE Earliest measure of earthquake size Dimensionless number measured various ways, including M L local magnitude m b body wave magnitude M s surface wave magnitude M w moment magnitude Easy to measure Empirical - except for M w, no direct tie to physics of faulting Note; not dimensionally correct

2 T s =D/V s T p = D/V p T s -T p = D/V s - D/V p = D (V p -V s ) / V s V p -> D = (T s - T p ) * V p V s /(V p - V s )

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6 COMPARE EARTHQUAKES USING SEISMIC MOMENT M 0 Magnitudes, moments (dyncm), fault areas, and fault slips for several earthquakes Alaska & San Francisco differ much more than M s implies M 0 more useful measure Units: dyne-cm or Nt-M Directly tied to fault physics Doesnʼt saturate Stein & Wysession, 2003

7 the big one

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 M w Magnitudes saturate: No matter how big the earthquake m b never exceeds ~6.4 M s never exceeds ~8.4 M w defined from moment so never saturates

10 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 earthquakeʼs size. This issue is crucial for tsunami warning because long periods excite tsunami, but are harder to study in real time

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

12 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

13 Earthquake Scaling Relations San Andreas Fault System log 10 A ~ M

14 ENERGY & MAGNITUDE ~ m b ~ M s 5 5

15 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. 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.

16 Working Group on California Earthquake Probabilities (2007) Uniform California Earthquake Rupture Forecast (UCERF2) M 6.7: 97% M 7.0: 81% M 7.5: 39% Southern California 30-year probabilities M 8.0: 2% UCERF2 ratio of time-dependent to time-independent participation probabilities for M 6.7

17 Intensity scale Measures damage to structures Often used is Mercalli I-XII Can be used to examine historic earthquakes without seismic records For example, eastern US.

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19 Intensity Observed Effects I Not felt at all II Felt only by a few individuals, indoors and at rest, usually on upper floors of tall buildings. III Felt indoors by many persons, but not necessarily recognized as an earthquake. Chandeliers and hanging plants swing. IV Felt both indoors and out. Feels like the vibration caused by a heavy truck or train passing. Windows rattle. V Strong enough to awaken sleeping persons. Small objects knocked off shelves. Beverages may splash out of cups or glasses on tables. VI Perceptible to everyone. May cause public fright. Pictures fall off walls. Weak masonry cracks. Some plaster may fall from ceilings. VII Difficult to stand upright. Ornamental masonry falls from buildings. Waves may be seen in ponds and swimming pools. VIII Mass panic may occur. Chimneys, smoke stacks and water towers may lean and fall. Unsecured frame houses slide off foundations. IX Panic is general. Heavy damage to masonry structures and to underground pipes. Large cracks open in ground. X Many buildings collapse. Water splashes over riverbanks. XI-XII Virtually total destruction.

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