Determination of petrophysical parameters is regarded as a critical task for the exploration and production of oil and gas reservoirs. Traditionally, the joint inversion of electromagnetic (EM) and seismic data under petrophysics constraints can be exploited to reconstruct the distribution of reservoir petrophysical parameters. However, methods involved with such schemes face challenges when solving high-contrast nonlinear inverse scattering problems due to the complexity of the relationship between resistivity/velocity and petrophysical properties and the nonuniqueness of these inverse problems. Here, to resolve these challenges, we have developed a field data transformation-joint inversion method (FDT-JIS) to directly reconstruct the distribution of porosity and water saturation. Specifically, the chain rule to transform geophysical parameters into petrophysical parameters is leveraged, and the field data transformation module is subsequently utilized to transform the scattered field data generated under the test configuration into those under the training configuration. Finally, a joint network is adopted to establish the mapping relationship between EM and acoustics data and petrophysical parameters to attain the inversion of petrophysical parameters. With numerical examples, we demonstrate that FDT-JIS not only allows different transceiver configurations to be used in training and testing, but also accurately reconstructs petrophysical parameters of complex models with high contrast in noisy environments.

In elastic wave inverse scattering problems, the material-property reconstruction, e.g. distributions of mass density, compressional wave speed, and shear wave speed from a limited set of measurement data, has attracted considerable research interest. However, simultaneous inversion of multiple parameters endures high computation costs, and reconstructed compressional and shear speeds may become unrealistic if no physical constraint is imposed. Meanwhile, because large objects with high contrasts over the background medium tend to induce high nonlinearity during the inversion process, it is difficult to obtain high-quality high-contrast material properties. To overcome such difficulties, we have developed a multi-module deep learning scheme with physical constraint for multi-parameter elastic wave inversion of high-contrast objects in inhomogeneous media. This scheme consists of (1) a preliminary imaging module (PIM), in which a deep residual network (ResNet) is employed to convert the scattered field data into the preliminary inversion images, (2) an image-enhancement module (IEM), in which a U-Net is employed to further enhance the image quality, and (3) a convolutional neural network (CNN) that is employed as the physical constraint module (PCM) to allow elastic wave parameters to satisfy actual physical constraint. Numerical examples have demonstrated that the proposed scheme not only accurately achieves multi-parameter elastic wave inversion, but also has good generalizability. Finally, the scheme can be applied to complex objects with high contrasts in both noise-free and noisy environments.

In 2010, Gentry and Halevi presented the first FHE implementation. FHE allows the evaluation of arbitrary functions directly on encrypted data on untrusted servers. However, even for the small setting with 2048 dimensions, the authors reported a performance of 1.8 s for a single bit encryption and 32 s for recryption on a high-end server. Much of the latency is due to computationally intensive multi-million-bit modular multiplications. In this paper, we introduce two optimizations coupled with a novel precomputation technique. In the first optimization called partial FFT, we adopt Strassen’s FFT-based multiplication algorithm along with Barret reduction to speedup modular multiplications. For the encrypt primitive, we employ a window-based evaluation technique along with a modest degree of precomputation. In the full FFT optimization, we delay modular reductions and change the window algorithm, which allows us to carry out the bulk of computations in the frequency domain. We manage to eliminate all FFT conversion except the final inverse transformation drastically reducing the computation latency for all FHE primitives. We implemented the GH FHE scheme on two GPUs to further speedup the operations. Our experimental results with small parameter setting show speedups of 174, 7.6, and 13.5 times for encryption, decryption, and recryption, respectively, when compared to the Gentry–Halevi implementation. The speedup is enhanced in the medium setting. However, in the large setting, memory becomes the bottleneck and the speedup is somewhat diminished.