Inversion of 3D electromagnetic data in frequency and time domain using an inexact all-at-once approach
Bibliographic record
Abstract
Abstract We present a general formulation for inverting frequency- or time-domain electromagnetic data using an all-at-once approach. In this methodology, the forward modeling equations are incorporated as constraints and, thus, we need to solve a constrained optimization problem where the parameters are the electromagnetic fields, the conductivity model, and a set of Lagrange multipliers. This leads to a much larger problem than the traditional unconstrained formulation where only the conductivities are sought. Nevertheless, experience shows that the constrained problem can be solved faster than the unconstrained one. The primary reasons are that the forward problem does not have to be solved exactly until the very end of the optimization process, and that permitting the fields to be away from their constrained values in the initial stages introduces flexibility so that a stationary point of the objective function is found more quickly. In this paper, we outline the all-at-once approach and apply it to electromagnetic problems in both frequency and time domains. This is facilitated by a unified representation for forward modeling for these two types of data. The optimization problem is solved by finding a stationary point of the Lagrangian. Numerically, this leads to a nonlinear system that is solved iteratively using a Gauss-Newton strategy. At each iteration, a large, indefinite matrix is inverted, and we discuss how this can be accomplished. As a test, we invert frequency-domain synthetic data from a grounded electrode system that emulates a field CSAMT survey. For the time domain, we invert borehole data obtained from a current loop on the surface.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".