Estimating and testing earthquake magnitude limits David D. Jackson, UCLA Yan Kagan, UCLA Peter Bird, UCLA Danijel Schorlemmer, U. Potsdam Jeremy Zechar, ETHZ

Quick Summary We don’t know what limits earthquake size. Maximum magnitude unknowable. “Maximum credible earthquake” totally subjective. Magnitude with defined excedance probability in specified time is a more useful concept. Common methods for estimating magnitude limits include (a) historic records, (b) fault or plate boundary segment size, and (c) moment balance in fixed area. All require subjective choices. Methods (a) and (b) have failed many times. Comprehensive assessments over large areas, e.g. all subduction zones, is safest method. Bird and Kagan (2004) applied moment balance to a handfull of global tectonic regions and have yet to be embarrassed. Methodology developed by the Collaboratory for Study of Earthquake predictability, (CSEP), can be used to test hypotheses of excedance probability in specified time.

Ways to estimate size limits History of earthquakes within region – May use proxy such as tsunami runup Fault-length or –area scaling – May use largest fault in a region to characterize the whole region. Copying Mmax of region with similar tectonics Tectonic and seismic moment balance, assuming a magnitude – frequency relation.

Problems for estimating size limits Data are limited, especially temporally. Choice of region and its size is arbitrary. Definition of segments and rupture termination are imprecise. Objectives conflict – Small region has inadequate data, large region may miss important tectonics – Different communities have biases: academics, developers, insurers, environmentalists.

Historical Record?

Prior estimates of Tohoku Magnitude Limits Ruff and Kanamori, 1980: 8.2 (historical, age and plate-rate systematics) Nishenko, 1991: 7.6 (characteristic), 8.1 (historical, 1611) Minoura et al., 2001: 8.3, 200x85 km, based on 869 Jogan Tsunami Bird and Kagan, 2004: Corner magnitude 9.6 for all subduction zones. Koravos et al., 2006: 7< Mmax <8, based on historical earthquakes since 599 AD. Annaka et al., 2007: 8.5 based on historical earthquakes since Stein and Okal, 2010: 9+ for all subduction zones.

Fault-length scaling doesn’t work; many S. Calif. quakes don’t stay on mapped faults. Comparison of prior fault length with rupture length, from UCLA PhD thesis of Natanya Black, 2009.

Fault map before (thin black lines) and after (thicker grey lines) the Elmore Ranch earthquake of 1987 (magnitude 6.7). From Natanya Black, UCLA.

(Do we really think the the Pacific-North America plate boundary remains unfaulted in some places? Or, is this map just incomplete?)

Roger Bilham, CIRES/U CO The fault that caused the 2001 Bhuj earthquake may have been previously mapped [Malek et al., 2000]; its length of 80 km suggests maximum magnitude 7.3 [Wells & Coppersmith, 1994]. Actual seismic moment was 3.5x greater than this.

USGS *Denali, AK earthquake of (m = 7.9) jumped from the Susitna Glacier fault, to the Denali fault, to the Totschunda fault.

Other Anomalously Large Earthquakes Violating “Segment” rules Sumatra, 2004, 9.4: Broke through “segment boundaries”, violated Ruff and Kanamori 1980 “fast and young” systematics (Gutscher and Westbrook, 2009). Solomon Islands, 2007, 8.1: Ruptured through plate triple junction (Furlong et al, 2009) Balleny Islands, 1998, 8.1. Strike slip earthquake on unknown fault in oceanic crust, 200 km from spreading center (Hjorleifsdottir et al., 2009). Macquarrie Ridge, 1989, 8.2: Strike slip on 120km long unknown fault, 5km oceanic crustal thickness. Darfield, New Zealand, 2010, 7.1. Unknown fault in well studies area. El Mayor – Cucupah, Mexico, 2010, km rupture on combination of known and unknown faults

Global Tectonic Zones Bird, Kagan, and Jackson 2010

+Sumatra, +Sendai Magnitude-frequency relation for all subduction zones combined [Bird & Kagan, 2004, BSSA]

5. Even outside of broad orogens, dangerous intraplate faulting is evident in catalogs: (c) The corner magnitude of intraplate earthquakes is >7.6, and unconstrained from above, on the moment magnitude scale [Bird & Kagan, 2004, BSSA].

How to test Mmax models prospectively Specify Mmax on a global (or very comprehensive) grid, 0.1 degree. – Requires definition of Mmax – Few people bold enough to risk writing it down – Requires location to be epicenter. Global CSEP probability forecasts with lower thresholds of 7.5, 8.0, 8.5, 9.0, 9.5. – Fits existing CSEP template – Allows finite time window

Global long-term potential based on smoothed seismicity. from the CMT catalog since Earthquake occurrence is modeled by a time- independent process. Colors show the long-term probability of earthquake occurrence.

Conclusions 1.We don’t know what limits earthquake size. It does not seem to be segment boundaries, pre-existing fault extent, plate boundary triple junctions, or crustal thickness. 2.Efforts to estimate maximum magnitude based on geographically specific earthquake histories or tectonic situations tend to underestimate because of limited observations. 3.Some global or generic estimates (e.g. all subduction zones) haven’t yet been falsified, but constructing facilities to withstand the implied upper limits could be impossibly expensive. 4.Unconditional maximum magnitude is not a scientifically meaningful concept, as it can’t be tested in a finite time. Time limited probabilistic hypotheses are more useful and could possibly be testable. 5. Simple hypotheses that can be applied over much of the globe can be tested in a reasonable time; more complicated ones can’t. 6.A CSEP experiment could fairly test some forecast probabilities of earthquakes over 7.5, 8.0, 8.5, 9.0 and 9.5 globally for 5 or 10 year period.

For example, this area of monotonous granodiorite in the southern Sierras has only a few faults mapped...

“Can diligent and extensive mapping of faults provide reliable estimates of the expected maximum earthquakes at these faults?” No. Peter Bird UCLA 2010 Fall AGU, S23B-02

2. Fault trace “lengths” are unreliable guides to maximum magnitude. Fault networks have multiply-branching, quasi- fractal shapes, so fault “length” may be meaningless. Naming conventions for main strands are unclear, and rarely reviewed. Gaps due to Quaternary alluvial cover may not reflect deeper seismogenic structure. Mapped kinks and other “segment boundary asperities” may be only shallow structures. Some recent earthquakes have jumped and linked “separate” faults:

4. A recent attempt [Bird, 2009, JGR] to model neotectonics of the active fault network in the western United States found that only 2/3 of Pacific-North America relative motion in California occurs by slip on faults included in seismic hazard models by the 2007 Working Group on California Earthquake Probabilities.

Simple Scaling Model for Length, Displacement, and Down-dip Width

What is Mmax? Mmax poorly defined, and not measurable. Maximum credible earthquake (MCE) is subjective, and still not measurable. Corner magnitude, where tapered GR (TGR) relationship tapers, presupposes the TGR distribution but it is measureable for large areas and long times. Assuming TGR with estimated corner magnitude and fixed time duration, one can estimate a “functional magnitude limit: (FML) which will be exceeded only at arbitrarily small probability. This may be more useful than “Mmax” because – Structures have finite lifetimes – FML can be estimated with enough data – Assumed FML can be tested

Nishenko (1991) Circum Pacific Characteristic Rupture Zones

but seismicity suggests that there may be at least one more...