levels by adding 4.5 dB so that these calculated results could be compared directly with measurements of (pressure-doubled) sonic boom levels.
In CHABA (1981), the mean peak level of the sonic booms (Borsky, 1965) was used to directly estimate the mean CSEL. However, the mean peak level does not correspond directly to the mean CSEL level. Rather, if the mean CSEL level comes from a Gaussian distribution, then the peak levels come from a lognormal distribution. Since Pierce and Maglieri (1972) have shown that sonic boom levels are normally distributed, Sutherland et al. (1990: Figure 3, Figure 4, and Figure 5) can be used to estimate standard deviations for sonic boom levels in the Oklahoma City study. These references show that the boom pressures follow a lognormal distribution since the levels are normally distributed. Aitchison and Brown (1969) give the equations to find the mean and standard deviation of the decibel levels given the mean and standard deviation of the pressures for a lognormal distribution. Including a factor of 47.85 Pa/(lb/ft2) to convert the reference sound pressure from pascals to the unit of pounds per square foot used to report the peak sound pressures of the sonic booms yielded an approximate constant of 127.6 dB instead of 94 dB for −10 log (p02). A scaling factor equal to 10 log (e2) decibels per neper was also needed to convert from base-e to base-10 logarithms and to introduce the decibel as the unit for the standard deviation and the mean peak sound pressure level. The results are given by the following equations:
σ2 = (10 log e2)2 1 n (1 + α2/η2) (25)
Lm = 127.6 + (10 log e2)α − 0.5 σ2 (26) (26)
where σ is the standard deviation of the sound levels, Lm is the mean of the sound levels, α is the mean of the peak sound pressures, and η is the standard deviation of the peak sound pressures. (Because σ was estimated from Fig. 3-5 in Sutherland et al., 1990, Eq. 25 was not used herein, but it is included for completeness.) As in CHABA (1981), a factor of about 25 dB is used to convert from the sonic boom peak sound pressure level to CSEL.