Sensitivity analysis using physics-based machine learning: an example from surrogate modelling for magnetotellurics

Geophysical simulations for complex subsurface structures and material distributions require the evaluation of partial differential equations by means of numerical methods. However, the mentioned high complexity often yields computationally very costly simulations, especially for electromagnetic (EM) and seismic methods. When used in the context of parameter estimation or inversion studies, this aspect severely limits the number of simulations that are affordable. However, especially for structured model analysis methods, such as global sensitivity analyses or inversions, often thousands to millions of forward simulation runs are required. To address this challenge, we propose utilizing a physics-based machine learning method, namely the non-intrusive reduced basis method, aiming at constructing low-dimensional surrogate models to significantly reduce the computational cost associated with the numerical forward model while preserving the physical principles.We demonstrate the effectiveness and benefits of the surrogate models using broad-band Magnetotelluric (MT) responses of a 2-D model that mimics a conceptual volcano-hosted geothermal system. Next to being a first such application, we also show how ML reduced basis method can be adapted to consistently treat complex-valued variables—an aspect that has been overlooked in previous studies. Additionally, reducing computation time by several orders of magnitude through the surrogate enables us to perform a global sensitivity analysis for MT applications. Despite additional insights, such an analysis has been normally deemed infeasible given the high computational burden. The methods developed here are presented in a generalized form, making this approach feasible for other electromagnetic techniques with a low-dimensional parameter space.