Unveiling the Mechanism of Continuous Representation Full-Waveform Inversion: A Wave Based Neural Tangent Kernel Framework

2026-03-22

AI Summary

This work addresses the well-known sensitivity of conventional full-waveform inversion (FWI) to initial models and the slow high-frequency convergence of existing implicit neural representation (INR)-based approaches, whose underlying mechanisms remain unclear. The study presents the first wave equation–driven neural tangent kernel (NTK) theory tailored for FWI, revealing its non-stationary nature and eigenvalue decay properties, thereby elucidating why INR-FWI reduces dependence on initial models yet converges slowly at high frequencies. Building on these insights, the authors propose IG-FWI, a hybrid method integrating INR with multi-resolution grids to controllably modulate spectral decay, achieving a balance between robustness and high-frequency reconstruction efficiency. Numerical experiments on benchmark models such as Marmousi and SEG/EAGE Salt demonstrate that IG-FWI significantly outperforms both traditional and current INR-based FWI methods in accuracy and stability.

Technology Category

• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Knowledge Representation and Reasoning: Knowledge Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Full-waveform inversion (FWI) estimates physical parameters in the wave equation from limited measurements and has been widely applied in geophysical exploration, medical imaging, and non-destructive testing. Conventional FWI methods are limited by their notorious sensitivity to the accuracy of the initial models. Recent progress in continuous representation FWI (CR-FWI) demonstrates that representing parameter models with a coordinate-based neural network, such as implicit neural representation (INR), can mitigate the dependence on initial models. However, its underlying mechanism remains unclear, and INR-based FWI shows slower high-frequency convergence. In this work, we investigate the general CR-FWI framework and develop a unified theoretical understanding by extending the neural tangent kernel (NTK) for FWI to establish a wave-based NTK framework. Unlike standard NTK, our analysis reveals that wave-based NTK is not constant, both at initialization and during training, due to the inherent nonlinearity of FWI. We further show that the eigenvalue decay behavior of the wave-based NTK can explain why CR-FWI alleviates the dependency on initial models and shows slower high-frequency convergence. Building on these insights, we propose several CR-FWI methods with tailored eigenvalue decay properties for FWI, including a novel hybrid representation combining INR and multi-resolution grid (termed IG-FWI) that achieves a more balanced trade-off between robustness and high-frequency convergence rate. Applications in geophysical exploration on Marmousi, 2D SEG/EAGE Salt and Overthrust, 2004 BP model, and the more realistic 2014 Chevron models show the superior performance of our proposed methods compared to conventional FWI and existing INR-based FWI methods.

Problem

• Full-waveform inversion
• Continuous representation
• Initial model dependence
• High-frequency convergence
• Implicit neural representation

Innovation

• Wave-based Neural Tangent Kernel
• Continuous Representation FWI
• Implicit Neural Representation
• Eigenvalue Decay
• Hybrid Representation