Deformation Models The rate of large events in fault-based ERFs depends directly on fault slip rates, which can be derived from measured and dated geologic offsets, and perhaps interpolated or extrapolated along faults. Slip rates can also be obtained by modeling geodetic measurements such as Global Positioning System (GPS) observations. Because it is impossible to identify all faults, another contribution to hazard can be “off-fault” deformation (in quotes here because this deformation is at least partially occurring on un-modeled faults), which can be inferred from observed seismicity and/or GPS observations. Only about thirty percent of UCERF2 faults had measured slip rate estimates, and most others had an estimate from only a single location. UCERF2 deformation models were therefore based on expert-opinion evaluation of geologic and geodetic data. In addition to on-fault slip rates, off-fault deformation was represented by a set of geographic polygons, referred to as “type C zones”, each of which was assigned an effective slip rate (Figure 5, top panel). As an a posteriori check, UCERF2 deformation models were summed across various transects to confirm that total plate tectonic rates were well matched. For UCERF3, we have developed four different deformation models. One is a geologically “pure” model (uninfluenced by GPS observations), while the other three are kinematically consistent models that directly include both geologic and geodetic constraints. By using these models, we minimize relying on expert opinion to broker discrepancies between geodetic and geologic data, as in UCERF2. Importantly, this approach has provided data-driven slip rate estimates for faults with no prior assigned rates (which were excluded from UCERF2) and has filled in slip rates along faults with sparse observations. The latter three models also provide off-fault strain rate maps, allowing us to abandon the UCERF2 type C zones.
The GR hypothesis states that each fault section nucleates a GR distribution of earthquakes, with a b-value of 1.0 and a maximum magnitude defined by the largest rupture in which the section participates, including multi-fault ruptures. The rate of events, or the GR for each fault section can then be found by satisfying the section moment rate. Even before any inversion, we can sum all the consequent fault-section MFDs to obtain a total on-fault MFD. Two examples are shown in Figure 16. The red curve, which represents the ABM Deformation model paired with the Shaw09mod magnitude-area Relationship, exceeds not only the on-fault target (orange) but also the total regional target (black). The magenta curve, which represents the Zeng Deformation Model pared with the HanksBakun08 magnitude-area relationship, is just below the total target, and well above the on-fault target. Results for all other GR branches fall between these two cases. This discrepancy can be quantified as an on-fault coupling coefficient, defined as the ratio of the total rate of the target on-fault MFD (orange in Figure 16) to the total rate of the on-fault MFD (red or magenta curve in Figure 16). The implied coupling coefficients, listed in the , range from 0.37 to 0.75 among all the GR branches in Figure 3 (slip rate reductions of sixty-three to twenty-five percent). One option for matching the target MFDs is to apply these implied coupling coefficients, which can be done via two of the “Fault Moment Rate Fix” options in the UCERF3 logic tree (Figure 3): Apply Implied Coupling Coefficient – reduce the slip rates on all fault sections by the implied coupling coefficient (same reduction on all faults). Do Nothing – let the inversion decide where to reduce slip rates in matching the target MFD. value,
Figure 34. Cumulative participation MFD statistics for 200 simulated annealing runs on the reference branch. The fault-section examples shown here represent the worst case, median case, and best case in terms of fractional uncertainty described in the test (which is proportional to the standard deviation (StdDev) divided by the mean). 108 Figure 35. Number of above-water-level ruptures for branch-averaged solutions as a function of the number of simulated annealing runs on each branch (for Fault Model 3.1). The maximum value on the y-axis is the total number of ruptures (~250,000). 109 Figure 36. PGA hazard curves for the Los Angeles and San Francisco site listed in 14, obtained by varying equation set weights on the UCERF3 reference branch, as summarized in the main text and detailed in Appendix N (Page et al., 2013). The minimum and maximum curves among these tests are plotted with the red dashed lines, which can be compared with the range implied by alternative logic tree branches (blue shaded region). The difference between the mean curves (red and blue solid lines) is not meaningful in this comparison. Results for other sites are available here. 111 Table 1. List of acronyms 5 Table 2. List of appendixes to technical report* 11 Table 3. WGCEP (2013) consensus-building activities 16 Table 4. Moment rates for the various types of sources in UCERF2 (, given in units of 1019 Nm/yr or 1026 dyne-cm/yr)5 28 Table 5. Moment rates (in units of 1019 Nm/yr) for the UCERF3 deformation models, plus implied values of maximum magnitude (Mmax) and mean recurrence interval (MRI) of M≥8 events 8. ABM is short for “Average Block Model”. Also listed are UCERF2 values, and the notes give important comparison details. 29 6. The grand inversion system of equations used in solving for the long-term rate of fault-based ruptures, where fr represents the frequency or rate of the rth rupture. Important implementation details, such as equation set weighting, are given in Appendix N (Page et al., 2013). 42 Table 7. Magnitude-area and slip-length model combinations used in UCERF3* 46