Compressive sensing approach for two-dimensional magnetotelluric inversion using wavelet dictionaries

We present a 2D inversion scheme for magnetotelluric data, where the conductivity structure is parameterised with different wavelet functions that are collected in a wavelet-based dictionary. The inversion model estimate is regularised in terms of wavelet coefficient sparsity following the compressive sensing approach. However, when the model is expressed on the basis of a single wavelet family only, the geometrical appearance of model features reflects the shape of the wavelet functions. Combining two or more wavelet families in a dictionary provides greater flexibility to represent the model structure, permitting, for example, the simultaneous occurrence of smooth and sharp anomalies within the same model. We show that the application of the sparsity regularisation scheme with wavelet dictionaries provides the user with a number of different model classes that may explain the data to the same extent. For a real data example from the Dead Sea Transform, we show that the use of such a scheme can be beneficial to evaluate the geometries of conductivity anomalies and to understand the effect of regularisation on the model estimate.