Spatially constrained inversion of semi-airborne transient electromagnetic data based on a mixed norm

The interpretation of semi-airborne transient electromagnetic data is mainly based on a one-dimensional inversion algorithm. The continuity of the resistivity profile is generally poor when the data noise is strong because the resistivity is laterally unconstrained, and the constraint between the resistivity in the vertical distribution is usually taken as the L2 norm regular term. However, the main disadvantage of this regularization constraint is that it over-smoothens the model and cannot effectively describe the interface information of an abrupt electrical change. To address these issues, this paper proposes a mixed norm spatially constrained inversion (SCI) algorithm that adopts the L1 norm regularization term for the vertical spatial constraint and the L2 norm regularization term for the lateral spatial constraint. The Gauss-Newton iterative method is used to solve the objective function. Fixed and adaptive strategies are proposed for the regularization factors, and a parameter is used to adjust the weights of the two constraints. The influence of different constraint weights on the results is analyzed. The inversion of noisy synthetic data verifies that the proposed SCI algorithm has a higher resolution for electrical interfaces and better noise suppression effect than the L2 norm SCI algorithm. The inversion of field data shows a good effect and practicability.