The sign convention for quadrature Parkinson arrows in geomagnetic induction studies

Abstract

Time series analysis, which is basic to modern geophysical data processing, involves a choice between working with a time dependence of e^+iωt or e^-iωt. In published work the choice made is sometimes not explicitly stated, leaving ambiguity in the interpretation of complex quantities with quadrature parts. Parkinson arrows are used in geomagnetic induction studies to summarize anomalous vertical magnetic fluctuations at different observing stations and to indicate regions of high electrical conductivity. Such arrows are now regularly computed as real and quadrature pairs. The general convention is often adopted of 'reversing' a calculated real arrow so that it will point toward a conductivity increase, but for quadrature arrows the practice between various published papers has generally not been so consistent. The present paper demonstrates that consistent practice for reversing or not reversing quadrature Parkinson arrows is possible when the initial convention for time dependence is taken into account. A reversal practice is determined for interpretation in terms of a simple channeling model. A related matter is the definition of phase. Phase values are also generally ambiguous unless the time dependence used (e^-iωt or e^+iωt) is stated.