MSc Internship: Data-driven inverse problem of gravimetric data with neural learning in geophysical exploration

Context

Within a collaboration between Inria Team Makutu and Orano, we propose a 6-month MSc internship on inverse problems in Earth imaging, with a focus on approaches based on neural models.
Gravity surveys provide a means of characterizing the subsurface by detecting variations in the Earth’s gravitational field arising from contrasts in rock density. Subsurface density contrasts can be associated with hydrothermal alteration, and are employed as indicators of geological environment hosting a mineral of interest. In this internship, we consider the inverse problem of imaging 3D density profiles of the Earth subsurface from ground gravimetric data measuring gravitational acceleration.
The internship will focus on machine-learning-based approaches to gravity inversion. In particular, we will investigate both surrogate-based inversion methods, in which neural models are used to approximate the forward or inverse mapping, and direct neural approaches that learn an approximation of the inverse mapping from gravity observations to subsurface density models. Depending on the work progress, complementary data-sets, such as electromagnetic data, may be considered.

Assignment

In a data- and machine-learning-driven perspective, we aim to develop an in-house computational framework for neural models to image subsurface density distributions from gravity data. The choice of methodology and neural architectures (Fourier Neural Operator, deep operator, convolutional network, etc.) will be guided by discretization invariance and flexibility with respect to the observable inputs and functional outputs. Computational cost and implementation complexity must also be controlled to enable scalability to realistic acquisition surveys.

Main activities

The research activities will explore the different steps of the inverse problem and its resolution with neural models.
1. Familiarize with the mathematical modeling of gravimetric data, as well as their characteristics in realistic surveys, e.g., the equations involved, the spatial configurations of receiver networks, and processed signals used for imaging.
2. Familiarize with existing neural architectures for forward and inverse (density imaging from gravimetric data) problems.
3. Create catalogs of training data with high-fidelity solvers. First, consider density profiles representative of geological host environments, in discussion with Orano. We will create a control group comprising profiles that are typically not candidates, as well as profiles that may lead to false predictions. Second, we compute noisy observables associated with the selected profiles using the Poisson kernel, with various types of noise added.
4. Consider at least two neural architectures and compare them in terms of training cost, out-of-distribution performance, robustness to noise, and scalability.