- Ground-motion model is: where a is in g, α = -1.237 ± 0.254, β = 0.278 ± 0.043, γ = -0.00220 ± 0.00042, h = 6.565 ± 0.547,
τ2 = 0.00645 ± 0.00382 and σ2 = 0.0527 ± 0.00525 (where τ2 is the inter-earthquake variance and σ2 is
the intra-earthquake variance and ± signifies the standard error of the estimate.
- Notes that errors in magnitude determination are one element that contributes to the between-earthquake
component of variance and could thus cause apparent differences between earthquakes, even if none existed.
- Develops a method to explicitly include consideration of magnitude uncertainties in a random earthquake
effects model so that the between-earthquake component of variance can be split into the part that is
due only to magnitude uncertainty (and is therefore of no physical consequence) and the part for which a
physical explanation may be sought.
- Applies method to data of Joyner and Boore (1981). Assume two classes of magnitude estimates: those
with estimates of Mw, which assumes to be associated with a standard error of 0.1, and those for which
ML was used as a surrogate for Mw, which assumes to be associated with a standard error of 0.3. Find
that the inter-earthquake variance is much lower than that computed assuming that the magnitudes are
exact but that other coefficients are similar. Believes that the high inter-earthquake variance derived using
the exact magnitudes model is largely explained by the large uncertainties in the magnitude estimates