Boundary-Enhanced Continuous Representation Full Waveform Inversion with Sobel-Integrated Convolutional Neural Network

High-resolution characterization of subsurface geophysical parameters is fundamental for hydrocarbon exploration, mineral prospecting, and geological structure analysis. Full waveform inversion (FWI) can potentially estimate high-precision parameter models by solving a wave equation constrained optimization problem when initialized with an accurate starting model. While implicit full waveform inversion (IFWI) employs multilayer perceptrons (MLPs) to reparameterize velocity models and reduces dependence on initial model accuracy, the inherent low-frequency bias and limited high-frequency representation capacity of MLPs result in blurred boundaries and poor robustness to noisy data. To further improve the performance, we propose a Boundary-Enhanced IFWI method (BEIFWI) that integrates implicit neural representations (INRs) with a Sobel-integrated convolutional neural network (CNN). Specifically, the Sobel layer is introduced to enhance boundary features in the inversion results, effectively mitigating the boundary blurring inherent in standard IFWI. Furthermore, a residual connection mechanism is employed to preserve shallow-layer details while optimizing deep-layer representations, thereby stabilizing the representation process and minimizing the least-squares seismic-data misfit during network training. Experimental results on the two-dimensional Marmousi and SEG/EAGE Salt models, as well as the Chevron 2014 blind test, show that BEIFWI obtains inversion results with sharper boundaries. Even under challenging scenarios, for severely noisy seismic data and low-frequency deficient records, BEIFWI can stably estimate velocity models, thereby highlighting its superior noise resistance and inversion accuracy improvement.