The measurement of velocity

Abstract

In the past forty years in many fields of physics and geophysics, signals, usually in the form of waves, have been observed by using arrays of receivers or detectors. The practical problems of estimating the velocity and direction of a signal observed with such an array, in the presence of noise not correlated between receivers, have been solved by many people and the statistical theory has been covered by E.J. Hannan. This thesis firstly extends this statistical theory to the situation where the noise is correlated between receivers. Many ad hoc attempts have been made to cover situations where more than one signal is present. We derive several consistent estimators of velocity and direction for this situation and discuss their asymptotic properties. These estimators are further examined using simulations and it is shown that they can separate signals which the array cannot resolve in the conventional sense. Also several methods of preliminary analysis are discussed using particular designs of arrays.