Magnitude-Area Scaling of Strike-Slip Earthquakes

Magnitude-Area Scaling of Strike-Slip Earthquakes • Review of data and methods • Different functional forms: L, W, SA • Compatibility with rupture dynamics • Compare current scaling models • Implications for earthquake forecast models • Implications for strong ground motion simulation • Recommended set of scaling relationships

Data Types for Area Estimation • Indirect measurements (aftershock zone; surface rupture length): Wells & Coppersmith (1994); Hanks & Bakun (2002); WGCEP(2002) • Direct measurements from rupture models derived from seismic radiation: Somerville et al. (1999); Mai & Beroza (2000), Somerville (2006)

Figure 3. Comparison of Moment – Area Scaling Relations

Table 4. Crustal Strike-slip Earthquakes used by Somerville (2006a)

Table 5. Fault Dimensions of Crustal Strike-slip Earthquakes used by Somerville (2006a)

Table 1. Comparison of Data used by WCGEP (2002) and Somerville (2006): 1999 Izmit Earthquake

Figure 1. Izmit earthquake slip distributions for layered elastic models. Left and right columns show results for the FE and WEA approaches. Though the slip patterns look similar for all of the inversions, the layered elastic models require more slip in the mid crust. Source: Hearn and Burgman (2005).

Figure 2. Weighted residual sum of squares (WRSS), centroid depth, and moment from layered Izmit models, as a function of maximum permitted rupture depth. The WRSS increases sharply when the maximum rupture depth is restricted to less than 20 km. Source: Hearn and Burgman, 2005.

Constraints on Rupture Width • Whole space geodetic inversions underestimate depth limit of rupture • Rupture models of recent large strike-slip earthquakes have rupture widths that generally exceed the seismicity width • Brittle behavior (e.g. in feldspars) may extend deeper than the seismicity width

Different functional forms for Mo – A beyond transition to large Mo Mo = u D L W SSim: D ~ L ~ W ~ Mo exp 1/3 below transition • L: D ~ L (large D, small A) • W: D = const (small D, large A) • SA: D ~ Mo exp 1/3 (intermediate; no change at transition; W saturates and L compensates by growing twice as fast) SSim = self-similar; SA = self similar in area

Table 2. Scaling Relations Between Rupture Area and Seismic Moment

Table 3. Scaling Relations Between Magnitude and Rupture Area

Figure 3. Comparison of Moment – Area Scaling Relations

Table 6. Estimates of Mw from Rupture Area for Large Strike-Slip Earthquakes Comparison with 1906 Earthquake Mathews & Segall (1993): W for 1906 in the range of 15 – 20 km

Compatibility with Rupture Dynamics • Bodin & Brune (1996); Mai and Beroza (2000): the final slip is not simply related to fault dimensions; scaling is intermediate between L and W models • Jing et al. (2005): with spatially heterogeneous slip, the nonlinear transition occurs at large L, and the relation between D and L for a suite of faults resembles Wells and Coppersmith

Implications for Earthquake Forecast Models • The main impact is on Mmax, which affects recurrence of smaller earthquakes • WGCEP02 found that Wells and Coppersmith overpredicted historical seismicity due to low Mmax • But many other factors could be involved

Factors that Influence Seismicity Rate Field et al (1999): explaining deficit in S Cal Seismicity: • The b-value and minimum magnitude applied to Gutenberg-Richter seismicity • The percentage of moment released in characteristic earthquakes • A round-off error in the moment magnitude definition • Bias due to historical catalog completeness • Careful adherence to the conservation of seismic moment rate • Uncertainty in magnitude estimates obtained from empirical regressions • Allowing multi-segment ruptures (cascades) • The time dependence of recurrence rates.

Implications for Strong Motion Simulation • SA models are compatible with recorded long period strong ground motion amplitudes • L models are not – predict ground motions that are much too large • Addressed in NGA-E Project • To be discussed further by Robert Graves

Figure 4. Combinations of magnitude and rupture area used in ground motion simulations for the NGA-E Project. Source: Abrahamson et al., 2004.

Table 6. Rupture Dimensions for Strike-Slip Simulations for the NGA-E Project

Figure 5. Scaling of ground motion amplitude in simulations using the SA (labeled constant stress drop) and L scaling models, compared with the empirical model of Sadigh et al. (1997). At 3 seconds period, the SA model is more compatible with empirical models than the L model

Figure 6. Scaling of simulated response spectral amplitude with rupture area for magnitude 7.5 strike-slip earthquakes. Rupture area scaling has a very large impact on simulated ground motions at long periods.

Table 7. Recommended Scaling Models and Weights

Table 8. Standard Deviation of Measurement Error

Table 9. Coefficient of Variation of Measurement Error and Aleatory Variability

Magnitude-Area Scaling of Strike-Slip Earthquakes