The physical characteristics of near-field and far-field earthquake records differ significantly. These differences can be seen in both the recorded acceleration and the ground motion displacement time-histories. The differences in the time-histories of the ground velocity corresponding to far-field and near-field records also require special considerations.
These differences stand out more than other characteristics in the physical nature of the near-field records containing forward directivity effects. The appearance of high-amplitude distinct pulses in the time history of strong earthquake records is the main subject of this discussion.
Significant efforts have been made to develop comprehensive mathematical models to handle coherent pulses as well as high-amplitude spikes before and after the main coherent wave-form, as accurately as possible.
The aim of this research is to approximate and simulate the distinct pulses displayed in the velocity time history of near-field earthquake records, according to computational implementations and analytical considerations with regards to closed-form mathematical models.
Yet, performing this calculation approach and processing the mathematical functions has been accomplished from the point of views of modeling and matching the companion algebraic statements.