Velocity and displacement of explosion-induced earth tremors derived from acceleration

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Abstract
Velocity and displacement time histories which are derived by integrating acceleration time histories of nuclear-explosion-induced earth tremors usually end in values that are obviously too large. It can be demonstrated that small errors, which are within the range of error one would expect from field-recorded data, could cause such unacceptable velocities and displacements. Assuming that such errors do exist but realizing that they cannot be determined exactly, two “correction” procedures are presented which adjust the acceleration data so that it is more rational. The two procedures are the least-mean-square-velocity technique (by G. V. Berg and G. W. Housner and used extensively with seismic data), which is based on the criterion of minimizing the mean of the velocity squared, and the end-time-zero technique, which depends on boundary conditions at the beginning and end of the tremor. The end-time-zero technique is recommended for use with nuclear-explosion-induced data.

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