Atmospheric refraction and focus of blast waves

An integral solution to the wave equation in an inhomogeneous half-space is used to derive the time-dependent pressure variation in the neighborhood of a first focus. Theoretically calculated signals are compared with barograph records. Conclusions are: (1) The curve of maximum peak-to-peak pressure versus distance is bell shaped; the dome of the bell is located on the far side of the caustic. (2) Width of the bell is proportional to the 2/9 power of the energy released to the atmosphere. (3) Height of the dome is proportional to the 5/18 power of the energy release. (4) The signal wave shape is quite sensitive to position near the caustic: on the near side the signal consists of a single long smooth wave; at the caustic the wave steepens into a spike followed by a dip; on the far side the signal divides into two separate portions, a relatively smooth wave followed by a period of silence followed by a wave containing a spike. (5) Close correlation between theoretical and observed signals is unlikely for a single event at a single recording station. (6) The theoretical focus is narrower and more intense than that experimentally observed.