For the characterization of heterogeneous aquifers, transient hydraulic tomography (THT) was proposed as a promising method to obtain the distribution of hydraulic parameters with satisfying spatial resolution using different approaches. These include hydraulic travel time, attenuation inversions, thermal tracer tomography, and geostatistical inversion with successive linear estimator (SLE). For the same hydrogeological test, different inversion methods tend to use different sub-data sets to obtain different hydraulic parameters. Up to now, however, few studies have focused on revealing the respective characteristics of these inversion methods and attempted to improve the accuracy of aquifer characterization by bridging the shortcomings of the inversion methods. The main objective of this study was to evaluate the utility of multiple inversion techniques on aquifer heterogeneity characterization. A series of warm water injection tests were first simulated in a fluvial aquifer analogue outcrop. The calculated head and temperature datasets from these tests were fully utilized to reveal the aquifer heterogeneity by using all of the four above-mentioned inversion methods. The results show that the thermal tracer tomography, hydraulic travel time, and attenuation tomography characterized the high permeability zones more accurately within the well area, whereas the geological statistical method tended to depict the overall distribution of $K$ values for a larger area. By comparison analysis and combinations of the individual inversion results, the scientific and economic complementarity can be studied and some valuable advice for the choice of different inversion methods can be recommended for future practices.

In the realm of groundwater science, characterization of heterogeneous aquifers is pivotal for resolving diverse groundwater resource and engineering-related problems that require the detailed spatial distribution of hydraulic parameters. As research progresses, one hydraulic tomographical method, which is based on hydraulic travel time inversion, emerges as a promising and rapid method due to its robust and efficient calculation. In the field, the acquisition of hydraulic excitation and head observation data required for inversion is less time-consuming. Data collection from a single hydraulic test (such as a pumping test) typically takes only a few minutes or even a few tens of seconds. However, the field application of this method faces challenges. Hydraulic travel time is typically generated in the early stages of hydrogeological tests (e.g., early drawdown of a pumping test), yet accurate data may not be readily available because of the noise signals from test equipment, which can contaminate travel time signals, leading to inaccurate inversion results. A potential solution lies in utilizing the smooth head observation during the recovery period after the pump is turned off, which yields more accurate travel times for inversion calculations. In this paper, the mathematical development suggests that the travel time of the recovery phase aligns with that of the pumping phase when pumping reaches a steady or quasi-steady state. Subsequently, by employing Monte-Carlo simulations, 1200 realizations of two-dimensional heterogeneous confined aquifer models were generated for simulating pumping tests with different pumping durations. The calculated head data were then utilized to compute the travel time derived from drawdown data (t) and recovery data (t′), respectively. Comparisons showed that t is equal to t′ when drawdown reaches a steady or quasi-steady state. Conversely, when the pump is turned off before reaching a quasi-steady state, t differs from t′. However, results also indicate the fact that a decent hydraulic travel time diagnosis can be obtained, especially for the cases when travel times are smaller than 15 s. Given the statistical results of Monte-Carlo simulations, as well as experience during pumping tests in the field with different scenarios, using the recovery data from 60 s of pumping duration, or extended pumping durations of 100 s or 200 s as a more conservative alternative, can replace the aquifer characterization based on drawdown data. The new inversion strategy not only has less data uncertainty and equivalent inversion accuracy, but also can greatly enhance the repeatability of field tests and reduce the environmental impact of long-term pumping tests.

Hydraulic tomography (HT) based on the successive linear estimator (SLE) offers the high-resolution characterization of aquifer heterogeneity but conventionally requires prolonged pumping to achieve steady-state conditions, limiting its applicability in contamination-sensitive or low-permeability settings. This study bridged theoretical and practical gaps (1) by identifying spatial periodicity (hole effect) as the mechanism underlying divergences in steady-state cross-correlation patterns between random finite element method (RFEM) and first-order analysis, modeled via an oscillatory covariance function, and (2) by validating a novel short-term sampling strategy for SLE-based HT using field experiments at the University of Göttingen test site. Utilizing early-time drawdown data, we reconstructed spatially congruent distributions of hydraulic conductivity, specific storage, and hydraulic diffusivity after rigorous wavelet denoising. The results demonstrate that the short-term sampling strategy achieves accuracy comparable to that of long-term sampling strategy in characterizing aquifer heterogeneity. Critically, by decoupling SLE from steady-state requirements, this approach minimizes groundwater disturbance and time costs, expanding HT’s feasibility to challenging environments.

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 t_peak) 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 t_peak 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.