GNGTS 2024 - Atti del 42° Convegno Nazionale

Session 3.3 GNGTS 2024 probability distributons through Gaussian Mixture Models (GMMs). Taking TEM inversion as an example, suppose we have N training datasets R ={( d i , m i ): i = 1, …, N }, where d and m represent the input space of TEM data and the output space of resistvity model parameters, respectvely. Given an input d i , if the trained resistvity model set m i satsfes a prior probability density functon distributon, the structure of a conventonal neural network will output the corresponding m i by minimizing the sum of squared errors on the set R . This output result will approximate the mean soluton of the Bayesian posterior distributon p ( m | d ) (Earp et al., 2020). In contrast, MDN can directly output an estmate of the Bayesian posterior distributon p ( m | d ). III cPNN network inversion results The cPNN inversion has been tested on a FloaTEM survey carried out on the south shore of the Iseo lake to study the lake-groundwater interacton ( Fig. 2 ) , we carry out a waterborne tTEM (or FloatTEM) survey with a total survey line length of approximately 200 kilometers and a total of nearly 35,000 survey points (Galli et al., 2024). When carrying out measurements with the FloatTEM system, we installed a sonar sounding device on the boat to measure the bathymetry. We compared the inversion results of the deep learning cPNN network with those based on the EEMverter (Fiandaca et al., 2024) modelling platorm. The number of inversion layers and layer thickness are consistent with the deep learning training parameters. As shown in Fig. 3 , both the DNN inversion results and the MDN inversion results output by the cPNN network similarly depict the hydrological characteristcs under the Iseo lake, and its imaging results of the underground clay layer and underground aquifer are in good consistency with the inversion results of EEMverter. The gray grid in the fgure is the bathymetry informaton of the lake water. It can be clearly seen that the imaging results of the cPNN network correspond well to the bathymetry informaton of the Sonar. The cPNN network takes about 35 seconds to invert Iseo data, while the EEMverter inversion based on the server platorm takes approximately 6500 seconds. IV Conclusions In this study, we proposed a cPNN network structure that integrates DNN imaging-Net and MDN Bayesian-Net, which can directly convert the observed tTEM data into a resistvity model and estmate its uncertainty. The MDN Bayesian-Net captures the posterior PDF of the geological model, providing both maximum probability model and DOI as references, while the DNN imaging- Net provides an estmaton of the posterior PDF mean soluton. The two imaging results of cPNN complement each other and provide fast and comprehensive geological resistvity informaton.

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