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    The advent of fast sensing technologies allow for real-time model updates in many applications where the model parameters are uncertain. Once the observations are collected, Bayesian algorithms offer a pathway for real-time inversion (a.k.a. model parameters/inputs update) because of the flexibility of the Bayesian framework against non-uniqueness and uncertainties. However, Bayesian algorithms rely on the repeated evaluation of the computational models and deep learning (DL) based proxies can be useful to address this computational bottleneck. In this paper, we study the effects of the approximate nature of the deep learned models and associated model errors during the inversion of borehole electromagnetic (EM) measurements, which are usually obtained from logging while drilling. We rely on the iterative ensemble smoothers as an effective algorithm for real-time inversion due to its parallel nature and relatively low computational cost. The real-time inversion of EM measurements is used to determine the subsurface geology and properties, which are critical for real-time adjustments of the well trajectory (geosteering). The use of deep neural network (DNN) as a forward model allows us to perform thousands of model evaluations within seconds, which is very useful to quantify uncertainties and non-uniqueness in real-time. While significant efforts are usually made to ensure the accuracy of the DL models, it is widely known that the DNNs can contain some type of model-error in the regions not covered by the training data, which are unknown and training specific. When the DL models are utilized during inversion of EM measurements, the effects of the model-errors could manifest themselves as a bias in the estimated input parameters and as a consequence might result in a low-quality geosteering decision. We present numerical results highlighting the challenges associated with the inversion of EM measurements while neglecting model-error. We further demonstrate the utility of a recently proposed flexible iterative ensemble smoother in reducing the effect of model-bias by capturing the unknown model-errors, thus improving the quality of the estimated subsurface properties for geosteering operation. Moreover, we describe a procedure for identifying inversion multimodality and propose possible solutions to alleviate it in real-time.

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  3. Abstract

    Recent advances in wavefront shaping have enabled complex classes of Structured Light which carry spin and orbital angular momentum, offering new tools for light-matter interaction, communications, and imaging. Controlling both components of angular momentum along the propagation direction can potentially extend such applications to 3D. However, beams of this kind have previously been realized using bench-top setups, requiring multiple interaction with light of a fixed input polarization, thus impeding their widespread applications. Here, we introduce two classes of metasurfaces that lift these constraints, namely: i) polarization-switchable plates that couple any pair of orthogonal polarizations to two vortices in which the magnitude and/or sense of vorticity vary locally with propagation, and ii) versatile plates that can structure both components of angular momentum, spin and orbital, independently, along the optical path while operating on incident light of any polarization. Compact and integrated devices of this type can advance light-matter interaction and imaging and may enable applications that are not accessible via other wavefront shaping tools.

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  4. Abstract

    Optical phase singularities are zeros of a scalar light field. The most systematically studied class of singular fields is vortices: beams with helical wavefronts and a linear (1D) singularity along the optical axis. Beyond these common and stable 1D topologies, we show that a broader family of zero-dimensional (point) and two-dimensional (sheet) singularities can be engineered. We realize sheet singularities by maximizing the field phase gradient at the desired positions. These sheets, owning to their precise alignment requirements, would otherwise only be observed in rare scenarios with high symmetry. Furthermore, by applying an analogous procedure to the full vectorial electric field, we can engineer paraxial transverse polarization singularity sheets. As validation, we experimentally realize phase and polarization singularity sheets with heart-shaped cross-sections using metasurfaces. Singularity engineering of the dark enables new degrees of freedom for light-matter interaction and can inspire similar field topologies beyond optics, from electron beams to acoustics.

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  7. Indigenous societies adopted horses of primarily Spanish origin before Europeans arrived in the Great Plains and the American West. 
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    Free, publicly-accessible full text available March 31, 2024