CyberShake UCERF2 ERF

All CyberShake studies through Study 24.8 utilize an earthquake rupture forecast (ERF) derived from UCERF2. Some details about the construction of this ERF for CyberShake are described below.

Event Types

There are three types of events given by the UCERF2 ERF: regular, median, and aleatory.

Regular

Regular events represent floating sources in UCERF2, about 85% of all events in CyberShake.

1. Compute target Magnitude Frequency Distribution (MFD) for each source as a Gutenberg-Richter (G-R) distribution up to maximum magnitude determined by two Mw-Area scaling relationships (Ellsworth-B; Hanks and Bakun, 2007). The G-R b-value depends on the fault type: b=0 for type A faults (e.g., the San Andreas), and the average of G-R distributions with b=0 and b=0.8 are used for type B faults. Then average the MFD from the two scaling relationships, which is discretized in 0.1 magnitude bins (i.e., UCERF2 magnitude) to determine the final source MFD.
2. Extend the down-dip width (DDW) of the fault to match the Somerville (2006) area for a full-fault rupture at the maximum magnitude. (CyberShake-only, not done for standard UCERF2)
3. For each magnitude bin, compute the rupture area with Somerville 2006 (or, for standard UCERF2, Hanks and Bakun, 2007).
4. Build N floating ruptures with that area.
5. Set rate of each rupture to G-R rate for magnitude divided by N (equal weight to each rupture for that magnitude bin).

Median

Median events represent the characteristic sources in UCERF2, whose rupture areas are modified to match the Somerville (2006) scaling relationship, which represent ~2% of events in CyberShake.

1. For each branch on UCERF2 logic tree (Ellsworth-B; Hanks and Bakun, 2007), compute median magnitude from area with given scaling relationship, discretized into 0.1 magnitude bins (i.e., UCERF2 magnitude)
2. For each source:
   1. compute implied area from Somerville 2006 from UCERF2 magnitude
   2. compute DDW correction factor as ratio of implied area to original UCERF2 (U2) area, intended to be: ddwCorrFactor = som06Area / origU2Area
      Note that there is a bug in the UCERF2 implementation such that ddwCorrFactor = som06Area / ellBArea (rather than origU2Area). This resulted in a constant ddwCorrFactor = 1.65959 for characteristic sources (this bug does not affect floating regular sources).
   3. extend DDW such that the new rupture area equals the implied Somerville 2006 area: newDDW = origDDW * ddwCorrFactor (to the nearest integer)
      Note: what this does, holding magnitude constant, is extend the area such that if you were to use Somerville 2006 to compute magnitude it would equal the input UCERF2 magnitude.

Aleatory

Aleatory events have the same rupture areas of Median events, but with varying magnitudes to capture the variations in magnitude-area relationship, which represent ~13% of events in CyberShake.

1. For each Median source, compute the total moment rate
2. compute moment balanced Gaussian aleatory magnitude distribution with sigma=0.12, two sided truncation at 2 sigma
   Note: this means that the resultant moment rate from this distribution will equal the moment rate from Median (1)
3. Compute magnitude discretized in 0.1 magnitude bins
   Note: the largest magnitudes in CyberShake are aleatory events that have very large stress drops, which can lead to very high seismic hazard at long return periods.

Summary: Both Regular and Median types follow the Somerville 2006 scaling relationship, hence have the same estimated stress drop values. Aleatory events, on the other hand, have a large range of stress drop values.