Traçamento de raios sísmicos com múltiplas condições iniciais usando Redes de Kolmogorov-Arnold com Informações Físicas

Abstract

Seismic wave propagation modeling is fundamental for seismic imaging and reservoir characterization in the oil and gas industry. While ray tracing is an efficient technique, traditional methods face challenges in complex geological models due to instability and high computational cost, as they require solving for a single initial condition at a time. This work proposes the use of Physics-Informed Kolmogorov-Arnold Networks (PIKANs) to overcome these limitations by allowing the simultaneous tracing of multiple rays with different initial conditions. The proposed methodology includes velocity model smoothing with B-spline filters, the use of a compound loss function, and the application of adaptive weights in the physics-informed loss function to enhance model training. Two experiments were conducted using synthetic data: the first with a parameterized velocity model, and the second with a non-parameterized model widely used as a benchmark in seismic processing, known as the Marmousi model. The results demonstrate the consistency of the approach, with R2 values close to 1 for the first experiment and exceeding 0.90 for the second. Qualitatively, the method accurately traces seismic rays, even in regions not used for training and in areas with rapid spatial velocity variation, proving to be more precise at predicting the ray’s spatial coordinates than the slowness vector.