  In the process of tunnel excavation, advance geological prediction technology
has become indispensable for safe, economical, and efficient tunnel
construction. Although traditional methods such as drilling and geological
analysis are effective, they typically involve destructive processes, carry
high risks, and incur significant costs. In contrast, non-destructive
geophysical exploration offers a more convenient and economical alternative.
However, the accuracy and precision of these non-destructive methods can be
severely compromised by complex geological structures and environmental noise.
To address these challenges effectively, a novel approach using frequency
domain full waveform inversion, based on a penalty method and Sobolev space
regularization, has been proposed to enhance the performance of non-destructive
predictions. The proposed method constructs a soft-constrained optimization
problem by restructuring the misfit function into a combination of data misfit
and wave equation drive terms to enhance convexity. Additionally, it
semi-extends the search space to both the wavefield and the model parameters to
mitigate the strong nonlinearity of the optimization, facilitating
high-resolution inversion. Furthermore, a Sobolev space regularization
algorithm is introduced to flexibly adjust the regularization path, addressing
issues related to noise and artefacts to enhance the robustness of the
algorithm. We evaluated the modified full waveform inversion with several
tunnel fault models by comparing the results of the enhanced method with those
of traditional least squares-based Tikhonov regularization and total variation
regularization full waveform inversion methods. The verification results
confirm the superior capabilities of the proposed method as expected.
