Wave Gradiometry in the Time Domain

A time-domain approach for solving for the change in geometrical spreading and horizontal wave slowness in wave gradiometry is presented based on the use of the analytic signal. The horizontal displacement gradient of a wave is linearly related to the displacement and its time derivative. The coefficients of this relationship give the change of geometrical spreading, the change in radiation pattern, and horizontal slowness. The new time-domain technique incorporates estimates of the instantaneous amplitude and frequency of the three time series to solve uniquely for the wave-field coefficients. The analysis is simpler and more suited to fast array processing of displacement gradient data sets compared with a spectral ratio method.