Atmospheric pressure changes due to volcanic eruptions and possible water level fluctuations

The data of Reed (1983) are analysed to produce the following empirical equations for the amplitude p ₀ (overall fluctuation) in Pascals of the air pressure wave associated with a volcanic eruption of volume V km³ or a nuclear explosion of strength M Mt: Here s is the distance from the source in km. $$\begin{gathered} \log _{10} p_0 = 4.44 + \log _{10} V - 0.84\log _{10} s \hfill \\ {\text{ }} = 3.44 + \log _{10} M - 0.84\log _{10} s. \hfill \\ \end{gathered} $$ Garrett's (1970) theory is examined on the generation of water level fluctuations by an air pressure wave crossing a water depth discontinuity such as a continental shelf. The total amplitude of the ocean wave is determined to be where c ₂ ¹ = gh ₁, c ₂ ² = gh ₂, g is acceleration of gravity, h ₁ and h ₂ are the water depths on the ocean and shore side of the depth discontinuity, c is the speed of propagation of the air pressure wave, and ? is the water density. $$B = \left {\frac{{c_2^2 }}{{c^2 - c_2^2 }} + \frac{{c^2 (c_1 - c_2 )}}{{(c - c_1 )(c^2 - c_2^2 )}}} \right]\frac{{p_0 }}{{g\varrho }}$$ It is calculated that a 10 km³ eruption at Mount St. Augustine would cause a 460 Pa air pressure wave and a discernible water level fluctuation at Vancouver Island of several cm amplitude.