Exploring model space via 1D extremal inversion of airborne TEM data: determination of depth and conductivity bounds of seawater and sediment in shallow coastal waters

Abstract

The aim of extremal inversion is to construct models with maximal or minimal characteristics, but which nonetheless fit the observed data acceptably well. Given one model which fits the data, extremal inversion enables the user to explore the permissible range of model parameters, hence determine parameter uncertainty. A 1D extremal inversion algorithm has been developed for horizontal loop TEM. Extremal inversion is effected via linear programming. The objective is maximisation or minimisation of a particular layer conductivity or depth. Bounds (on conductivity or depth) can be imposed explicitly as inequality constraints. Extremal models can differ markedly from the first model which fits the data. Extremal inversion is non-linear and is not confined to a neighbourhood which is 'linearly close' to the first model. As an example of the application of this method, 1D extremal inversion is applied to airborne TEM data acquired over shallow seawater to determine upper and lower bounds on depths of seawater and bedrock and on conductivities of seawater and marine sediment. The results compare favourably with available ground truth data. Estimates of parameter uncertainty derived from extremal inversion are as follows: ±0.6 S/m for seawater conductivity, ±0.2 S/m for sediment conductivity, ±0.7 m for seawater depth, and ±8 m for bedrock depth.