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DeepStratNet: A Context-Aware Coordinate Regression Framework for Seismic Horizon Tracking under Sparse Labels

Aniq Ahmad, Musham Ahmad Malik, Ahmad Mustafa, Heather Bedle

arXiv:2610.02494v1cs.CV

TL;DR

Seismic horizon tracking is commonly framed as dense segmentation, although interpreter picks are sparse and 2D models do not inherently capture context across slices. This paper uses coordinate regression with recurrent cross-slice context and geology-informed supervision; across four backbones, it reports better performance than segmentation counterparts and greater robustness as training picks become sparser.

  • Problem

    Dense segmentation requires converting horizon picks into masks and distinguishing horizon from background, while 2D approaches do not inherently capture context across neighboring seismic slices.

    Source: §I · pp. 1–2

  • Method

    The framework directly predicts horizon coordinates, uses an LSTM to model neighboring-slice context, and combines valid-pick regression supervision with geology-informed continuity regularization.

    Source: §I · p. 2, §VI · p. 9

  • Results

    Across four backbone architectures, coordinate regression consistently outperforms segmentation quantitatively and qualitatively and is more robust as training picks become sparse.

    Source: §V · p. 8, §VI · p. 9

  • Takeaways & Limitations

    Variation in predictions across successive traces reflects local geological complexity and can serve as a confidence measure to flag ambiguous zones for expert review.

    Source: §VI · p. 9

    The study tracks one horizon, and further research is needed on strongly dipping or discontinuous horizons, including those interrupted by faults or unconformities.

    Source: §V · p. 9

Abstract

from arXiv · show

Automatic horizon tracking is a foundational task in 3D seismic interpretation. Most existing deep learning approaches formulate it as dense semantic segmentation, typically using U-Net-based architectures. The model produces a probability map over all pixels that must be post-processed to extract precise horizon coordinates, while horizon picks in time/depth must be converted into dense masks for training. Unpicked seismic traces are consequently treated as background, which can hinder convergence, and both pre- and post-processing can introduce errors into the final interpretation. Moreover, 2D segmentation models do not inherently capture inter-slice context, while 3D models are often computationally prohibitive. We instead formulate horizon tracking as a bounded coordinate regression problem, where the model directly predicts the time/depth coordinate of the target horizon at each lateral position. We propose a lightweight regression head compatible with any pretrained vision backbone, coupled with an LSTM module to model inter-slice context and produce a continuous horizon surface across the volume. A combination of L1 and L2 losses supervises predictions at valid horizon picks, while a geology-informed regularization enforces lateral continuity between successive traces. Under controlled experimental conditions, we evaluate four pretrained vision backbones under both segmentation and regression configurations on a seismic volume from New Zealand. The proposed approach consistently outperforms its segmentation counterparts quantitatively, using metrics including RMSE and PCC, and qualitatively, while also demonstrating greater robustness to increasing sparsity of training picks. Finally, we show that prediction variation across successive traces captures local variations in geological complexity, providing an automated quality control measure for downstream seismic interpretation.

I. INTRODUCTION

The introduction identifies limitations of dense segmentation for horizon tracking and proposes bounded coordinate regression with cross-slice context and geology-informed supervision. The framework predicts horizon coordinates directly and trains only on valid picks while regularizing lateral continuity.

I. INTRODUCTION

  • Segmentation turns horizon picks into dense masks and predicts pixelwise labels, while unpicked regions may be treated as background and mask post-processing can add interpretation error.Mask-label errors may depend on pick density and preprocessing; raw predictions may also overestimate the horizon’s vertical extent or include distant false predictions.Source: §I · pp. 1–2
  • Neighboring seismic slices share spatial context, but image-based models often treat slices as standalone images and have limited opportunity to exploit that context.The introduction notes that this context may be especially useful in structurally complex settings where continuity across slices carries geological information.Source: §I · p. 2
  • The proposed bounded regression formulation predicts exactly one horizon-depth point per lateral position within the seismic image’s time/depth range.The authors argue that these constraints narrow the solution space of an otherwise highly ill-posed problem.Source: §I · p. 2
  • An LSTM and attention module use neighboring slices to contextualize the target prediction, while masked regression and geology-informed smoothness losses supervise valid picks and discourage implausible lateral jumps.The masked loss excludes unlabeled regions from the pick-based penalty; the smoothness term links successive lateral positions.Source: §I · p. 2
  • DeepStratNet pairs a lightweight, backbone-agnostic regression head with pretrained vision features to predict horizon coordinates directly.The head predicts a length-W coordinate vector rather than an H × W probability map, avoiding heavy spatial decoders and heuristic coordinate extraction.Source: §I · p. 2

II. RELATED WORK

Prior horizon-tracking work spans patch classification, semantic segmentation, and probability estimation, with outputs that generally require post-processing or label conversion. The paper contrasts these approaches with direct coordinate prediction and a plug-in module that models context across neighboring slices.

II. RELATED WORK

  • Prior approaches include patch-based classification, pixelwise or volumetric segmentation, and continuous probability estimation for locating horizons.Patch methods classify a central sample; segmentation predicts labels or probabilities across pixels or voxels, while density approaches estimate continuous horizon probabilities.Source: §II · pp. 2–3
  • Direct coordinate prediction avoids converting interpreter picks into intermediate masks or probability distributions and permits geological consistency regularization unavailable to dense-output approaches.The related-work discussion also notes that post-processing dense outputs to extract coordinates can introduce error.Source: §II · p. 3
  • Horizon-tracking architectures progressed from CNN classifiers and encoder-decoder networks to transformer-based models with attention across 2D or 3D spatial context.The reviewed examples include SegNet-style and U-Net variants, TransUnet, and a 3D shifted-window transformer.Source: §II · p. 3
  • The paper’s module plugs into pretrained backbones, predicts horizon coordinates directly, and models context across neighboring slices rather than proposing one specific architecture.The authors state that this design can leverage pretrained visual representations while keeping computational cost lower than 3D approaches.Source: §II · p. 3

III. METHODOLOGY

DeepStratNet represents the seismic volume as adjacent 2D inlines and predicts each target horizon as a vector of normalized depth coordinates across crossline positions.

A. Problem Formulation and Dataset Representation

  • The seismic volume is modeled as a sequence of 2D images along the inline coordinate axis.Training data comprise paired input sequences and corresponding horizon interpretations.Source: A. Problem Formulation and Dataset… · p. 3
  • Each input sample is a context window of adjacent inlines centered on the target inline, with neighboring slices supplying spatial context.The window contains T = 2k+1 slices; the central slice is evaluated and surrounding slices provide contextual constraints.Source: A. Problem Formulation and Dataset… · p. 4
  • The target horizon is represented as a 1D vector of continuous, normalized depth coordinates across crossline positions.Coordinates lie in [0, 1], and columns without valid interpretations are masked during optimization.Source: A. Problem Formulation and Dataset… · p. 4

B. DeepStratNet Architecture

DeepStratNet processes a sequence of seismic slices through feature extraction, sequential modeling, attention aggregation, and horizon regression. Slice embeddings are passed chronologically to an LSTM to model structural variation across adjacent inlines.

B. DeepStratNet Architecture

  • The model processes the input sequence through spatial feature extraction, temporal sequence modeling, attention aggregation, and horizon regression.This end-to-end pipeline is illustrated in Figure 1.Source: B. DeepStratNet Architecture · p. 4

1) Spatial Feature Extraction and Global Pooling:

  • Each seismic slice is independently processed by a 2D convolutional or vision-transformer backbone, then globally pooled into a feature vector.The pooled vectors are ordered across the sequence to form the latent sequence.Source: 1) Spatial Feature Extraction and… · p. 4

2) Spatial Sequence Modeling:

  • An LSTM processes the chronological feature sequence to model structural variations across adjacent inlines.Its output is a sequence of temporal hidden states, one at each sequence index.Source: 2) Spatial Sequence Modeling · p. 4

3) Spatial Attention Mechanism:

A soft attention mechanism weights hidden states from adjacent seismic slices before the aggregated context is projected to normalized horizon coordinates.

3) Spatial Attention Mechanism:

  • Soft attention assigns each hidden state an importance score to account for differing relevance and noise across adjacent seismic slices.The scores are normalized with Softmax to obtain attention weights, which form the weighted context vector.Source: 3) Spatial Attention Mechanism · p. 4

4) Horizon Prediction Head:

  • A fully connected projection layer followed by a Sigmoid maps the aggregated context to normalized horizon coordinates.The prediction has dimension W and lies in [0, 1]^W.Source: 4) Horizon Prediction Head · p. 4

C. Loss Functions

The objective combines pointwise prediction fidelity with a crossline smoothness constraint to encourage structurally continuous horizon predictions.

C. Loss Functions

  • The objective combines pointwise spatial-distance metrics with a structural crossline smoothness constraint.Figure 1 describes the composite loss as masked L1/L2 reconstruction losses plus a smoothness regularization term.Source: C. Loss Functions · p. 4, Figure 1 · p. 5

1) Pointwise Regression Loss:

  • The pointwise regression loss combines MSE and MAE over valid crossline indices.Only valid indices contribute to this discrepancy measure.Source: 1) Pointwise Regression Loss · p. 4

2) Crossline Smoothness Regularization:

3) Total Objective Function:

  • The total loss balances pointwise fidelity with spatial structural continuity using a scalar hyperparameter λ > 0.Nv denotes the total number of labeled seismic inlines available for training.Source: 3) Total Objective Function · p. 4

D. Evaluation Metrics

Evaluation is restricted to valid annotated horizon columns and reports RMSE, PCC, and R2, with RMSE converted to milliseconds.

  • Evaluation uses only valid annotated horizon columns and reports RMSE, PCC, and R2.Source: D. Evaluation Metrics · p. 5
  • Normalized RMSE is converted to pixel units and then milliseconds using the image-height ratio and the original 4 ms sampling interval.The original sections have 176 vertical samples and are resized to 224 pixels.Source: D. Evaluation Metrics · p. 5
  • Metrics are reported for both training and test sets and averaged across seismic slices; PCC and R2 remain dimensionless after scaling.Source: D. Evaluation Metrics · p. 5

IV. RESULTS

The results compare segmentation and regression across four pretrained backbones and report average training and test metrics for three configurations. Visual examples show the predicted horizon, including a continuous time surface.

A. Dataset

  • The Maui 3D seismic dataset contains 572 inlines; 22 uniformly spread, fully labeled inlines were used for training and 32 other inlines for held-out validation/test.The slices were resized to 224 x 224 pixels.Source: A. Dataset · p. 5

B. Backbones

  • For the highest-performing ConvNeXt backbone, regression directly follows the target reflection character more consistently than segmentation-derived picks.Fig. 2 contrasts argmax-extracted segmentation picks with directly predicted regression coordinates.Source: Figure 2 · p. 6, B. Backbones · p. 7
  • Four pretrained backbones were evaluated under identical conditions with segmentation and the proposed regression module; regression predicts coordinates without label-thickening or heuristic post-processing.The backbones were ResNet-50, ResNet-101, ViT-Large, and ConvNeXt-Large.Source: B. Backbones · pp. 6–7
  • The segmentation baseline thickens binary horizon masks for training, then extracts picks by selecting the maximum logit along each vertical trace.Source: B. Backbones · pp. 6–7
  • Fig. 3 presents a horizon time surface whose travel times increase toward the northwest, indicating a northwest dip.The vertical axis is two-way travel time in milliseconds.Source: Figure 3 · p. 6
  • Fig. 4 shows irregular predicted picks on some inlines, which the caption identifies as marking a channel.Source: Figure 4 · p. 7
  • Table I reports average training and test RMSE, PCC, and R2 for the evaluated backbones in segmentation, regression, and regression-without-LSTM configurations.Source: B. Backbones · p. 7

C. Sparsity Analysis

As training picks become sparse, regression performance degrades less than segmentation across the tested backbones. The discussion connects this robustness to coordinate-based supervision and spatial context, and describes prediction variance as a potential quality-control signal.

C. Sparsity Analysis

  • Segmentation degrades faster than regression as training picks decrease across all backbones; the sparsity experiment randomly removed 25%, 50%, or 75% of picks.The experiment evaluated average test-set r2 at each pick density.Source: C. Sparsity Analysis · p. 7, Figure 5 · p. 8

V. DISCUSSION

  • Direct coordinate regression estimates a horizon position per trace, avoiding dense pixel classification and better preserving continuous reflections and horizon surfaces.The discussion also notes reduced discretization effects when low-resolution features are converted back to image resolution.Source: §V · p. 8
  • The LSTM's improvement reflects the value of modeling spatial dependencies: neighboring-slice information can constrain predictions where seismic responses are locally ambiguous.Reflector continuity extends beyond the information available in an individual inline or crossline.Source: §V · p. 8
  • Sparse picks leave unlabeled traces unsupervised in regression, whereas segmentation treats them as background, an increasingly inconsistent assumption as label density falls.The discussion relates this difference to the greater degradation observed for segmentation under sparse labeling.Source: §V · p. 8
  • The geology-based smoothness constraint discourages unrealistic local variation while allowing changes in reflector geometry; its usefulness depends on local horizon continuity.The regularization links prediction behavior between sparse observations to the physical structure of the seismic volume.Source: §V · p. 8

D. Uncertainty Analysis

  • High prediction variance coincides with complex channel features and structural discontinuities, providing a signal for flagging ambiguous zones for expert review.The uncertainty band widens where structural continuity breaks down.Source: §V · pp. 8–9, Figure 6 · p. 9

V. DISCUSSION

  • The present work tracks one horizon; future work is needed for multiple horizons and for strongly dipping, discontinuous, fault-interrupted, or unconformable horizons.The discussion also identifies adaptive weighting of geological consistency regularization as a research direction.Source: §V · p. 9

VI. CONCLUSION

The paper presents a model-agnostic coordinate-regression module for 3D seismic horizon tracking and reports better quantitative performance and smoother picks than segmentation across four backbones. It also identifies spatial-context modeling, sparse-pick supervision, and predictive uncertainty as operational advantages.

VI. CONCLUSION

  • Across four backbones, replacing segmentation heads with coordinate regression yields superior quantitative performance and qualitatively smoother horizon picks.The evaluated backbones are ResNet-50, ResNet-101, ViT-Large, and ConvNeXt-Large.Source: §VI · p. 9
  • The module directly predicts continuous horizon depth coordinates along vertical traces, avoiding artificial label-thickening, spatial upsampling, and heuristic post-processing extraction.The proposed regression module is described as generic and model-agnostic.Source: §VI · p. 9
  • The framework uses an LSTM across adjacent slices, valid picks with a geology-based consistency prior, and predictive uncertainty to highlight ambiguous zones for expert review.The conclusion presents these as operational advantages of the formulation.Source: §VI · p. 9
  • The work is presented as a flexible, plug-and-play alternative to dense segmentation for automated seismic interpretation workflows.Source: §VI · p. 10

APPENDIX

The appendix describes seismic-volume preparation and spatial splitting, then specifies the pretrained backbones, sequence setup, and optimization settings used in the experiments.

A. Data Storage, Preparation, and Splits

  • The seismic volume and horizon masks use Zarr storage; amplitudes are standardized, clipped, scaled, and duplicated across three channels for pretrained RGB inputs.Spatial dimensions are resized to 224 by 224, and target masks are mapped to one-dimensional coordinates.Source: A. Data Storage, Preparation, and… · p. 10
  • The volume is partitioned along the inline axis to minimize spatial overlap, with training and evaluation/testing samples drawn at different strides.Training inlines are 0–571 at stride 25; evaluation/testing inlines are 181–565 at stride 12, with edge slices replicated to maintain sequence length 3.Source: A. Data Storage, Preparation, and… · p. 10

B. Architecture and Training Configurations

  • ImageNet-pretrained ResNet-50, ResNet-101, ConvNeXt-Large, and ViT-Large serve as feature extractors; the sequence window is three slices and the unidirectional LSTM has hidden dimension 256.The primary benchmark uses ConvNeXt-Large with feature dimension 1536; LSTM dropout is 0.2.Source: B. Architecture and Training… · p. 10
  • Models use Adam for 100 epochs with learning rate 10^-4, batch size 4, and smoothness-loss coefficient 10^-4; experiments use global random seed 42.Source: B. Architecture and Training… · p. 10
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