Joint inversion of gravity and magnetic data using indicator functions
Bibliographic record
Abstract
Gravity and magnetic joint inversion using petrophysical information can recover more accurate geophysical models, but the petrophysical constraints often require complex objective functions. We introduce a simple and efficient mathematical device called indicator functions to couple multiple physical properties determined from petrophysical information. The indicator function is flexible enough to represent arbitrary ranges and relationships of multiple physical property parameters by a set or a union of several subsets. Our objective function combines the indicator function with the L1-norm regularization for more accurate and stable results. Such objective function involving non- differentiable terms is then conveniently solved by an extended version of the alternating direction method of multipliers (ADMM). ADMM treats each term in the objective function as an independent subproblem that can be solved easily and quickly in parallel, and has the advantage of solving some non-differentiable terms. To demonstrate the performance of the indicator function and ADMM, we apply our method to the gravity and magnetic data synthesized from the realistic model of DO-27 kimberlite pipe at Tli Kwi Cho in northern Canada. The results show that our new inversion method has improved accuracy and efficiency while being simple.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".