Enforcing Reciprocity in Operator Learning for Seismic Wave Propagation

TL;DR

This paper introduces RENO, a transformer-based neural operator that enforces reciprocity in seismic wave modeling, improving physical consistency and inference speed for multi-source scenarios.

Contribution

The paper presents a novel neural operator architecture that hard-codes reciprocity, ensuring physical consistency and enabling faster inference in seismic wave simulations.

Findings

RENO guarantees invariance under source-receiver swapping.

RENO achieves an order-of-magnitude speedup over traditional neural operators.

RENO is applicable to various wavefield types, including particle velocity and pressure fields.

Abstract

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. This yields an order-of-magnitude inference speedup at a similar memory footprint over a conventional neural operator on a realistic multi-source 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.