Estimating Transmissivity in One‐Dimensional Heterogeneous Aquifers With Groundwater Head Data: From Time or Frequency Perspectives
Bibliographic record
Abstract
Abstract Time series of groundwater head in a semi‐infinite, one‐dimensional confined aquifer due to variable boundary forcing can be decomposed into two signals: head rise from a sudden boundary increase, and head fluctuation from boundary sinusoidal changes. Analyzed from time and frequency domains, these signals reconstruct the original series via convolution or superposition, offering insights into transmissivity ( T ). In this study, the time‐domain head data and frequency‐domain fluctuation data are used to estimate T . For a two‐zone aquifer with a pair of T values, the information content on T from the head at a given time is similar to that of the amplitude of the fluctuation at a certain frequency. In addition, the phase shift of the fluctuation also contains non‐redundant information on T . We introduce two concepts, that is, equivalent and interpreted T , to describe representative T , with which homogeneous aquifer can produce the same head/amplitude/phase shift signal and its temporal/frequency derivative as those observed in a heterogeneous aquifer. By applying Fréchet kernels as a spatial weight, we provide a connection between equivalent/interpreted T and the heterogeneous spatial distribution of T . Based on Monte Carlo simulations, we compare the equivalent/interpreted T against the local‐scale geometric mean T . The equivalent T from high‐frequency phase shift produces the better estimation. Finally, we investigate the effectiveness of observations at different frequencies and times for estimating heterogeneous T during a hydraulic tomography survey. The results show the amplitude and phase shift of multi‐frequency fluctuations can better characterize aquifer heterogeneity than head from the time‐domain perspective alone.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".