Estimating noise for airborne electromagnetic data from repeat flight lines or inversion residuals

TL;DR

This paper presents a comprehensive method for estimating and correcting noise in airborne electromagnetic data using repeat flight lines, including Gaussianising data and accounting for data correlations, to improve subsurface imaging accuracy.

Contribution

It introduces a novel algorithm for estimating multiplicative noise, non-linear altitude correction, and a statistically valid Gaussian likelihood function for AEM data inversion.

Findings

The method accurately estimates multiplicative noise from repeat lines.

Non-linear altitude correction improves noise characterization.

Diagonal covariance matrix is sufficient for regularised AEM imaging.

Abstract

Characterising the noise of an airborne electromagnetic (AEM) system is critical in correctly imaging the earth's subsurface conductivity. Deterministic and probabilistic geophysical inversion algorithms require foreknowledge of the system noise to specify stopping criteria or a valid model likelihood. Repeat flight lines provide a way for geophysicists to calculate the statistical variability in AEM data acquired over the same ground, and therefore estimate the levels of noise to propagate into the inversion. The total noise can be separated into multiplicative and additive components. The multiplicative noise is derived by repeat lines at survey altitude. The method to calculate the multiplicative noise is scarcely documented and usual methods for height correcting acquired data require a linear trend removal. This study will outline the algorithm used to estimate multiplicative noise of an AEM system, and non-linearly correct for varying altitudes during repeat flights. Additionally, this paper details a methodology to Gaussianise the data noise and provide a statistically valid Gaussian data misfit or likelihood function. Significantly, we provide methods for estimating the off-diagonal elements in the data covariance matrix used within the misfit function, taking into account the time-channel data correlation that is usually neglected. While our methodology is general, our study of a rotary-wing system leads us to conclude that for regularised time-domain AEM imaging, a diagonal data covariance suffices -- an important implication for rigorous yet practical AEM inversion.