A hybrid physics and machine learning approach for velocity prediction

Elastic well logs play an important role in reservoir characterization in the subsurface. However, due to the high expense of drilling, only a few wells are drilled to limited depths, making it difficult to understand the deposition and execute geophysical activities such as building background models for seismic inversion and property models for seismic forward modeling. We begin with P-velocity prediction between the wells and extension along the wellbore to tackle this problem. A hybrid workflow is introduced based on seismic and available P-velocity logs, including well-log decomposition, relative rock physics, seismic forward modeling, feature engineering based on seismic transform, optimal attribute selection, and machine learning network training and prediction. In this hybrid workflow, relative P-velocity instead of absolute P-velocity is used for labeling. The rock-physics study and seismic forward modeling contribute to label augmentation. The machine learning approach assists in discovering the relationship between the relative P-velocity and the optimal seismic attributes. Under physics rules, the predicted relative velocity through the trained network is integrated with the compaction trend to estimate the final absolute velocity. This hybrid workflow is applied to a case study of sand-shale sequences in northern China. The model-based deterministic inversion and data-driven machine learning approaches are also compared. The results of blind well testing indicate that the data-driven approach lacks generalization capability and fails to predict extension in some blind wells. The physics-based inversion performs differently in blind wells in different locations. By contrast, P-velocity prediction with the hybrid workflow improves prediction accuracy in all blind wells, horizontally and vertically. The results indicate that this hybrid workflow promises interpolating and extending elastic well logs when the deposition environment does not vary significantly. Further studies are recommended to discuss the applicability of this workflow.