Pareto Efficient Multi-objective Joint Optimisation of EM Data

Abstract

Jointly inverting different data sets can greatly improve model results, provided that the data sets are sensitive to similar features. Such a joint inversion requires assumed connections between the different geophysical data sets, which can either be of analytical or structural nature. Classically, the joint problem is expressed as a scalar objective function that combines the misfit functions of all involved data sets and a joint term accounting for the assumed connection. This approach has two major disadvantages: Firstly, by aggregating all misfit terms a weighting of the data sets is enforced, and secondly, false models are produced, if the connection between data sets differs from the assumed one. We present a Pareto efficient multi-objective evolutionary algorithm, which treats each data set as a separate objective, avoiding forced weighting. The algorithm jointly inverts one-dimensional datasets from different electromagnetic techniques and also treats any additional information as separate objectives, rather than imposing them as a fixed constraint. Additional information can include, for example a priori models, seismic constraints, or well log data. Statistical analysis of the final solution ensemble yields an average one-dimensional model with associated uncertainties. Furthermore, the shape and evolution of the Pareto fronts is analysed to evaluate dataset compatibility and to judge if the assumed connection between datasets was valid.