Shallow Focus Explosion in a Liquid Sphere

Theoretical seismograms are obtained for the motion of the surface of a homogeneous fluid sphere of radius <it>a</it> due to an impulsive point pressure source located at a small depth <it>a</it>—<it>b</it> below the surface. Two values of <it>b/a</it> are considered such that if we put <it>a</it> equal to the radius of the Earth, the depths are 1 km and 200 km, respectively. The duration of the sources is 0.8 <it>a/c</it> s, 0.4 <it>a/c</it> s and 0.04 <it>a/c</it> s in each case. The seismogram due to a source of duration 0.04 <it>a/c</it> s at 1 km depth is of high frequency and is characterized by the arrival of doublet-pulses and by the arrival of a large number of reflected rays during a short time interval which precedes a limiting value τ*. There is gradual interference of pulses during these time-intervals. The amplitudes of the pulses decrease to zero at τ*. <it>C</it> denotes the velocity of sound in the fluid. A similar source at 200 km depth causes a less complicated pulse pattern: fewer pulses arrive, they are spread more widely and the amplitude of the waves decreases only very near to points of accumulation τ*. Diffracted waves can be distinguished. In contrast to the differences between the high frequency seismograms due to the sources at the two depths, the low-frequency seismograms due to sources of duration 0.1 <it>a/c</it> s and 0.2 a/c s are of almost identical form at both depths.