In most cases, interpretation of resistivity measurements is performed using 1D multilayered formation models that are used to fit data locally in real-time applications. While drilling high-angle or horizontal wells, more complex scenarios may occur, such as faults, pinch-outs, or unconformities. In these cases, resistivity logging data inversion should be performed using at least a 2D model, which is a more complex computational problem. This paper presents a neural networks approach for solving this problem exemplified by the application of a deep azimuthal resistivity tool for geosteering in the vicinity of a tectonic fault. The tool operational frequencies of 400 kHz and 2 MHz produce eight measurements with a coaxial arrangement of transmitters and receivers, and two azimuthally sensitive measurements with axial transmitters and transverse receivers. This paper considers a 2D model of a tectonic fault composed of three parallel layers on the one side of a displacement plane and the same three layers on the other side dislocated at a certain distance along the displacement plane. The model is described with nine independent parameters. The artificial neural networks (ANNs) were designed and trained to calculate the tool signals based on the model parameters. The training was carried out using a synthetic database of 4·105 elements containing the model parameters and corresponding tool signals. The database was calculated using distributed computations with in-house Pie2D software that used the boundary integral equation technique. To estimate the accuracy of the ANNs designed, the signals calculated with the networks were compared against the exact values obtained with Pie2D for an independent sample of 1.8·104 points. The comparison gave a good match for all 10 measurements, with the relative error comprising less than one standard tool measurement error for most points of the sample. Computation with the ANN required a few microseconds to calculate one signal, while the algorithm based on boundary integral equations required several minutes. The obtained acceleration of ~106 indicates many opportunities for modeling and inversion of logging-while-drilling data.

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Fast and accurate simulation of responses of logging-while-drilling (LWD) electromagnetic (EM) tools in complex 2D and 3D formations is very important for reconstruction of the resistivity distribution in proactive geosteering. Currently, real-time interpretation is based on the 1D parametric inversion. Advances in fast simulation beyond the 1D model would open a way for real-time 2D inversion. We developed, implemented numerically, and tested an efficient method for simulation of LWD EM tools in complex 2D formations with an arbitrary 3D position of the tool. The method is based on the boundary integral equations for the tangential components of the field and the Fourier transform, which reduces the problem to a series of 1D integral equations. Computations are carried out simultaneously for the whole set of measurement points with the same matrix, which provides a short computation time per point. We verified the method by comparing our results with those obtained by the well-known explicit 1D method and by commercial software in the 2D case. Numerical results justified that the method is accurate and time efficient. Also, as an example, we simulated the signals of real propagation and azimuthal resistivity tools for a complex 2D formation model with fault. The software based on our method can be useful in planning geosteering jobs in complex formations.

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The present paper considers certain problems of gravity monitoring at oil and gas fields arising due to inversion of repeat measurement data, when finding the positions of water–oil and water–gas contacts. The main sources of noise in gravity data are errors in vertical positioning of the tool, changes in atmospheric pressure, and variations in groundwater level and soil moisture. An algorithm based on using a multisensor borehole tool is proposed for a more accurate inversion. Examples of locating successfully the water front while solving model problems with the help of this algorithm are provided.