Pixel-Based Inversion of Electromagnetic Logging Data

Electromagnetic logging technology is widely utilized for hydrocarbon resources exploration and production. Since the responses captured by the logging tools are too complex, inverse problems are generally resolved to reconstruct the subsurface structure. The inverse problem is known to be highly non-linear and ill-posed, thus posing many challenges to research. As a result, this thesis aims to develop algorithm frameworks that can correctly recover the formation from measured data, with an emphasis on pixel-based inversion methods. In this thesis, two inversion frameworks are presented including the one-dimensional (1D) pixel-based inversion method and the two-dimensional (2D) pixel-based inversion method. For 1D inversion method, it can be applied for formations with parallel or mildly changed boundaries. The non-uniform mesh scheme is recommended for higher efficiency. For the 2D inversion method, the general framework is implemented, based on which we investigate two complex scenarios. The first is simultaneous inversion for resistivity and dielectric constant. It is found that dielectric effects cannot be ignored in some circumstances. The gradients of measurements with respect to dielectric constant are derived and validated. Besides, several examples are used to demonstrate the performance. The second scenario is reconstructing formations ahead of the drill bit under complicated formations. A reference model is added into the objective function to stabilize the problem and it is found to be very useful to improve the look-ahead capability. Several examples validate the effectiveness of the 2D inversion ability. Although the implemented 2D pixel-based inversion algorithm shows robust performance, the efficiency is not enough to support real-time applications. As a result, a general workflow for fast calculating the responses of the electromagnetic logging tools is proposed, with the assistance of deep neural networks. The accuracy and efficiency are evaluated by comparing with rigorous modeling. It is found that the proposed workflow can accurately calculate the tool responses with several milliseconds.