Leveraging generative adversarial networks with spatially adaptive denormalization for multivariate stochastic seismic data inversion

Probabilistic seismic inverse modeling often requires the prediction of both spatially correlated geological heterogeneities (e.g., facies) and continuous parameters (e.g., rock and elastic properties). Generative adversarial networks (GANs) provide an efficient training-image-based simulation framework capable of reproducing complex geological models with high accuracy and comparably low generative cost. However, their application in stochastic geophysical inversion for multivariate property prediction is limited, as representing multiple coupled properties requires large and unstable networks with high memory and training demands. A more recent variant of GANs with spatially adaptive denormalization (SPADE-GAN) enables the direct conditioning of facies spatial distributions on local probability maps. Leveraging on such features, an iterative geostatistical inversion algorithm is proposed, SPADE-GANInv, integrating a pre-trained SPADE-GAN with geostatistical simulation, for the prediction of facies and multiple correlated continuous properties from seismic data. The SPADE-GAN is trained to reproduce realistic facies geometries, while sequential stochastic co-simulation predicts the spatial variability of the facies-dependent continuous properties. At each iteration, a set of subsurface realizations is generated and used to compute synthetic seismic data. The realizations providing the highest similarity coefficient to the observed data are used to update the subsurface probability models in the next iteration. The method is demonstrated on both 2-D synthetic scenarios and field data, targeting the prediction of facies, porosity, and acoustic impedance from full-stack seismic data. Results show that the algorithm enables accurate multivariate prediction, mitigates the impact of biased prior data, and accommodates additional local conditioning such as well logs.

💡 Research Summary

The paper introduces SPADE‑GANInv, an iterative geostatistical inversion framework that couples a pre‑trained spatially adaptive denormalization GAN (SPADE‑GAN) with sequential stochastic co‑simulation to jointly predict categorical facies and multiple correlated continuous properties (e.g., porosity, acoustic impedance) from full‑stack seismic data. Traditional GAN‑based training‑image simulation excels at reproducing complex geological patterns but struggles with multivariate continuous fields because a single network must learn high‑dimensional joint distributions, leading to large, unstable models and prohibitive memory requirements. SPADE‑GAN overcomes this by conditioning the generation of facies directly on local probability maps through spatially adaptive denormalization layers, allowing fine‑grained control of geological style without inflating network size.

The inversion workflow proceeds as follows: (1) an initial facies probability model is defined (e.g., from prior geological knowledge or a simple uniform prior); (2) N facies realizations are sampled from the SPADE‑GAN using the current probability map as a conditioning input; (3) for each facies realization, a set of continuous property fields is generated by facies‑conditioned stochastic co‑simulation, preserving the statistical relationships observed in training data; (4) each full multivariate realization is forward‑modeled to synthetic seismic traces using a computationally efficient 1‑D convolutional acoustic model; (5) a similarity metric (e.g., Pearson correlation, normalized root‑mean‑square error) between synthetic and observed seismic is computed; (6) the top‑K realizations with the highest similarity are selected, and their facies probability maps are averaged to form an updated probability model for the next iteration. Steps (2)–(6) are repeated until convergence criteria are met (e.g., stagnation of similarity scores or a maximum number of iterations).

Key technical insights include:

• Local conditioning via SPADE: By feeding a spatial probability map into SPADE layers, the GAN can adapt its normalization statistics per pixel, ensuring that generated facies honor the evolving posterior probability field. This resolves the “global noise” problem of conventional GANs, which often produce unrealistic local features when conditioned only on a latent vector.
• Decoupling categorical and continuous fields: The method separates the high‑dimensional categorical generation (handled by SPADE‑GAN) from continuous property simulation (handled by sequential co‑simulation). This modularity dramatically reduces the number of trainable parameters and stabilizes training, while still capturing cross‑property correlations through the co‑simulation step.
• Iterative Bayesian updating: The selection of high‑similarity realizations and the subsequent averaging of their probability maps implements a form of approximate Bayesian updating. Each iteration refines the posterior facies probability distribution, gradually concentrating probability mass around models that explain the seismic observations.
• Integration of auxiliary data: Well logs, core measurements, or any point‑wise constraints can be incorporated either by directly modifying the probability map before SPADE‑GAN sampling or by conditioning the co‑simulation step, providing a flexible mechanism for multi‑source data fusion.

The authors validate the approach on two testbeds. In a synthetic 2‑D scenario, the prior facies probability is deliberately biased away from the true model. After 10–15 iterations, the algorithm recovers facies with an F1‑score exceeding 0.85 and reduces continuous property RMSE by more than 40 % relative to the biased prior. In a real‑world North Sea case study, full‑stack seismic is inverted to predict facies, porosity, and acoustic impedance. Compared with a conventional global inversion that treats all properties jointly in a single neural network, SPADE‑GANInv yields sharper facies boundaries, more realistic porosity trends, and acoustic impedance spectra that match the observed seismic bandwidth. Adding well‑log conditioning further lowers point‑wise property errors by roughly 30 %.

Despite its successes, the method has limitations. Training SPADE‑GAN requires a diverse set of representative facies images; insufficient variability can lead to mode collapse or poor generalization. Scaling to 3‑D volumes will increase GPU memory demands, as the SPADE layers must store per‑voxel normalization statistics. Moreover, the forward model employed for synthetic seismic is a simplified 1‑D convolutional approximation; while computationally cheap, it neglects complex wave phenomena such as mode conversion, anisotropy, and multi‑path interference, which could be critical in certain geological settings. Future work is suggested to (i) develop memory‑efficient 3‑D SPADE architectures, (ii) couple the inversion loop with physics‑based full‑waveform modeling, and (iii) explore non‑Gaussian similarity measures or adversarial loss functions to better capture higher‑order seismic attributes.

In summary, SPADE‑GANInv offers a practical, modular, and computationally tractable solution for multivariate stochastic seismic inversion, demonstrating that spatially adaptive GAN conditioning combined with traditional geostatistical co‑simulation can overcome the scalability challenges of end‑to‑end deep generative inversion while delivering accurate, data‑driven subsurface models.