Forward Modelling of Electrical Resistivity and Induced Polarization Using the Spectral‐Infinite‐Element Method
Bibliographic record
Abstract
ABSTRACT Accurate and efficient modelling of subsurface electrical properties is critical for a wide range of applications, including mineral exploration, environmental studies and hydrogeological investigations. Traditional numerical approaches often use low‐order discretization and impose artificial boundary conditions to approximate the unbounded spatial domain. These approximations can lead to inaccuracies and computational inefficiency, particularly in geologically complex environments. In this study, we present a spectral‐infinite‐element method (SIEM) for forward modelling of electrical resistivity and induced polarization. The approach couples high‐order spectral elements within the finite domain with a single outer layer of mapped infinite elements, enabling precise representation of far‐field boundary conditions. To achieve optimal numerical performance, we employ two distinct quadrature schemes: Gauss–Legendre–Lobatto quadrature for the spectral elements and Gauss–Radau quadrature for the infinite elements. We first verify the accuracy of our method by comparing the computed electric potential from a buried charged block with direct numerical integration. We conducted a convergence study by refining the mesh and increasing the order of the interpolation polynomials. To further evaluate the robustness of SIEM, we benchmark its results for a layered earth model against an analytical solution and an open‐source Python‐based geophysical modelling library, SimPEG. The comparisons demonstrate the accuracy, convergence and efficiency of SIEM. Finally, we apply SIEM to a complex heterogeneous conductivity model incorporating topography, generating apparent resistivity and chargeability pseudo‐sections to illustrate its practical applicability under realistic survey conditions.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 teacher head, 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".