AccScience Publishing / JSE / Online First / DOI: 10.36922/JSE025330059
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ARTICLE

Application of the spatial autocorrelation method incorporating damping optimization for identifying goafs in cultural heritage sites

Jiale Liu1 ,  Xiaodong Wang1* ,  Yanhai Liu2 ,  Ke Ren3 ,  Shangqing Zhang4
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1 Department of Geophysics and Information, College of Geoscience and Surveying Engineering University of Mining and Technology-Beijing, Beijing, China
2 China Energy Shendong Coal Group Co., Ltd., Ordos, Nei Mongol Autonomous Region, China
3 School of Remote Sensing Science and Technology, Aerospace Information Technology University, Jinan, Shandong, China
4 Shanxi Key Laboratory of Metallogeny and Assessment of Strategic Mineral Resources, Taiyuan, Shanxi, China
JSE, 025330059 https://doi.org/10.36922/JSE025330059
Submitted: 16 August 2025 | Revised: 16 October 2025 | Accepted: 21 October 2025 | Published: 10 November 2025
© 2025 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License ( https://creativecommons.org/licenses/by/4.0/ )
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Abstract

As a World Cultural Heritage Site, the Yungang Grottoes face the risk of geological disasters caused by underground goafs. To accurately detect the surrounding void zones of the grottoes and analyze their distribution and structural characteristics, this study uniquely applied the passive-source surface wave spatial autocorrelation (SPAC) method. Four high-density linear arrays were deployed in the Yungang Grottoes area to collect microtremor signals. By extracting the Rayleigh wave dispersion curve and combining it with a non-linear least-squares inversion technique incorporating a damping regularization term, a shallow shear wave velocity profile was established, successfully identifying potential low-velocity anomalies. During the inversion process, the optimized damping factor effectively suppressed the oscillation effects under complex geological conditions, significantly improving the stability and accuracy of the imaging. The results showed that 15 typical low-velocity anomalies with wave velocities below 1,200 m/s were identified, and these anomalies were highly consistent with the locations of goaf areas in historical mining data. The imaging results revealed that the goaf exhibits multiple layers and a multi-center distribution, with the L1 and L4 survey lines being the main areas of goaf activity. With a horizontal resolution of 10–20 m and a maximum detection depth of 320 m, the method presented differences in the integrity and fragmentation of underground rock masses. The SPAC method demonstrated advantages such as high resolution, non-destructive testing capability, and imaging stability in the detection of abandoned mine areas within cultural heritage sites. By optimizing the inversion regularization parameters, this study significantly improves imaging accuracy in complex geological environments, providing effective technical support for the stability assessment of the Yungang Grottoes and for the prevention and control of geological disaster risks at cultural heritage sites.

Keywords
Spatial autocorrelation method
Damping factor
Yungang Grottoes
Goaf
Funding
This research was funded by the National Key Research and Development Project (grant number 2022YFC2903402).
Conflict of interest
The authors declare that they have no competing interests.
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