Rational function neural networks for learning rock physics models from field data

Abstract Seismic wave velocity estimation is critical for understanding Earth's internal structure. Traditional rock physics models require careful physical assumptions and mathematical derivations, often facing challenges when applied to complex field data. Empirical formulas, while simple, lack a solid physical foundation. To address these limitations, we propose a data-driven approach using rational function neural networks (RafNN) for rock physics modelling. By analysing logging data, RafNN establishes a rational equation capturing the interdependencies among rock modulus, matrix stiffness, porosity, and fluid. The results show that RafNN accurately extracts the Gassmann's equation when the training data adheres to its constraints. Moreover, RafNN can derive general models from logging data that deviate from the Gassmann's equation. These data-driven models exhibit lower prediction errors while maintaining consistency with Gassmann's model. RafNN's adaptability to field data variability is a key advantage, facilitating better comprehension of the underlying mathematical and physical principles. Additionally, we explore the relationship between modulus, porosity, and compressibility, shedding light on the physical interpretation of RafNN models. Notably, RafNN derives analytical models directly from field data, reducing reliance on mathematical derivations and physical assumptions. Although further research is needed to understand the convergence theory of RafNN, this study presents a promising approach for data-driven rock physics modelling. It contributes to the exploration of Earth's heterogeneous structure and advances the field of seismic wave velocity estimation.