### 2.242 McGarr and Fletcher (2005)

• Ground-motion model is:

where y is in cms2, a = -0.9892, b = 0.8824, d = -1.355, k = -0.1363, s1 = 0.337 (for stations on surface), s2 = 0 (for station at depth) and σ = 0.483.

• Use data from seven stations, one of which (TU1) is located underground within the mine. Determine site factors (constrained to be between 0 and 1) from PGV data. Originally group into three site categories: one for stations with close to horizontal straight-line ray paths, one for stations with steeper ray paths and one for underground station. Find site factors for first two categories similar so combine, partly because there is no precedent for topographic site factors in empirical ground-motion estimation equations. Believe that low site factors found are because stations are on solid rock V s > 1.5kms.
• Most data from Trail Mountain coal mine from between 12/2000 and 03/2001 (maximum MCL2.17). Supplement with data (2 records) from a M4.2 earthquake at Willow Creak mine to provide data at much higher magnitude.
• Most data from Mw < 1.7.
• Lower magnitude limit dictated by need for adequate signal-to-noise ratio.
• Focal depths between 50 and 720m (relative to the ground surface).
• Note that although data may be poorly suited to determine both d and k simultaneously they are retained because both attenuation mechanisms must be operative. State that d and k should be solely considered as empirical parameters due to trade-offs during fitting.
• Do not include a quadratic M term because it is generally of little consequence.
• Use rhypo because earthquakes are small compared to distances so can be considered as point sources.
• Selected events using these criteria:
• event was recorded by 6 stations;
• data had high signal-to-noise ratio;
• to obtain the broadest M-range as possible; and
• to have a broad distribution of epicentral locations.
• Find that Mw (estimated for 6 events) does not significantly differ from MCL.
• Find that constrains must be applied to coefficients. Constrain k to range -20 because otherwise find small positive values. Believe that this is because data inadequate for independently determining d and k.