Multiscale forward and inverse problems with the DGFD method and the deep learning method

A fast electromagnetic (EM) forward solver has been developed for the subsurface detection, with application includes producing synthetic logging data and instructing large-scale field test and inversion. A deep learning based full wave inversion method has also been developed to reconstruct the underground anomaly.

Since the gas and oil industry has very high demands for the forward modeling speed when doing inversion, the inversion model is usually simplified to a 1D or 2D problem by supposing the geometry of object invariant in two or one direction. The full 3D inversion is still a hot topic for research, which requires both fast 3D forward solver and efficient inversion method. The bottleneck for the forward solver is how to solve the large-scale linear system efficiently; the bottleneck for the inversion is how to pick the global minimum from lots of local minimums efficiently for the inverse problem.

For the forward part, the domain decomposition method (DDM) inspired discontinuous Galerkin frequency domain (DGFD) method has been extended to model the vertical open borehole resistivity measurement with structured gradient meshes; besides, the DGFD method has been extended to model the logging-while-drilling (LWD) resistivity measurement in high-angle and horizontal (HA/HZ) well and curved layers with a flipped total field/scattered field (TF/SF) mixed solver. An approximated casing model has also been proposed to accelerate the large-scale curved casing modeling with borehole-to-surface measurements.

For the inversion part, a convolutional neural network based inversion has been developed to reconstruct the lateral extent and direction of the hydraulic fracture through scattered electromagnetic field data under borehole-to-surface measurements; further, the deep transfer learning is applied in the same scenario to improve the performance of the inversion. Additionally, a fully connected neural network has been developed for the Devine field data and successfully reconstruct the shape of the hydraulic fracture with good agreement to the conventional inversion.