Causal and uncertainty-aware digital-twin framework for ultra–low-noise geoscientific inertial sensors

Abstract. Ultra–low-noise inertial sensors are a cornerstone of modern geoscientific instrumentation, enabling high-resolution observations across seismology, geodesy, gravimetry, and vibration isolation. Achieving and reliably predicting their performance requires a rigorous treatment of physical causality, noise propagation, and uncertainty, particularly in force-feedback architectures operating near fundamental limits. In this study, we introduce a causal and uncertainty-aware digital-twin framework for the design and metrological assessment of ultra–low-noise geoscientific inertial sensors. The proposed framework integrates mechanical dynamics, force-feedback control, transduction, and digital acquisition within a physically realisable model that explicitly enforces causality and stability constraints. Starting from a minimal equation-of-motion description, the digital twin is formulated in the frequency domain to construct causal transfer functions and a comprehensive noise-budget model. The framework enables the systematic separation of fundamental thermal noise limits from implementation-dependent noise sources, including readout, actuation, and digital acquisition effects. We introduce quantitative performance metrics based on self-noise spectra, dominant noise regimes, crossover frequencies, and near-plateau bandwidths, allowing complex spectral behaviour to be condensed into actionable design indicators. Parameter uncertainties are propagated through the digital twin to provide uncertainty-aware performance estimates and robustness diagnostics. Through a series of illustrative analyses, we demonstrate how the proposed digital twin supports informed design trade-offs, identifies performance bottlenecks, and prevents non-physical or overly optimistic sensitivity estimates arising from non-causal modelling assumptions. While focused on inertial sensors, the methodology is general and transferable to other classes of geoscientific instruments. The framework provides a transparent and extensible foundation for next-generation sensor design, virtual experimentation, and metrologically consistent performance prediction.