Open AccessWeighted Least Squares Estimates of the Magnetotelluric Transfer Functions from Nonstationary Data
Author(s) -
John A. Stodt
Publication year - 1982
Language(s) - English
Resource type - Reports
DOI - 10.2172/893411
Subject(s) - weighting , noise (video) , electrical impedance , magnetotellurics , signal (programming language) , least squares function approximation , mathematics , random noise , algorithm , statistics , computer science , physics , acoustics , engineering , electrical engineering , artificial intelligence , estimator , image (mathematics) , electrical resistivity and conductivity , programming language
Magnetotelluric field measurements can generally be viewed as sums of signal and additive random noise components. The standard unweighted least squares estimates of the impedance and tipper functions which are usually calculated from noisy data are not optimal when the measured fields are nonstationary. The nonstationary behavior of the signals and noises should be exploited by weighting the data appropriately to reduce errors in the estimates of the impedances and tippers. Insight into the effects of noise on the estimates is gained by careful development of a statistical model, within a linear system framework, which allows for nonstationary behavior of both the signal and noise components of the measured fields. The signal components are, by definition, linearly related to each other by the impedance and tipper functions. It is therefore appropriate to treat them as deterministic parameters, rather than as random variables, when analyzing the effects of noise on the calculated impedances and tippers. From this viewpoint, weighted least squares procedures are developed to reduce the errors in impedances and tippers which are calculated from nonstationary data