Blind Deconvolution of Seismograms Regularized via Minimum Support
Bibliographic record
Abstract
The separation of earthquake source signature and propagation effects (the Earth?s ?Green?s function?) that encode a seismogram is a challenging problem in seismology. The task of separating these two effects is called blind deconvolution. By considering seismograms of multiple earthquakes from similar locations recorded at a given station and that therefore share the same Green?s function, we may write a linear relation in the time domain ui(t)*sj(t) ? uj(t)*si(t) = 0, where ui(t) is the seismogram for the ith source and sj(t) is the jth unknown source. The symbol * represents the convolution operator. From two or more seismograms, we obtain a homogeneous linear system where the unknowns are the sources. This system is subject to a scaling constraint to deliver a non-trivial solution. Since source durations are not known a priori and must be determined, we augment our system by introducing the source durations as unknowns and we solve the combined system (sources and source durations) using separation of variables. Our solution is derived using direct linear inversion to recover the sources and Newton?s method to recover source durations. This method is tested using two sets of synthetic seismograms created by convolution of (i) random Gaussian source-time functions and (ii) band-limited sources with a simplified Green?s function and signal to noise levels up to 10% with encouraging results.
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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 | 0.004 |
| 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 | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".