A depth-sensitive thermal correction method allowing for quantitative monitoring of changes in soil water content from ambient noise measurements

Abstract. Dynamic changes in soil water content (SWC) are a crucial controlling factor for ecosystem function, agricultural productivity, and geotechnical stability against settlement and seepage failures. Real-time and accurate monitoring is essential for understanding hydrological processes and their response to climate change. Estimates of relative velocity variations (dv/v) from ambient seismic noise measurements have emerged as a highly sensitive and non-invasive geophysical tool for long-term surveillance of near-surface property changes. However, during non-frozen periods, dv/v signals are jointly affected by changes in both subsurface temperature and SWC. Inadequate corrections of temperature effects are indeed emerging as a key limitation for the quantitative interpretation of dv/v measurements for changes in SWC. To date, most temperature correction schemes approximate the subsurface thermal state using surface temperature, thus, overlooking the depth-dependent attenuation of thermal diffusion, which, in turn, biases the estimations of soil water content changes (SWCC). We propose a frequency-depth thermal correction framework that links the depth sensitivity of dv/v at different frequencies with the subsurface temperature profile. By establishing a quantitative relationship between frequency and depth, the temperature profile is transformed into frequency-dependent equivalent temperatures. This allows to correct dv/v estimates in each frequency band using the corresponding equivalent temperature rather than the surface temperature, thereby capturing the true depth-dependent thermal state governed by heat diffusion. Using temperature-corrected dv/v estimates and rock physics models combining Hertz–Mindlin contact theory and Gassmann’s fluid substitution, we retrieve dynamic changes in surficial SWC. Tests on both synthetic and field data ground-trothed by time-domain reflectivity (TDR) measurements demonstrate that the proposed FDTC method effectively suppresses temperature-induced artifacts in relating dv/v estimates to changes in SWC. The proposed method thus provides a robust temperature correction for ambient-noise-based SWC monitoring during non-frozen periods.

Acknowledgements. This project was funded by the National Key Laboratory of Jilin Province (Discipline Category) Major Project (Research and Development of Geophysical Imaging and Equipment for Freeze-Thaw Hydrological Processes in Black Soil in High-Latitude Regions, No. SKL202502020JC).