Calibrating rock physics models using physics guided neural networks

Abstract

Rock physics models characterize reservoirs by linking reservoir properties to their elastic response. The accuracy of these quantified properties depends on selecting and calibrating a model that accurately represents this underlying relationship. Complex reservoirs, such as anisotropic ones, require models with calibration parameters that are often difficult or costly to obtain. This challenge has created a barrier to applying certain rock physics models to characterize complex real-world reservoirs.

The variation in these calibration parameters can significantly influence the modeled elastic properties, which, in turn, affect seismic responses. For instance, variations in fluid distribution within the reservoir can alter the measured velocity, while anisotropy in shale layers can impact amplitudes versus offset (AVO) analysis. Therefore, it is reasonable to assume that the effects of these unknown calibration parameters are implicitly captured in the seismic response. However, due to the complex interplay of factors such as porosity, lithology, and fluid content, these parameters cannot be directly inferred from seismic data.

Neural networks are powerful tools for addressing geophysical challenges, particularly in identifying complex patterns and relationships between seismic attributes and reservoir properties. However, they require large training datasets that consist of measured reservoir properties and their seismic responses to adjust their weights accurately and capture the underlying intricate relationships. Such datasets are rarely available in real field data.

Physics-guided neural networks (PGNNs) have emerged as a promising approach, utilizing customized loss functions to penalize unrealistic predictions based on physics equations and models. This thesis proposes a novel PGNN workflow that facilitates the application of uncalibrated rock physics models, using a limited set of basic field measurements to constrain the training process. The workflow trains the network on two weighted datasets. The first dataset is generated from uncalibrated rock physics models, allowing the network to learn the underlying relationship between known and unknown model parameters and their impact on seismic responses. The second dataset comprises field data points—such as well log measurements of porosity and saturation, along with their seismic responses—which inherently contain information about unknown model parameters, that the network can extract to help constrain the training. A hyperparameter ($\lambda$) controls the influence of each dataset in the training process.

This workflow introduces a groundbreaking approach that enables the characterization of complex reservoirs without costly calibration measurements, thereby reducing exploration risks. By analyzing variations in seismic responses, it captures information about unknown calibration parameters and optimizes the prediction of reservoir properties, even for complex reservoir conditions.

Additionally, the workflow addresses the data scarcity issue that often hinders the application of machine learning in reservoir characterization during the early stages of exploration. It provides an alternative by using rock physics models as a data augmentation tool, allowing the network to be properly trained on the underlying relationships between reservoir properties and seismic responses, even with limited field data.

Furthermore, the workflow integrates and capitalizes on field measurements as they become available, enhancing prediction accuracy over time. By incorporating these measurements into the training process, the workflow ensures continuous calibration and improved predictive performance. This workflow has shown enhanced prediction accuracy for synthetic models of dispersive and vertical transverse isotropy (VTI) reservoirs compared to networks trained on limited measurements or uncalibrated rock physics models.

The workflow relies on three key assumptions. First, variations in unknown parameters influence seismic responses. This is evident with the effects of anisotropy on AVO analysis, where changes in these parameters can significantly alter seismic data. Second, seismic modeling of rock physics data can replicate field gathers, enabling the transfer of learned relationships between reservoir properties and seismic signatures from modeled data to actual field data. Many rock physics applications use synthetic modeling to quantify field observations based on modeled elastic properties. Third, I assume that unknown parameters remain consistent across field measurements. This consistency enables the network to accurately isolate their impact and calibrate accordingly. This assumption is valid for geographically constrained reservoirs formed by similar geological processes, where these parameters are likely uniform and can be reliably isolated.