Forward-Modeling-Driven Quantification of Karst ERT Responses and Borehole-Constrained AI-Assisted Interpretation

Technical Summary: Forward-Modeling-Driven Quantification of Karst ERT Responses and Borehole-Constrained AI-Assisted Interpretation

Problem Statement
Electrical Resistivity Tomography (ERT) is the primary method for detecting concealed karst cavities and fractured zones, yet its interpretation faces significant challenges. The mapping from apparent resistivity to subsurface structure is an ill-posed inverse problem characterized by volume-weighted averaging, sampling geometry effects, and non-uniqueness. These factors cause systematic distortions in observed responses, leading to blurred boundaries and equivalence ambiguity. While recent studies have introduced end-to-end deep learning to interpret ERT data, three critical gaps remain: (1) a lack of auditing for parameter-distribution bias in synthetic training datasets, which may cause models to learn dataset shortcuts rather than physical patterns; (2) insufficient quantification of how the quality of borehole constraints (specifically, whether they intersect the target) affects interpretation gains; and (3) a lack of interpretable intermediate layers that characterize forward-response distortion patterns, making it difficult to link AI conclusions to underlying physical mechanisms.

Methodology
The study proposes a forward-modeling-driven framework that explicitly separates physical response analysis from AI-assisted prediction. The workflow consists of the following components:

1. Controllable Model Library: A ground-truth-complete library of 5,000 synthetic models was constructed, covering eight representative karst geoelectrical scenarios (e.g., simple layering, single/multiple water-filled or dry cavities, shallow interference/shielding, undulating topography). The background consists of three layers (topsoil, weathered layer, bedrock), with karst cavities defined as low-resistivity (water-filled) or high-resistivity (dry) anomalies.
2. Forward Modeling: Apparent-resistivity responses and pseudosections were generated using the open-source finite-element library pyGIMLi with a Wenner-α array (60 electrodes, 1 m spacing). To ensure numerical robustness, 12 representative models were independently evaluated using RES2DMOD.
3. Dataset-Bias Audit: The study implemented a three-part audit to detect systematic bias: anchor-strategy comparison (comparing random vs. midpoint drilling), spatial clustering analysis of false positives, and cross-version stability testing of distortion patterns.
4. Distortion Quantification: Forward responses were compared against ground-truth models to quantify seven specific distortion patterns: depth compression, lateral displacement, morphological distortion, shallow shielding, multi-anomaly merging, polarity differences, and array sensitivity.
5. Borehole Simulation: Boreholes were simulated using six placement strategies (random, naive evenly spaced, anomaly-center, anomaly-edge, maximum-gradient, and ground-truth upper bound). Crucially, all borehole observations were extracted exclusively from the ground-truth models, not from the pseudosections, to ensure physical consistency.
6. Deep Learning Interpretation: A lightweight U-Net (approx. 1.9 million parameters) was trained to predict resistivity images and anomaly masks from pseudosections, with optional borehole channels as input. The network was evaluated on a test set of 512 samples.

Key Contributions

• Framework Development: Established a forward-modeling-driven workflow that places interpretable response analysis before AI prediction, linking conclusions to deterministic modeling evidence.
• Distortion Quantification: Systematically quantified seven forward-response distortion patterns and validated their numerical robustness through cross-software comparison (pyGIMLi vs. RES2DMOD).
• Bias Auditing: Demonstrated that parameter-distribution design is as critical as sample size, introducing reusable audit methods to prevent models from learning dataset shortcuts.
• Borehole Constraint Analysis: Explicitly evaluated the relationship between borehole "hit quality" (intersection with the target) and the magnitude/direction of improvement in AI-assisted interpretation.

Results

• Numerical Robustness: RES2DMOD and pyGIMLi showed close agreement with a relative RMS error of 2.03% across 12 models, confirming the reliability of the reported distortion patterns.
• Distortion Patterns:
  • Depth Compression: Response peaks are systematically shallower than true burial depths (compression ratio decreases from ~0.54 in shallow regions to ~0.24 in deeper regions).
  • Lateral Displacement: The median horizontal offset of response peaks is ~3.1 m (approx. three electrode spacings), increasing near survey line ends.
  • Morphological Distortion: The response half-amplitude width is significantly narrower than the true anomaly width (median ratio ~0.33).
  • Shallow Shielding: High-resistivity shallow bodies can almost completely attenuate deep-target responses (shielding index ~1.0), while low-resistivity bodies may cause false confirmations.
  • Multi-Anomaly Merging: Multiple cavities often merge into fewer peaks in pseudosections (e.g., 61% of 3-cavity samples showed fewer peaks).
• Borehole Hit Rates: In the debiased library, engineering-feasible strategies achieved first-borehole hit rates of only 21–24%, far below the 97–99% achieved by the ground-truth upper bound (oracle). Response-driven placement improved hit rates by only ~5 percentage points over random drilling.
• AI Interpretation Performance:
  • No-Borehole Baseline: The network achieved an anomaly-region Intersection over Union (IoU) of 0.114 and a false-positive rate (FPR) of 0.84.
  • Oracle Constraints: When boreholes were guaranteed to intersect the target (99% hit rate), IoU increased to 0.506, and FPR dropped to 0.
  • Engineering Constraints: Gains from feasible strategies were limited and variable. For instance, two boreholes placed at anomaly edges reduced FPR but caused the largest loss in recall. The study found that improvements in AI interpretation were strongly associated with the probability of boreholes intersecting the target, rather than the mere presence of borehole data.
• Observable Gating: A zero-training audit revealed that field-observable features (e.g., peak signal-to-noise ratio) could not reliably screen for samples where boreholes would hit the target; in some cases, stronger responses correlated negatively with hit rates due to shielding or merging effects.

Significance and Claims
The paper claims that forward-response distortion must be quantified before AI-assisted ERT interpretations are assessed. It argues that the value of large-scale forward-modeling datasets depends not just on sample size but on the design of parameter distributions to avoid bias. The study highlights that the benefit of borehole constraints in AI interpretation is not linear; it depends critically on the likelihood of the boreholes intersecting the target. Consequently, the authors suggest that improving constraint quality through denser ground-truth exposures is a more defensible engineering route than relying on response-based screening.

The authors maintain a modest scope, stating that the deep-learning component is a "proof of concept" limited to synthetic Wenner-α data and should not be interpreted as a general-purpose field inversion system. They acknowledge limitations, including the narrow range of hit rates sampled by engineering strategies and the lack of comparison with conventional smoothness-constrained inversions or field case studies. The primary contribution is methodological: providing a framework to audit dataset bias and quantify physical distortions to better understand the limitations and potential of AI in geophysical interpretation.