Evaluation of Travel–Time Definitions for Thermal Tracer Tomography Under Varying Data Density: A Laboratory Sandbox Study

Travel–time-based thermal tracer tomography (TTT) has emerged as a promising technique for characterizing aquifer heterogeneity. However, the influence of travel–time definitions and data density on inversion performance is not well understood. In this study, we present a controlled two-dimensional sandbox experiment designed to systematically investigate three travel–time definitions (early-time t10, intermediate t50, and peak-time tpeak) under data-rich (32 travel times) and data-sparse (10 travel times) conditions. The obtained hydraulic conductivity (K) fields are benchmarked against permeameter measurements and a geostatistical inversion that assimilates dense steady-state head observations. The results demonstrate that all three travel–time definitions satisfactorily reproduce the primary layered heterogeneity when abundant travel–time data are available, with t50 and tpeak providing marginally better structural fidelity under data-rich conditions. However, only the early-time t10 definition preserves the spatial continuity of dominant geological structures under data-sparse conditions, exhibiting superior robustness. All TTT inversions systematically underestimate the K ranges and exhibit pronounced range compression, whereas the geostatistical inversion overestimates K and introduces spurious high-value extremes. Forward thermal transport simulations reveal that TTT-derived K fields yield systematically delayed thermal breakthroughs, while the geostatistical inversion yields more accurate predictions. These findings highlight the critical interplay between travel–time diagnostics and observation density. They also underscore the necessity of jointly inverting hydraulic and thermal data to overcome the limitations of single-dataset approaches for reliable aquifer characterization and transport prediction.