Spectral induced polarization tomography inversion: Hybridizing homotopic continuation with Bayesian inversion
Bibliographic record
Abstract
ABSTRACT Induced polarization tomography offers the potential to better characterize the subsurface structures by considering spectral content from data acquisition over a broad frequency range. Spectral induced polarization (SIP) tomography is generally defined as a nonlinear inverse problem commonly solved through deterministic gradient-based methods. To this end, the spectral parameters, i.e., direct current resistivity, chargeability, relaxation time, and frequency exponent, are resolved by individually or simultaneously inverting all frequency data, followed by fitting a generalized Cole-Cole model to the inverted complex resistivities. Due to the high correlation between the Cole-Cole model parameters and a lack of knowledge about the initial approximation of the spectral parameters, using the classical least-squares methods may lead to inaccurate solutions and impede reliable uncertainty analysis. To cope with these limitations, we introduce a new approach based on a hybrid application of a globally convergent homotopic continuation method and a Bayesian inference to reconstruct the distribution of the subsurface spectral parameters. The homotopic optimization, owing to its fast and global convergence, is first implemented to invert multifrequency SIP data sets aimed at retrieving the complex-valued resistivity. Then, Bayesian inversion based on a Markov chain Monte Carlo (MCMC) sampling method, along with a priori information including the lower and upper bounds of the prior distributions, is used to invert the complex resistivity for the Cole-Cole model parameters. By applying the MCMC inversion algorithm, a full nonlinear uncertainty appraisal can be provided. We numerically evaluate the performance of our method using synthetic and real data examples in the presence of topographical effects. Numerical results prove that the homotopic continuation method outperforms the classic, smooth inversion algorithm in the sense of approximation accuracy and computational efficiency. In addition, we determine that our hybrid inversion strategy provides reliable representations of the main features and structure of the earth’s subsurface in terms of the spectral parameters.
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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 | 0.000 | 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".