Enforcing Reciprocity in Operator Learning for Seismic Wave Propagation
This addresses the need for efficient and physically accurate wavefield modeling in seismic studies, though it is incremental as it builds on existing neural operator methods by adding a specific physical constraint.
The paper tackled the problem of incorporating strict physical consistency, specifically the reciprocity principle, into data-driven methods for seismic wave propagation modeling, resulting in an order-of-magnitude inference speedup at a similar memory footprint compared to an unenforced neural operator.
Accurate and efficient wavefield modeling underpins seismic structure and source studies. Traditional methods comply with physical laws but are computationally intensive. Data-driven methods, while opening new avenues for advancement, have yet to incorporate strict physical consistency. The principle of reciprocity is one of the most fundamental physical laws in wave propagation. We introduce the Reciprocity-Enforced Neural Operator (RENO), a transformer-based architecture for modeling seismic wave propagation that hard-codes the reciprocity principle. The model leverages the cross-attention mechanism and commutative operations to guarantee invariance under swapping source and receiver positions. Beyond improved physical consistency, the proposed architecture supports simultaneous realizations for multiple sources without crosstalk issues. This yields an order-of-magnitude inference speedup at a similar memory footprint over an reciprocity-unenforced neural operator on a realistic configuration. We demonstrate the functionality using the reciprocity relation for particle velocity fields under single forces. This architecture is also applicable to pressure fields under dilatational sources and travel-time fields governed by the eikonal equation, paving the way for encoding more complex reciprocity relations.