Uncertainty quantification of multimodal surface wave inversion using artificial neural networks

摘要

An inversion of surface wave dispersion curves (DCs) is a non -unique and ill-conditioned problem. The inversion result has a probabilistic nature, which becomes apparent when simultane-ously restoring the 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 because they demand multiple solutions to the inverse problem. We have developed an alternative method based on a multilayer fully connected artificial neural network (ANN). We improve the current unimodal approach, which is known from publications, to multimodal inversion. We use Cox's and Teague's algorithm to determine optimal parameterization (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 weights map the phase velocity DCs to values of the S-wave velocity and layers thickness. To estimate the uncertainties, we adapt the Monte Carlo simulation strategy, according to which the frequency dependent data noise and the inverse operator errors are projected onto the resulting velocity model. The inverse operator errors are evaluated by the prediction of the training data set. The proposed combination of surface wave data processing methods, configured with each other, provides a novel surface wave multi -modal dispersion data inversion and uncertainty quantification ap-proach. We first test our approach on synthetic experiments for various velocity models: a positive gradient velocity, a low -veloc-ity layer, and a high-velocity layer. This is done considering un-imodal inversion at first and then compared with the multimodal inversion. Afterward, we apply our approach to field data and compare the resulting models with the body S-wave processing by the generalized reciprocal method. The experiments indicate high-potential results - using ANN yields the possibility to ac-curately estimate the PPD of restored model parameters without a significant computational effort. The PPD-based comparison dem-onstrates the advantages of a multimodal inversion over a unim-odal inversion. The trained ANN provides reasonable model parameters predictions and related uncertainties in real time.