Uncertainty quantification of multi-modal surface wave inversion using artificial neural networks

An inversion of surface waves dispersion curves is a non-unique and ill-conditioned problem. The inversion result has a probabilistic nature, which becomes apparent when simultaneously restoring the shear wave (S-wave) velocity and layer thickness. Therefore, the problem of uncertainty quantification is relevant. Existing methods through deterministic or global optimization approaches of uncertainty quantification via posterior probability density (PPD) of the model parameters are not computationally efficient since they demand multiple solutions of the inverse problem. We present an alternative method based on a multi-layer fully connected artificial neural network (ANN). We improve the current uni-modal approach, which is known from publications, to multi-modal inversion. We use the Cox's and Teague's algorithm to determine optimal parametrization (number of layers) and the ranges of possible model parameters. We uniformly draw training data sets within estimated ranges and train the ANN. Saved ANN's weights map the phase velocity dispersion curves to values of the S-wave velocity and layers thickness. To estimate the uncertainties, we adapt the Monte-Carlo simulation strategy and project onto the resulting velocity model both frequency-dependent data noise and inverse operator errors, which are evaluated by the prediction of the training data set. The proposed combination of surface waves data processing methods, configured with each other, provides a novel surface waves multi-modal dispersion data inversion and uncertainty quantification approach. We first test our approach on synthetic experiments for various velocity models: a positive velocity gradient, a low-velocity layer and a high-velocity layer. This is done considering uni-modal inversion at first and then compared to the multi-modal inversion. Afterwards, we apply our approach to field data and compare resulting models with the body S-wave processing by the generalized reciprocal method (GRM). The experiments show high-potential results - using ANN yields the possibility to accurately estimate PPD of restored model parameters without a significant computational effort. The PPD-based comparison demonstrates advantages of a multi-modal inversion over uni-modal inversion. The trained ANN provides reasonable model parameters predictions and related uncertainties in real-time.