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SeisEvo: Evolution of Seismic Data Reconstruction Algorithms by Agents
Yingjie Xu, Siwei Yu, Jianwei Ma
TL;DR
Seismic reconstruction algorithms are difficult to design systematically because classical methods rely on manually engineered, mechanism-specific choices. SeisEvo uses constrained LLM-driven program evolution to search for legal white-box operators, and its evolved methods improve reconstruction SNR across interpolation and simultaneous interpolation-denoising tasks.
Problem
Classical reconstruction improvements rely on expert-guided, mechanism-specific design, leaving the broader coupled design space difficult to explore systematically.
Method
SeisEvo evolves editable components of a classical seed algorithm under hard physical-legality and parameter-provenance constraints, returning a standalone white-box operator.
Results
3.49 dB average SNR gain over classic POCS and more than 7 dB over classic MSSA, with gains also retained on data unused during search.
Takeaways & Limitations
The resulting operators remain explicit, inspectable algorithms that can be tested independently and require no agent, prompt, or neural network at inference time.
Takeaways & Limitations
Operator discovery is substantially more computationally expensive than running a fixed hand-designed solver, and current evidence is restricted to seismic data reconstruction.
Abstract
from arXiv · showhide
Classical seismic data reconstruction relies on manually designed structural priors and iterative operators, whose coupled design space is far larger than manual trial and error can explore systematically. Deep-learning methods encode the reconstruction rules in learned weights rather than in an explicit operator that can be inspected and modified. We propose SeisEvo (Seismic Algorithm Evolution), which does not optimize a single reconstruction result but searches for the algorithm that produces it. Starting from a classical reconstruction algorithm, an LLM-driven multi-agent search modifies only the components that the user has opened for editing, without prescribing the mechanism to be discovered. Candidates that violate the physical constraints of the task are rejected outright, and the remaining ones are scored by execution. The output is neither an agent system nor a neural network, but a standalone white-box algorithm that requires no agent or neural network at inference time. For interpolation without added noise, the search discovered a residual-gated, phase-aligned dip-consistency projection; Evo-POCS improves the SNR over classic POCS by 3.49 dB on average across missing ratios from 30% to 70%. For simultaneous interpolation and denoising, it discovered a reliability-grouped singular-value shrinkage; Evo-MSSA improves the average reconstruction SNR by more than 7 dB over classic MSSA and by more than 3 dB over a stronger rank-reduction baseline. Both operators retain their gains on data not used during the search. To the best of our knowledge, this is the first study to formulate the design of a seismic reconstruction operator as a constrained, LLM-driven program evolution task. Agentic algorithm evolution can thus complement deep learning in discovering explicit, inspectable, and deployable seismic processing algorithms.
1 Introduction
Seismic reconstruction remains constrained by manually designed operators and structural priors, while deep learning shifts rather than removes this design burden. SeisEvo addresses this gap by searching for domain-constrained, executable reconstruction algorithms instead of individual reconstructed outputs.
- Motivation: Missing traces and irregular spatial sampling degrade the reliability of seismic imaging, inversion, and interpretation.These acquisition limitations arise from surface obstacles, economic cost, and practical field conditions.
- Motivation: Classical methods explicitly encode structural priors in interpretable procedures, but reconstruction performance depends on manually chosen representations, operators, and data-consistency mechanisms.Manual improvements alter components such as transforms, shrinkage rules, threshold schedules, embeddings, rank selection, and singular-value processing.
- Motivation: Deep learning moves design effort to network architecture, loss functions, and training strategy, while both classical and learned methods retain computational structures defined in advance by humans.The passage also notes that supervised methods require re-examined generalization when acquisition conditions, noise, or geological structures differ from training data.
- SeisEvo: SeisEvo formulates reconstruction-operator design as a domain-constrained autonomous discovery task that searches for executable algorithms producing high-quality reconstructions.It starts from a classical seed, lets candidates evolve, and enforces task-specific data-fidelity requirements throughout the search.
- SeisEvo: The framework uses a multi-agent evolutionary backend while contributing seismic-specific algorithm representation, constraint design, executable search, and validation procedures.The agents iteratively propose and refine candidate programs, but the domain-specific seismic framework is presented as the paper’s contribution.
2 Method
SeisEvo searches over editable components of classical seismic reconstruction algorithms while fixing task-specific data fidelity and physical-legality constraints. An agent-generated candidate is admitted through execution-based gating and scoring, then returned as a standalone white-box algorithm that requires no agents or neural networks at inference time.
- Problem formulation: The reconstruction task estimates a complete seismic volume from incomplete, potentially noisy observations using a regularized inverse-problem formulation.The objective combines fidelity to acquired traces with a prior-encoding regularization term.
- Algorithm evolution: SeisEvo treats the reconstruction algorithm, rather than an individual reconstruction, as the search object, starting from classical POCS and MSSA seed algorithms.POCS encodes transform-domain sparsity, whereas MSSA uses truncated low-rank projection of block-Hankel embeddings.
- Algorithm evolution: The task specification defines the seed algorithm, editable components, objective, and constraints, while leaving the mechanism itself for the search to discover.The mask-based data-fidelity structure and physical-legality constraints remain fixed, while components such as thresholding, decay schedules, or low-rank projections may be edited.
- Output and validation: The highest-scoring legal candidate is frozen as a standalone white-box solver, and its generalization is validated outside the search loop.Inference requires no agent, prompt, or neural network; post-search validation uses full-volume generalization and robustness tests.
- Search procedure: SeisEvo repeats candidate generation, gating and scoring, and evidence binding with context updates for T search rounds after one-time human task instantiation.Multiple coding agents propose candidates within the editable set, while the framework records execution-derived scores and failure logs.
- Search procedure: Physical legality is a hard gate: candidates violating data consistency, failing to run, or diverging numerically are rejected before surviving candidates are scored on search-time sub-blocks.Examples include breaking observed traces or altering the sampling mask during interpolation.
3 Numerical experiments
Numerical experiments show that SeisEvo improves classical POCS and MSSA by discovering explicit structural modifications while preserving their core reconstruction frameworks. Evo-POCS improves interpolation across missing ratios and datasets, while Evo-MSSA improves simultaneous interpolation and denoising against classical and stronger baselines.
- Evo-POCS: Evo-POCS adds a data-driven local dip-consistency correction after each Fourier thresholding step, moving missing samples only toward self-consistent local wavefield predictions.The Fourier-sparse projection and data-consistency constraint remain part of the operator.
- Evo-POCS: More than 3 dB average improvement: Evo-POCS generalizes to synthetic and field datasets not used during the search, producing better event continuity and smaller reconstruction errors than classic POCS.On a representative field dataset with 50% random sampling, its advantage is also visible in the F-K spectrum through better aliasing suppression.
- Evo-POCS: 3.49 dB average SNR gain: Evo-POCS consistently outperforms POCS across missing ratios from 30% to 70%, with gains ranging from 1.58 to 5.42 dB.The gain gradually decreases as the missing ratio becomes more severe.
- Evo-MSSA: Evo-MSSA discovers reliability-grouped singular-value shrinkage, grouping Hankel patches by local observation reliability and fitting each group with its own low-rank subspace.The fixed Hankel window, rank limit, and reconstruction count remain unchanged from the MSSA seed.
- Evo-MSSA: 10.70 dB average reconstruction SNR: Evo-MSSA exceeds MSSA and ODRR by 7.15 and 3.31 dB, respectively, across five noise levels.Evo-MSSA achieves the highest SNR at every tested noise level, although weak events and spectral energy remain attenuated under low-input-SNR conditions.
4 Discussion
SeisEvo’s contribution is the constrained discovery and selection of explicit, inspectable operators rather than entirely new mechanisms. Its current protocol depends on offline computation, fixed seeds and objectives, reference-based evaluation, and a single search backend, leaving broader generalization unresolved.
- What the search contributed: Evo-POCS and Evo-MSSA combine known seismic ideas with newly selected components that were not specified in advance.Evo-POCS uses directional candidates, phase estimation, residual-weighted consensus, and confidence gating; Evo-MSSA groups Hankel columns by local reliability and projects each group separately.
- What the search contributed: The resulting operators remain explicit, inspectable algorithms that can be related to interpretable seismic mechanisms and tested independently.This distinguishes algorithm evolution from replacing the operator with an agent system or an opaque learned model.
- Scope and cost of the protocol: SeisEvo may extend to denoising, deconvolution, and inversion when executable quality measures, physical contracts, and modular classical algorithms are available.Its main current cost is substantial offline search computation because discovery requires many candidate executions.
- Design of the objective and evaluator: The seed and objective are fixed before each run, and the effects of their choices have not been studied systematically.The objective incorporates human quality judgments through executable scoring rules, with different scoring structures used for the POCS and MSSA case studies.
- From offline discovery to continual discovery: Reference-based SNR and structural similarity restrict the present protocol to offline discovery when complete references or constructible degraded observations are available.Genuinely missing traces in acquired surveys are unobservable, motivating strategies such as hiding observed traces for evaluation.
- From offline discovery to continual discovery: Each case study uses one classical seed and a fixed backend, leaving seed comparability and the effects of more geophysically specific objectives and constraints unresolved.Examples include band preservation, amplitude fidelity, and forward-modelling residuals; continual discovery could use a discovered operator as the next seed.
5 Conclusions
SeisEvo searches for standalone seismic reconstruction algorithms rather than individual reconstructed volumes, using constrained LLM-driven evolution within expert-defined boundaries. Its discovered operators improve reconstruction performance across interpolation and simultaneous interpolation-denoising tasks while remaining explicit and deployable without agents or neural networks.
- Framework: SeisEvo searches for the reconstruction algorithm itself rather than optimizing a single reconstructed volume.A domain expert specifies the seed algorithm, editable components, objective, and legality constraints.
- Framework: The final output is a standalone white-box operator requiring no agent, prompt, or neural network at inference time.The resulting operator remains executable, explicit, and independent of the search system during deployment.
- Results: 3.49 dB average SNR improvement over classic POCS was achieved by Evo-POCS across missing ratios from 30% to 70%.The gain decreased from 5.42 dB at 30% missing to 1.58 dB at 70% missing.
- Results: More than 7 dB average reconstruction SNR improvement over classic MSSA was achieved by Evo-MSSA for simultaneous interpolation and denoising.The passage also reports more than 3 dB improvement over a stronger rank-reduction baseline.
- Implications: SeisEvo assigns experts responsibility for defining legal and useful algorithms while discovering the mechanism through search.The conclusions position agentic algorithm evolution as complementary to deep learning for interpretable geophysical processing algorithms.
A Mathematical formulation of the dip-consistency correction in Evo-POCS
Evo-POCS applies a phase-aligned dip-consistency correction independently on each frequency slice using twelve candidate directions. It selects locally reliable directions through residual-based consensus weighting and gates the update by confidence while preserving observed samples.
- Direction bank: The correction evaluates twelve small-integer spatial offsets as a discrete bank of local dip directions.The offsets have steps of at most two.
- Local phase coefficient: For each direction, a normalized complex coefficient estimated from observed trace pairs provides an approximately unit-modulus phase rotation.The coefficient is computed once from the observed slice and mask, using jointly observed trace pairs within a 7 × 7 window.
- Directional prediction and residual: Each direction predicts the current sample by symmetric phase-aligned continuation from neighboring locations, then measures prediction reliability by a residual on observed samples.A smaller residual indicates better local dip agreement.
- Consensus prediction: The three lowest-residual directions are combined into a consensus prediction with cubic residual-margin weights, giving greater influence to more self-consistent directions.The mean residual across all twelve directions determines the residual margins.
- Confidence gate and update: A confidence gate strengthens the correction when the best direction improves over the mean residual and weakens it when directional residuals are similar.The correction is applied after classic POCS sparse projection, while the outer projection restores observed traces exactly and updates only missing traces.
- Fallback rules: Fallback phase and residual rules maintain operator stability when local observed pairs or samples are unavailable.After processing all slices, Hermitian symmetry is imposed before the inverse temporal Fourier transform to produce a real-valued volume.
B Mathematical formulation of Evo-MSSA
Evo-MSSA reconstructs each temporal-frequency slice through tapered patch overlap-averaging, data-calibrated singular-value shrinkage, and reliability-grouped projections. Cross-iteration consensus and explicit fallback rules stabilize updates while preserving observed traces through weighted, rather than hard, restoration.
- Patch reconstruction: The patch operator extracts overlapping 6×6 spatial patches, while its adjoint performs Hanning-tapered, normalized overlap-averaging rather than a Moore–Penrose pseudoinverse.The taper is separable on the 6×6 support, with pointwise normalization by accumulated taper weights.
- MP–GD singular-value shrinkage: MP–GD shrinkage calibrates matrix noise with the Marchenko–Pastur law, sets thresholds using the Gavish–Donoho coefficient, and applies quadratic shrinkage under an inherited rank limit.Components beyond the inherited rank limit receive zero weight; if all weights vanish, the projected group is zero.
- Reliability-grouped projection: After the initial complete-matrix projection, Evo-MSSA separates columns into reliability groups and projects each group using its own spectrum and aspect ratio before restoring original positions.This reliability-grouped operation is denoted GroupMPGD in Algorithm 3.
- Reliability weighting: Reliability weighting retains more noisy observations when reliability is high and gives more weight to low-rank predictions when reliability is low, without hard-restoring observed traces.The reliability uses residual and noise-calibrated local quantities together with iteration progress.
- Cross-iteration consensus and safeguards: A centered Cesàro average reduces iteration-to-iteration fluctuations without a forgetting factor, while malformed states and failed spectral estimates trigger global MP–GD or slice-level fallbacks.The operator uses all 30 reconstruction iterations, and invalid reconstructed frequency slices fall back to the observed slice.