The generally large source area for seawave generated microseisms does not readily allow consideration of these events as unidirectional. Rather, these wave patterns must be due to a complicated interference system, whose properties can be described only by statistics. In this study it is postulated that the generation of microseisms results as the superpositon of the outputs of a large number N of seismic oscillators. These oscillators are randomly distributed both in space and time. This random distribution necessarily implies that the phase angles of incoming waves are randomly distributed too. The statistical properties of the resultant ground motion, outside of the generation area, is investigated theoretically. Special attention is given to the probability distributions of the vertical amplitudes and the horizontal vector amplitudes. Good agreement is found between these theoretical results and the measurements obtained from particle motion diagrams.
Additionally, the theoretical results lead to two methods for determination of the microseismic directions of approach. Both of these techniques were applied to the microseismic storm of January 28, 1963. This storm was generated by a well-developed cyclonic system off the east coast of the United States and Canada. Basic data for the study were obtained from the long-period seismograms of 5 stations (Rolla and Florissant, Mo., Bloomington, Ind., Dubuque, Iowa, and Ann Arbor, Mich.). The resulting analysis gave generation areas off the southern coast of Newfoundland and eastern coast of the United States.
Further use was made of the theory developed to investigate the character of the microseismic waves. This application showed the microseisms to be composed not only of clear, fundamental mode Rayleigh waves, but that Love wave motion was also present. Surprisingly the proportion of Love wave motion was found to be different at different stations. At Rolla, Florissant and Bloomington, it was predominant, while at Dubuque and Ann Arbor the Rayleigh wave motion was dominant.