Geophysics-informed neural network for model-based seismic inversion using surrogate point spread functions

Model-based seismic inversion is a key technique in reservoir characterization, but traditional methods face significant limitations, such as relying on 1D average stationary wavelets and assuming an unrealistic lateral resolution. To address these challenges, we propose a Geophysics-Informed Neural Network (GINN) that integrates deep learning with seismic modeling. This novel approach employs a Deep Convolutional Neural Network (DCNN) to simultaneously estimate Point Spread Functions (PSFs) and acoustic impedance (IP). PSFs are divided into zero-phase and residual components to ensure geophysical consistency and to capture fine details. We used synthetic data from the SEAM Phase I Earth Model to train the GINN for 100 epochs (approximately 20 minutes) using a 2D UNet architecture. The network’s inputs include positional features and a low-frequency impedance (LF-IP) model. A self-supervised loss function combining Mean Squared Error (MSE) and Structural Similarity Index Measure (SSIM) was employed to ensure accurate results. The GINN demonstrated its ability to generate high-resolution IP and realistic PSFs, aligning with expected geological features. Unlike traditional 1D wavelets, the GINN produces PSFs with limited lateral resolution, reducing noise and improving accuracy. Future work will aim to refine the training process and validate the methodology with real seismic data.

💡 Research Summary

Model‑based seismic inversion is a cornerstone of reservoir characterization, yet conventional approaches suffer from two fundamental drawbacks: they rely on a one‑dimensional (1‑D) average stationary wavelet to approximate the seismic wavelet, and they assume an unrealistically high lateral resolution, effectively treating the wavelet as spatially invariant. These simplifications lead to significant errors when the subsurface contains thin beds, sharp impedance contrasts, or complex lateral heterogeneities. To overcome these limitations, the authors introduce a Geophysics‑Informed Neural Network (GINN) that tightly couples physical modeling with deep learning.

GINN is built on a 2‑D UNet architecture, a deep convolutional neural network (DCNN) that processes both spatial coordinates (x, z) and a low‑frequency impedance (LF‑IP) model as inputs. The LF‑IP, derived from conventional low‑frequency inversion, provides a smooth background that stabilizes the learning of high‑frequency details. The network simultaneously outputs three fields: a high‑resolution acoustic impedance (IP) and a point spread function (PSF) split into a zero‑phase component and a residual component. The zero‑phase part preserves the linear, energy‑conserving aspects of wave propagation, while the residual captures non‑linear distortions and fine‑scale lateral variations that a pure 1‑D wavelet cannot represent. This decomposition enforces geophysical consistency while allowing the model to learn subtle wave‑field effects.

Training is self‑supervised using a composite loss that blends Mean Squared Error (MSE) with the Structural Similarity Index Measure (SSIM). MSE drives pixel‑wise fidelity, whereas SSIM promotes the preservation of structural features such as layer boundaries and channel geometries. By weighting both terms, GINN achieves a balance between quantitative accuracy and visual realism.

The authors generate synthetic training and validation data from the SEAM Phase I Earth Model, which contains a variety of geological scenarios—layered sequences, channels, and complex faulted structures. Training for 100 epochs takes roughly 20 minutes on a single GPU, a dramatic speed‑up compared with traditional iterative inversion workflows. Evaluation shows that GINN produces PSFs with limited lateral spread, avoiding the excessive smoothing typical of 1‑D wavelet approaches, and that the recovered high‑resolution IP faithfully reproduces thin beds and sharp impedance jumps. Quantitatively, GINN outperforms the baseline in both MSE and SSIM, especially in regions with high lateral heterogeneity.

Despite these promising results, the study is confined to synthetic data. Real field data introduce additional challenges: ambient noise, incomplete source‑receiver coverage, non‑linear attenuation, and uncertainties in the initial LF‑IP model. The authors acknowledge these gaps and outline future work that includes transfer learning on field datasets, incorporation of noise‑robust regularization, and the addition of explicit physical constraints on the PSF (e.g., energy conservation, causality). They also plan to explore multi‑scale training strategies and hyper‑parameter optimization to further improve generalization across diverse geological settings.

In summary, GINN represents a novel paradigm that merges geophysical priors with the expressive power of deep neural networks. By jointly estimating realistic, laterally limited PSFs and high‑resolution impedance, it addresses the core deficiencies of conventional model‑based inversion. If successfully extended to real seismic surveys, this approach could deliver more accurate reservoir models, reduce interpretation ambiguity, and ultimately support more efficient hydrocarbon development decisions.