Seismic Inversion Eval

---
name: seismic-inversion-eval
description: Evaluates a model's ability to perform semi-supervised seismic impedance inversion using ultra-sparse well-log labels. It probes voxel-level accuracy, patch-level structural similarity, and percentage error on both synthetic and real-world 3D seismic volumes. Use when the user wants to benchmark on SEAM Phase I, Netherlands F3, Delft, or asks about evaluating this task. Reports MAE.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2302.06441
  bibtex_key: dou2023contrasinver
  confidence: high
---

# seismic-inversion-eval

> ContrasInver: Ultra-Sparse Label Semi-supervised Regression for Multi-dimensional Seismic Inversion — Dou et al. (2023) (arXiv:2302.06441, 2023)

## What this evaluates

Evaluates a model's ability to perform semi-supervised seismic impedance inversion using ultra-sparse well-log labels. It probes voxel-level accuracy, patch-level structural similarity, and percentage error on both synthetic and real-world 3D seismic volumes.

## Datasets

- **SEAM Phase I** — total ?; splits: test (-1), validation (-1)
- **Netherlands F3** — total ?; splits: test (-1)
- **Delft** — total ?; splits: test (-1)

## Metrics

- `MAE` **(primary)** — range: other
  - Mean Absolute Error. Computes the average absolute difference between predicted and true impedance values across all voxels. Used for both synthetic and field data.
- `SSIM` — range: [0, 1]
  - Structural Similarity Index. Measures patch-level accuracy using a sliding window (7x7x7). Formula: ((2μμ'+c1)(2σ+ c2)) / ((μ²+μ'²+c1)(σ²+σ'²+c2)), where μ and σ are means and variances, and c1, c2 stabilize division.
- `MAPE` — range: percent
  - Mean Absolute Percentage Error. Computes the average absolute percentage difference between predicted and true values: (1/n)Σ|(|(y-ŷ)/y|)| × 100%. Used only for field data where ground truth is unavailable.

## Input / output format

**Input**: 3D seismic volume data and sparse well-log impedance values at specific spatial coordinates.

**Output**: 3D impedance volume (predicted acoustic impedance values for each voxel).

## Scoring recipe

```python
def compute_metrics(pred, gt):
    mae = np.mean(np.abs(pred - gt))
    ssim = sliding_window_ssim(pred, gt, window=(7,7,7)) if gt is not None else None
    mape = np.mean(np.abs((gt - pred) / gt)) * 100 if gt is not None else None
    return mae, ssim, mape
```

## Common pitfalls

- Field data lacks complete ground truth, making SSIM inapplicable and requiring MAPE instead.
- Well-seismic calibration accuracy varies due to time-depth conversion errors and interpreter subjectivity, introducing label ambiguity.
- 1D methods fail to capture lateral continuity, requiring 3D evaluation frameworks to properly assess inversion quality.

## Evidence (verbatim from paper)

> In the synthetic data, we have access to the complete impedance ground truth, so we use two metrics: Mean Absolute Error (MAE) and Structural Similarity Index (SSIM). MAE represents voxel-level accuracy, and its expression is well-known and requires no additional parameter settings. Additionally, it is the only evaluation metric used during the validation process. SSIM measures patch-level accuracy... Considering that complete ground truth data cannot be obtained from the field data, and thus SSIM cannot be calculated, we replace it with Mean Absolute Percentage Error (MAPE), which measures the percentage difference between predicted values and ground truth.

## Citation

```bibtex
@misc{dou2023contrasinver,
  title={ContrasInver: Ultra-Sparse Label Semi-supervised Regression for Multi-dimensional Seismic Inversion},
  author={Dou et al. (2023)},
  year={2023},
  note={arXiv:2302.06441}
}
```

- arXiv: 2302.06441