# Magnitude Scaling Relationship

A magnitude-scaling relationship gives mean Magnitude as a function of rupture area or length (or visa versa), where length and area are given in units of km and km-sq, respectively.

Currenly Implemented Magnitude-Area Relationships:

• Wells and Coppersmith (1994, Bull. Seism. Soc. Am.):
• Mag = 4.07+0.98*log(Area) (all rupture types)
• Mag = 3.98+1.02*log(Area) (strike slip rupture)
• Mag = 4.33+0.90*log(Area) (reverse or thrust rupture)
• Mag = 3.93+1.02*log(Area) (normal rupture)
• Area = 10^(-3.49+0.91*Mag) (all rupture types)
• Area = 10^(-3.42 + 0.90*Mag) (strike slip rupture)
• Area = 10^(-3.99 + 0.98*Mag) (reverse or thrust rupture)
• Area = 10^(-2.87 + 0.82*Mag) (normal rupture)
• Uncertainty on Mag is 0.24, 0.23, 0.25, and 0.25 for all, strike slip, reverse, and normal ruptures, respectively.
• Uncertainty on log(Area) is 0.24, 0.22, 0.26, and 0.22 for all, strike slip, reverse, and normal ruptures, respectively.
• Hank & Bakun (2002 & 2008, Bull. Seism. Soc. Am.)
• Mag = 3.98+log(Area) (if Area <= 537)
• Mag = 3.07+(4/3)*log(Area) (if Area > 537)
• These equations are inverted to get Area from Mag
• No uncertainty estimates given
• Ellsworth (2003, published in Chapter 4 and Appendix D of the 2002 Working Group on California Earthquake Probabilities)
• Mag = 4.1+log(Area) (Equation 4.5a, AKA "Ellsworth A")
• Mag = 4.2+log(Area) (Equation 4.5b, AKA "Ellsworth B")
• Mag = 4.3+log(Area) (Equation 4.5c, AKA "Ellsworth C")
• These equations are inverted to get Area from Mag
• Uncertainty on Mag is 0.1

Currenly Implemented Magnitude-Length Relationships:

• Wells and Coppersmith (1994, Bull. Seism. Soc. Am.):
• Mag = 5.08+1.16*log(Length) (all rupture types)
• Mag = 5.16+1.12*log(Length) (strike slip rupture)
• Mag = 5.00+1.22*log(Length) (reverse or thrust rupture)
• Mag = 4.86+1.32*log(Length) (normal rupture)
• Length = 10^(-3.22+0.69*Mag) (all rupture types)
• Length = 10^(-3.55+0.74*Mag) (strike slip rupture)
• Length = 10^(-2.86+0.63*Mag) (reverse or thrust rupture)
• Length = 10^(-2.01+0.50*Mag) (normal rupture)
• Uncertainty on Mag is 0.28, 0.28, 0.28, and 0.34 for all, strike slip, reverse, and normal ruptures, respectively.
• Uncertainty on log(Length) is 0.22, 0.23, 0.20, and 0.21 for all, strike slip, reverse, and normal ruptures, respectively.