Bianco, Luigi (2024) Facing ambiguity in potential fields modelling with inverse-theory and AI algorithms. [Tesi di dottorato]

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Abstract

In this work, starting from the concept of absolute and relative ambiguities, I studied the behaviour of ambiguities in potential fields and possibilities of reducing it via multiscale methods of imaging, inversion and Machine Learning. Through a careful multiscale analysis of the fields generated by the two sources, I defined the existence of a region of ambiguity and a region in which the sources could be distinguished. The multiscale inhomogeneous properties of the fields due to general sources were adopted to generalize the imaging method called Depth from Extreme Points (DEXP) in the Inhomogeneous DEXP (INDEXP). Then, proposed a new approach on joint inversion of gravity data for dealing with the ambiguity due to the field of vertically-stacked sources. It is based on the sequential joint inversion with cross-gradient constraint applied to gravity field and its second-order vertical derivative so resulting in a Multi-Order Sequential Joint Inversion (MOSJI). In this way, I wanted to exploit the different wavenumber-contents of the two dataset to reliably model sources at different depths. The opportunities represented by the use of a sequential strategy lit the idea of performing a two-step joint inversions workflow for cross-gradient constrained inversion of gravity data with seismic models. The proposed method avoids the computationally-expensive seismic inversion and recover a final density model which fits the gravity measurements and presents structural features from the seismic model. The final density model which images both the main bodies and the background is also able to provide information to update and improve seismic models. Finally, I studied the ambiguity generated by the need of a synthetic training set in supervised ML methods. For this reason, I proposed to generalize the training set of ML algorithm with a set of simple sources, the so-called building blocks, and their gravity anomalies (FaultNet3D). This is possible under the assumption that complex geometries could be analysed by a CNN as the ensemble of the gravity anomalies generated by the edges. However, to preserve the validity of the assumption it requires the interpretation of 2D gravity data (e.g., extracted profiles from gravity maps). To overcome this limitation, I merged 2D interpretations into a reference model to constrain a 3D gravity inversion, so constituting a “self-constraint". All the synthetic tests and real case applications were selected to target the United Nation Sustainable Development Goals (UN SDG), including energy transition, environmental safety and hazard assessment.

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