Phase derivatives can be used to compute instantaneous frequency and envelope delay (also known as group delay). Envelope delay, in the guise of phase differences, has been used by engineers in the simulation of strong ground motion, particularly as a way of controlling the duration of motion. Simulations using the stochastic method, in which duration is a simple function of source duration and a path-dependent duration, possess envelope delay properties similar to those from simulations based on phase differences. Envelope delay provides a way of extending the standard stochastic method to produce nonstationary frequency content, as produced by ground motions containing surface waves.

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