View source for CyberShake Magnitude Area Relationship

This page documents the magnitude-area relationship used in CyberShake, for Studies 1.0 to 18.8.

== Original UCERF2 Modifications ==

Characteristic sources:

<ol>
<li> For each branch on UCERF2 logic tree (relevant here are the 2 M(A) branches: Ellsworth B and HB 2002):
<ol>
<li> compute median magnitude from area with given scaling relationship</li>
<li> compute total moment rate for source </li>
<li> compute moment balanced Gaussian aleatory magnitude distribution with sigma=0.12, two sided truncation at 2 sigma.
<ul><li>Note 1: this means that the resultant moment rate from this distribution will equal the moment rate from (1.2)</li>
<li>Note 2: this is now discretized into 0.1 magnitude units</li></ul></li></ol>
<li> Create a single averaged source across all above branches (average the MFDs for the ruptures from (1), which could be multi-modal if the two M(A) relationships are significantly different) </li>
<li> If the CyberShake DDW fix is enabled (true for all CS studies to date), then for each source:
<ol><li> compute implied area from Somerville 06 from UCERF2 magnitude</li>
<li> compute DDW correction factor as ratio of implied area to original U2 area: ddwCorrFactor = som06Area / origU2Area </li>
<li> extend DDW such that the new rupture area equals the implied Somerville 06 area: newDDW = origDDW * ddwCorrFactor 
<ul><li>Note: what this does, holding magnitude constant, is extend the area such that if you were to use Somerville 06 to compute magnitude it would equal the input UCERF2 magnitude.</li></ul></li></ol>
</ol>

Floating sources:

# Compute target G-R MFD for source up to maximum magnitude (do this individually for each of the 2 M(A) branches, then average the MFD). This MFD is discretized in 0.1 magnitude bins
# for each magnitude bin in G-R MFD:
## compute rupture area from scaling relationship
### If CyberShake DDW fix is enabled, use Somerville 06 and extended source surface
### Else use HB 02 and original source surface (not sure why it's only HB 02 and not an average with Ellsworth B here)
## build N floating ruptures with that area
## set rate of each rupture to G-R rate for magnitude divided by N (equal weight to each floating rupture for that magnitude bin)