Four-dimensional fast inversion based on deep learning forward modeling

Throughout the optimization and iterative stages of the inversion, forward modeling needs to be performed frequently, which means that the validity of the forward simulation directly affects the precision of the inversion outcomes. The traditional forward simulation algorithm based on the finite element method has high computational cost and cannot meet the time requirements of the four-dimensional fast inversion of resistivity. In contrast, deep learning networks can be employed to approximate the forward modeling process, greatly enhancing its speed. Introducing deep learning into forward modeling of inversion problems requires building a network that can respond sensitively to minor modifications in the model, to ensure accurate inversion refinement. Mix Transformer has the capabilities of global modeling and feature extraction. In this study, we design a forward network model DC-ForwardNet, whose core architecture is the Transformer model. DC-ForwardNet first extracts feature information hierarchically, then uses a multi-scale method to provide the characteristic information to the decoder, together with finally outputs the forward modeling results. By leveraging the forward data produced by the conventional iterative inversion strategy, the sample data set required for deep learning forward modeling was established. The trained network is able to calculate forward responses quickly and accurately. While maintaining high accuracy, DC-ForwardNet delivers a forward computation speed that is several hundred times faster than the conventional four-dimensional inversion approach, even with identical processing steps.