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Trimming the UCERF2 Hazard Logic Tree

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Trimming the UCERF2 Hazard Logic Tree Trimming the UCERF2 Hazard Logic Tree a) b) c) Keith Porter , Edward Field , and Kevin Milner The Uniform California Earthquake Rupture Forecast version 2.0 (UCERF2) has 480 branches on its logic tree of 9 modeling decisions, often called epistemic uncertainties. In combination with 4 next-generation attenuation (NGA) relationships, UCERF2 has 1,920 branches. This study examines the sensitivity of a statewide risk metric to each epistemic uncertainty. The metric is expected annualized loss (EAL) to an estimated statewide portfolio of single-family woodframe dwellings. The results are depicted in a so-called tornado diagram. The uncertainties that matter most to this risk metric are the recurrence model, aperiodocity under a Brownian-passage-time recurrence model, and the choice of ground-motion-prediction equation. Risk is much less sensitive to the other uncertainties. One implication is that a statewide risk calculation employing only 5 branches of the UCERF2 tree and 4 NGA relationships captures virtually all the uncertainty produced by the full complement of 1,920 branches, allowing for a 100x reduction in computational effort with no corresponding underestimation of uncertainty. Another implication is that efforts to reduce these two epistemic uncertainties might be the most cost-effective way of reducing uncertainty in statewide risk resulting from UCERF2 and ground-motion-prediction equations. INTRODUCTION Assessing which sources of hazard uncertainty matter. The Uniform California Earthquake Rupture Forecast 2 (UCERF 2) is a fully time-dependent hazard model developed under the sponsorship of the California Earthquake Authority and delivered in September, 2007 (WGCEP 2007; Field et al. 2009). UCERF 2 contains 480 logic-tree branches reflecting choices among 9 modeling uncertainties or adjustable parameters in the earthquake rate model shown in Figure 1. For probabilistic seismic hazard analysis, it is also necessary to choose a ground-motion prediction equation (GMPE) and set its adjustable parameters, which a) SPA Risk LLC, 2501 Bellaire St, Denver CO 80207, (626) 233-9758, [email protected] b) US Geological Survey, Golden CO c) University of Southern California, Los Angeles CA can involve up to four additional branches, for a total of 1,920 hazard calculations for a single site. Figure 1. Branches of the UCERF logic tree that received non-zero weights (black numbers) in the final model calculations (WGCEP 2007). For the reader unfamiliar with UCERF2, it may be valuable to briefly review the meaning of each branching point (often called its epistemic uncertainties). In the following, quotations are drawn from WGCEP (2007). Fault models FM2.1 and FM2.2. As noted in the figure, the fault models specify the geometry of larger, more-active faults. According to the UCERF2 authors, “A fault model is a table of fault sections that collectively constitute a complete, viable representation of the known active faults in California.” The parameters of this representation are (1) section name, (2) fault trace, (3) average dip, (4) average upper seismogenic depth, (5) average lower seismogenic depth, (6) average long-term slip rate, (7) average aseismic slip factor, and (8) average rake. The authors define a new section only where one or more of these parameters are significantly different from those of a neighboring section along a fault. The major distinctions between FM2.1 and FM2.2 have to do with “how faults geometrically interact at depth,” especially in the Santa Barbara Channel area and western Transverse Ranges, in their north-dipping thrust faults. See Figure 2a. Deformation models DM2.1-DM2.6. These refer to assigning a slip rate, an aseismic slip factor, and their uncertainties, to each fault section. The UCERF2 preferred deformation model (DM2.1 and DM2.4) and alternatives are consistent with slip-rate studies, geodetic data, and the overall Pacific-North America plate rate. The alternatives pertain to tradeoffs between slip on the San Jacinto and the southernmost San Andreas faults. See Figure 2b. Magnitude-area relationships. These give the average magnitude for a given rupture area, and also influence earthquake rates where constraints are applied to match fault slip rates. The UCERF2 authors point out that “The global database of rupture areas and magnitude determinations has significant spread, leaving room for alternative interpretations.” The two alternatives used in UCERF2 amount to a choice between a loglinear regression (Ellsworth-B) relating the logarithm of rupture area to magnitude, and a bi-loglinear regression (Hanks and Bakun 2008) whose 2nd segment has a higher slope for larger rupture areas (A ≥ 537 km2, or M ≥ 6.7). See Figure 2c. Segmentation for type-A faults. Type-A faults are those that have paleoseismic constraints on the rate of large ruptures at one or more points on the fault. Segmentation imposes rupture boundaries—locations along a fault that are believed to prevent a rupture on one side from propagating to the other. In the segmented model all viable ruptures are composed of one or more segments, and never just part of any segment. To account for the fact that this assumption might be wrong (or a bad approximation), and alternative un- segmented model was also established for the type-A faults. This alternative essentially involved treating them as type-B faults, where a magnitude-frequency distribution is assumed and ruptures that don’t extend the entire length are “floated” down the fault with a uniform probability of occurring anywhere. Figure 2d shows the Type-A faults included in the UCERF model. Fault-slip rates within the segmented model on type-A faults. Two alternative models employ, on the one hand, an a-priori rate model “derived by a community consensus of paleoseismic and other geologic observations,” and on the other a moment-balanced version of the model, which “modifies the earthquake rate to match the observed long- term slip-rate data…. These two models balance a consensus of geologic and seismologic expert opinion with strict adherence to specific observational data.” Figure 3 illustrates of the alternative slip-rate models. Type-B earthquake rate models: connect more type-B faults? This refers to the model allowing nearby type-B faults to rupture together to produce larger earthquakes, especially San Gregorio, Green Valley, Greenville, and Mt Diablo Thrust. Doing so helps to reduce an over-prediction between M6.5 and M7 (referred to as “the bulge” by the UCERF2 authors, and shown in Figure 4 here). Type-B fault b-values. This branching point refers to the downward slope of the Gutenberg-Richter component of the magnitude-frequency relationship for type-B faults. Allowing an alternative b = 0.0 helps to reduce the bulge shown in Figure 4. Recurrence models and aperiodicity. The alternatives are a time-independent (Poisson) model, an empirical model that “includes a geographically variable estimate of California earthquake rate changes observed during the last 150 years,” and a Brownian passage time (BPT) model motivated by elastic-rebound theory. The BPT model involves computing the probability that each segment will rupture, conditioned on the date of last event, and then mapping these probabilities onto the various possible ruptures according to the relative frequency of each (from the long-term rate model) and the probability that each segment will nucleate each event. The BPT model involves an uncertain parameter referred to as aperiodicity, which relates to how irregularly earthquakes occur on a given fault. The lower the value of aperiodicity, the nearer events occur to their expected recurrence time, i.e., the more like ticks on a metronome. Three possible values have been considered. Figure 5a illustrates the effect on rupture probability as a function of time (normalized by mean recurrence interval) for Poisson versus BPT models. Ground-motion-prediction equation. Though not an element of UCERF2, GMPEs are required for a probabilistic seismic hazard analysis. Figure 5b illustrates the potential difference between Sa(1.0 sec, 5%) for a site with Vs30 = 280 m/sec, 500 m depth to 1000 m/sec, for two of the next-generation attenuation relationships given a M7 rupture. The same general trend holds for these two relationships—Chiou and Youngs (2008) and Abrahamson and Silva (2008) for M6.5 and M7.5 ruptures, and for higher Vs30 (say 760 m/sec), with AS2008 producing generally higher shaking than CY2008 for distances greater than about 15 km. (a) (b) 9 8 7 Ellsworth B Hanks & Bakun Magnitude 6 5 1 10 100 1,000 10,000 Rupture area, km2 (c) (d) Figure 2. Some of the epistemic uncertainties in UCERF2: (a) Fault models 2.1 and 2.2 differ in the elements shown here; (b) deformation models differ in the distribution of slip rates (colors) between the San Jacincto (western or left-hand of the two systems) and southern San Andreas Faults (eastern or right-hand of the two systems) (c) magnitude-area relationships; and (d) maps showing ttypes A, B, and C sources. All but (c) are from WGCEP (2007). Figure 3. Comparison of fault slip rates on Type-A segmented faults under a priori and moment-balanced models (WGCEP 2007). Figure 4. Difference between observed (red) and modeled (blue and black) magnitude-frequency relationships. UCERF2 reduces but does not eliminate "the bulge," the discrepancy between observed and modeled rates of M6.5-7.0 events. Crosses represent 95% bounds on the oberved rates (WGCEP 2007). 1.00 0.75 0.50 0.25 AS2008 Mean Sa(1.0 sec, 5%), g 5%), sec, Mean Sa(1.0 CY2008 0.00 0 255075 100 Rupture distance, km (a) (b) Figure 5. (a) Time dependence and the BPT versus Poisson recurrence models (WGCEP 2007); (b) shows that Abrahamson and Silva (2008) tends to produce hiigher median 1-sec, 5%-damped spectral acceleration response than does Chiou and Youngn s (2008) for distances greater than about 10 km, giveen a M7 event, 5 km to top of rupture, Vs30 of 330 m/sec, and 500m depth to 1km/sec shearwave velocity.
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