Aperture Field Research Articles

Analysis and Generation of Rough-Surfaced Fractures with Variable Aperture Based on Self-Affine Methods Using Surface Scan Measurements

Abstract Methods founded on self-affine principles have successfully been used to generate synthetic rough-surfaced fractures, which can be based on properties inferred from measurements of fracture surfaces. Two key parameters, the Hurst exponent H and a scaling parameter Sp, together with a function describing the correlation between the surfaces forming the fracture, are needed. There are several methods for determining H and Sp in the literature, which are primarily adopted for measurements of 1-dimensional fracture traces. However, comparatively few studies have used these methods and applied them to aperture generation. In this study, we evaluate two commonly employed methods, the root-mean-square correlation function (RMS-COR) and the Fourier power spectrum (FPS) approach, each with several variations of their possible implementation when applied to measurements of fracture surfaces. We use high-resolution surface scans of a natural fracture sample to obtain an accurate representation of the aperture field and rough surfaces. Multiple realisations of aperture fields are generated for each method variation and their respective ensembles are evaluated against the aperture distribution of the measured fracture sample. For the fracture studied, the RMS-COR method is the most accurate method for obtaining H and Sp. We show that a linear relationship exists between H and Sp which provides a best fit of synthetically generated fractures when compared to the measured sample. Additionally, we introduce an improved approach for representing the correlation function between the two rough surfaces. Finally, we demonstrate that the model can successfully generate upscaled fracture apertures based on restricted subsections of the sample.

Time-dependent 3-D caustic beams over arbitrary trajectories.

In this study, we introduce a method for synthesizing a time-dependent caustic beam along a generic beam-axis trajectory with arbitrary curvature and torsion. Our approach evaluates the pulsed aperture field that radiates the beam along a predefined trajectory by constructing a time-dependent caustic surface around the beam-axis skeleton. Initially, we derive the aperture field delay to form a caustic of rays along the beam-axis, extending this to other points over the aperture to construct a smooth caustic surface for points near the beam-axis. The amplitude is selected to confine the transverse (off-axis) beam. We also provide a theoretical analysis of the pulsed caustic beam propagation speed along the curved beam-axis. Finally, we present several numerical examples demonstrating the method's ability to synthesize aperture field distributions that generate pulsed beams propagating along trajectories with various curvatures and torsions.

Novel Unified Model for Geofluid Nonlinear Flows in Rock Fractures

AbstractIn this study, we numerically investigated the multi‐scale flow features of 43 types of geofluids (including 18 real geofluids and 25 parametric fluids) within rock fractures under different roughness and hydrodynamic conditions. Our findings demonstrate that the generalized Forchheimer equation, an extension of Darcy's law for nonlinear flows, effectively captures the nonlinear flow features of these diverse fluids. While changes in fluid properties have minimal impact on Darcy's viscous permeability, they significantly influence Forchheimer inertial permeability and the critical Reynolds number. These dependencies are mechanistically attributed to the regulation of eddy growth rate in fractures by fluid properties. Building on these mechanistic insights, we developed two types of models for predicting inertial permeability and critical Reynolds number across various geofluids within a unified framework. One model extrapolates predictions from the results of classical standard water flow, while another enables direct prediction based on the mean and variance of the fracture aperture field.

Electromagnetic fields transformation in UWB infinite antenna arrays in the cluster excitation mode

Infinite ultra-wideband (UWB) arrays of TEM horns and Vivaldi antennas were considered. At the first stage we used an array model in the quasi-periodic excitation mode in the form of a Floquet channel. It was implemented in the HFSS electromagnetic modeling system. At the second stage the array parameters in the cluster excitation mode were determined using the calculated scattering matrix of the Floquet channel. Two clusters of TEM horns and Vivaldi antennas were analyzed. They were finite along one coordinate and infinite along the other. It was investigated how the cluster size, frequency, amplitude distribution of exciting waves, scanning in the sector of angles affect the shape of the amplitude-phase distribution of the field in the array aperture. It was shown that the field distribution in the emitting aperture may differ significantly from the distribution of exciting waves at the inputs of the array elements. An explanation of this effect based on the representation of the field in the array in the form of a superposition of its eigen waves was proposed.

Far-field Pattern Analysis Based on Piecewise Aperture Field Integration for Leighton Chajnantor Telescope Antenna under Gravity and Wind Load

The Caltech Submillimeter Observatory telescope will be relocated from Mauna Kea, Hawaii to Chajnantor Plateau, Chile, refurbished there and renamed the Leighton Chajnantor Telescope (LCT). At the new site, the open-air environment, as well as the high altitude, will amplify the influence of gravity and wind load on structural deformation, thus affecting the antenna’s radiation characteristics, which can be characterized by a far-field pattern. To quickly and accurately compensate for the effect of reflector structural deformation on the far-field pattern of LCT’s antenna, we propose a far-field pattern quick calculation method (FPQCM) to analyze the antenna’s radiation characteristics under gravity and various wind loads, which combines the optical path difference calculation method on the aperture plane, the piecewise Zernike polynomial function, and the piecewise aperture field integration method. Through extensive experimental comparisons with the numerical method based on physical optics and physical theory of diffraction, it is validated that the proposed FPQCM significantly reduces the time by more than 100 times for acquiring the far-field patterns while maintaining the accuracy of the main figure of merits at the highest frequency (i.e., 856 GHz). In addition, we analyzed the far-field pattern of the antenna at different zenith angles, gravity, and winds of different strengths and directions by FPQCM, which provided guidance for performing more precise control through an active surface optimization system after LCT resumes operation, thus facilitating the acquisition of higher surface accuracy and better observation effect.

Advancements in coupled processes numerical models: Upscaling aperture fields using spatial continuity

Fluid flow through fractured geological media is crucial in addressing the challenges posed by climate change, resource management, and energy exploration. Numerical models commonly employ fracture surface representations and aperture distribution models to simulate these processes. However, conventional statistical approaches often overlook the inherent spatial continuity and directionality within fracture data, impacting the accuracy of aperture geometry and subsequent flow simulations. This study investigates the benefits of incorporating spatial continuity information, derived from semi-variogram analysis, into numerical models. A Freiberg gneiss fracture aperture field was upscaled using both spatial continuity-informed and traditional arithmetic averaging methods. The comparative analysis reveals that incorporating spatial continuity during the upscaling process yields notable improvements in the accuracy of flow simulations, particularly when employing coarser mesh resolutions. This approach presents a promising alternative for enhancing the representation of fracture and aperture fields in numerical modeling across diverse applications, promoting a deeper understanding of fluid flow behavior in complex geological systems.

Aperture Field Anisotropy Control on Immiscible Displacement Patterns in Rough Fractures

AbstractTwo‐phase flow displacement in rock fractures is crucial for various subsurface mass transfer processes and engineering applications. In fractures, the displacement of a less viscous fluid by a more viscous one (i.e., viscosity ratio M > 1) involves viscous forces help stabilizing the displacement front in presence of capillary pressure fluctuations. Although previous studies have reported displacement patterns in isotropic fractures, the impact of anisotropic fractures on displacement patterns has not been systematically examined. In this study, we conducted flow‐rate‐controlled drainage experiments to examine how anisotropic aperture fields affect displacement patterns. We observed the transition of displacement patterns from capillary fingering (CF) to crossover zone (CZ) to compact displacement pattern (CD) based on variations in transverse pore‐filling event (TPFE) frequency, which characterizes the competition between capillary and viscous forces. Increasing aperture correlation length in the transverse direction leads to increased TPFE frequency at a low flow rate, destabilizing displacement front. While the increasing aperture correlation length in longitudinal direction suppressed TPFE frequency, stabilizing displacement front. Therefore, the critical capillary number (CaCF‐CZ), which indicates the onset of the CF‐CZ transition, decreases as the aperture field varies from transversely to longitudinally correlated. At high flow rates, TPFEs almost disappeared, indicating that anisotropy did not affect CZ‐CD transition (CaCZ‐CD). Furthermore, we modified theoretical models of CaCF‐CZ and CaCZ‐CD by incorporating the aperture anisotropy factor, achieving a good fit with the experimental data. This study demonstrates the critical role of aperture field anisotropy in controlling two‐phase displacement patterns and provides a theoretical framework for predicting multiphase flow behavior in natural fractures.

High–precision determination of carbon stable isotope in silicate glasses by secondary ion mass spectrometry: Evaluation of international reference materials

Secondary ion mass spectrometry (SIMS) has been used for isotope analysis of volatile components dissolved in silicate melts for decades. However, carbon in situ stable isotope analysis in natural silicate glasses has remained particularly challenging, with the few published attempts yielding high uncertainties. In this context, we characterized 31 reference silicate glasses of basaltic and basanitic compositions, which we then used as reference materials to calibrate δ13C − value analyses in silicate glasses by SIMS. This set of reference materials covers a wide range of CO2 concentrations (380 ppm – 12,000 ppm) and δ13C values (−28.1 ± 0.2 to −1.1 ± 0.2 ‰, ±1σ). The sets of reference materials were analyzed using large−geometry SIMS at two ion microprobe facilities to test reproducibility across different instrumental setups. The instrumental mass fractionation (IMF) varied widely with two different large−geometry SIMS instruments as well as with different analytical parameters such as field aperture size and primary beam intensity. We found that a precision better than ±1.1 ‰ (both average internal and external precision, ±1σ) for CO2 content higher than 1800 ppm could be achieved using a primary beam intensity of less than 5 nA, resulting in a final spot size of 10–20 μm, allowing precise analysis of δ13C in mineral−hosted melt inclusions. This level of precision was achieved at CO2 concentrations as low as 1800 ppm. This advance opens a wide range of new possibilities for the study of δ13C − value in mafic melts and their mantle sources. The reference materials are now available at the CNRS–CRPG ion microprobe facility in Nancy, France and will be deposited at the Smithsonian National Museum of Natural History, Washington, USA where they will be freely available on loan to any researcher.

Orthonormal aberration decomposition for circular aperture and rectangular field with extension to multiple-aperture systems

A new set of orthogonal polynomials and the traditional Zernike polynomials are combined to construct the wavefront of the sparse aperture (SA) optical system. The new set of orthogonal polynomials in the rectangular domain is derived based on the Zernike polynomials. The modulation transfer functions (MTFs) of the SA system under different fields of view are calculated. The effects of some wavefront terms on the field-related MTF are analyzed. Imaging simulation and restoration are conducted for the SA system. The results indicate that the wavefront of the SA system can be represented by the combination of the new set of orthogonal polynomials and the Zernike polynomials. The former represents the field term, and the latter represents the pupil term of the wavefront. The field-related Wiener filter is constructed to restore the imaging results of the SA system, and the results show that the image quality can be improved greatly through restoration.

Surface Rupture and Fault Characteristics Associated With the 2020 Magnitude (MW) 6.6 Masbate Earthquake, Masbate Island, Philippines

AbstractOn 18 August 2020, Masbate Island was struck by a magnitude (MW) 6.6 earthquake. This seismic event represents the second occurrence of a strong earthquake (M > 6) in 17 years, emphasizing the necessity for further investigation into the characteristics of this event. In this study, we employ Interferometric Synthetic Aperture Radar, seismicity analysis, and field investigations to comprehensively characterize the coseismic and postseismic slip associated with the event. Our findings reveal a 50‐km‐long fault rupture along the Masbate segment of the Philippine Fault, with ∼23 km surface rupture mapped onshore, despite the occurrence of interseismic creep. The slip distribution demonstrates decreasing displacements northwestward toward the creeping section, with a maximum left‐lateral displacement of 0.97 m near the epicenter. Toward the southeast offshore, the rupture terminates at a left stepover of a fault. While the surface rupture appears relatively straight and narrowly concentrated, the secondary ruptures and mapped offshore faults reveal a more complex transtensional fault structure in the southeastern part of Masbate Island. This fault complexity represents an asperity that facilitates high‐stress accumulation and rupture initiation. Postseismic slip persists for several months along the onshore creeping segment. Based on comprehensive measurements of both cumulative and coseismic slip along the Masbate fault segment, we calculate a slip rate ranging between 2.8 and 3.8 cm/year and a recurrence interval of 16–41 years for earthquakes similar to the 2020 earthquake. Our study highlights how heterogeneity in fault properties, including geometry and coupling state, influences the distribution of slip and magnitude of earthquakes. The 2020 Masbate earthquake provides valuable insights into the rupture dynamics and fault behavior of the Philippine Fault in the Masbate region.

A broad-beam reflective metasurface enhancing signal coverage for indoor wireless communication

ABSTRACT A broad-beam planar reflective metasurface design for indoor signal coverage is presented in this letter. The proposed metasurface unit is designed as a multi-resonant structure using an additional branch on the double ring, which achieves a reflection phase shift covering 360° and a reflection magnitude remaining above 0.8 by varying the length of the square ring. To simplify the array configuration, the unit incorporates 2-bit phase quantization. In order to broaden the reflection beam of metasurface, the phase distribution of the array is determined by the aperture field superposition method. The angles of the different electromagnetic (EM) waves within the single aperture are adjusted to be moderately distinct. The co-simulation and measurement of the horn antenna and the reflective metasurface are carried out. The results show that the metasurface can generate a broad beam at 4.8 GHz with a 3 dB beamwidth of 21°, achieving a beam gain of 18dBi. The broad beam can maintain a 3 dB beamwidth greater than 19° in the 4.2–5.6 GHz band. The reflective metasurface can be used as a passive repeater to optimize signal quality and enhance wireless communication coverage in indoor non-line-of-sight (NLOS) paths.

Selecting Appropriate Model Complexity: An Example of Tracer Inversion for Thermal Prediction in Enhanced Geothermal Systems

AbstractA major challenge in the inversion of subsurface parameters is the ill‐posedness issue caused by the inherent subsurface complexities and the generally spatially sparse data. Appropriate simplifications of inversion models are thus necessary to make the inversion process tractable and meanwhile preserve the predictive ability of the inversion results. In this study, we investigate the effect of model complexity on fracture aperture inversion and thermal performance prediction in a field‐scale EGS model. Principal component analysis was used to map the aperture field to a low‐dimensional latent space. The complexity of the inversion model was quantitatively represented by the percentage of total variance in the original aperture fields preserved by the latent space. Tracer, pressure and flow rate data were used to invert for fracture aperture through an ensemble‐based inversion method, and the inferred aperture field was used to predict thermal performance. With an over‐simplified aperture model, ensemble collapse occurred. The inverted aperture models failed to resolve necessary flow and transport features, leading to a biased thermal performance prediction. A complex aperture model involved excessive features and was prone to overinterpreting the inversion data. Both the tracer/pressure/flow rate data reproduction and thermal prediction showed significant uncertainties, making it difficult to properly estimate long‐term thermal performance. Fortunately, our results indicate that there exists an appropriate model complexity which can simultaneously match inversion data and predict thermal performance with an acceptable uncertainty. The quality of the fit of tracer data appears to be a useful indicator of such an appropriate model complexity.

Deep learning-based inversion framework by assimilating hydrogeological and geophysical data for an enhanced geothermal system characterization and thermal performance prediction

Enhanced geothermal systems (EGS), which are developed by creating artificial fractures to enhance the permeability of deep reservoir, show their its advantage in power generation. However, due to the limited wells in deep depth, characterizing fractured geothermal reservoirs with sparse data is difficult and poses challenges for long-term thermal performance prediction. Interpreting observation data through inversion to characterize the fracture aperture and predict EGS long-term thermal performance is a hopeful scheme. Thus, a joint inversion framework, convolutional variational autoencoder-ensemble smoother with multiple data assimilation (CVAE-ESMDA), is proposed with the following aspects: (i) CVAE is trained to parameterize the high-dimensional Non-Gaussian aperture field, (ii) ESMDA is applied to integrate hydrogeological and geophysical data for aperture characterization. Based on the inversion results, the long-term performance is predicted. The normalized root mean square errors (NRMSEs) of inversion results decrease from 27.66 % to 24.52 % after multi-type data are integrated for CVAE-ESMDA. Furthermore, the NRMSEs of long-term thermal prediction of two production wells also decrease to only 2.3 % and 8.2 %. To further exhibit the advantages of CVAE-ESMDA, another joint inversion framework, principal component analysis (PCA)-ESMDA, is also compared. However, PCA is limited in addressing Non-Gaussian aperture field and its long-term thermal prediction performance is unsatisfactory.

An analytic expression for the field dependence of three-order Zernike aberrations in decentered and/or tilted optical systems

The double Zernike polynomials can describe the aperture dependence and field dependence of non-coaxial optical system aberrations simultaneously, and characterize the complex optical aberrations, which are of great value in the optical system design and alignment. In this paper, the specific analytic forms of all third-order double Zernike aberrations in decentered and/or tilted optical systems are derived based on the nodal aberration theory. This paper realizes the orthogonalization of the third-order aberrations with different aperture dependence and field dependence. The calculation process of the third-order double Zernike aberrations is presented. The ray tracing of the Cassegrain telescope verifies the analytic derivation of the double Zernike aberrations.

Effects of thermoelasticity induced aperture variation on performances of Enhanced geothermal system

Geothermal energy, as one of the renewable energy types, has great potential to balance the variable energy supply from photovoltaic and wind energy types. This, however, requires the development of an Enhanced Geothermal System (EGS). Injecting cold water into deep geo-reservoirs induces thermoelastic deformation and changes the fracture apertures, which may significantly affect the EGS lifetime and energy performance. In this case, this study develops a fully coupled thermal–hydraulic-mechanical model to investigate the impacts of temperature, pressure, and aperture heterogeneity on the alterations of fracture aperture. Then, considering the reservoir lifespan, the research takes a further step into the influence of heterogeneous aperture variation on EGS production temperature and long-term energy performance. Results show that aperture significantly varies once a temperature breakthrough occurs in the production well for both homogeneous and heterogeneous aperture fields. The thermoelasticity-induced aperture variations enhance water flow rate, leading to a considerable increase in reservoir heat production rate, but a shorter EGS lifespan. Furthermore, temperature variation shows a more substantial influence on aperture alteration compared to pressure change. Additionally, a sensitivity analysis indicates that the 30-year total energy output is proportional to the injection/production pressures and injection temperatures. However, the fracture with either excessively large or small initial apertures leads to worse EGS energy performance.

Visual Field Restriction in the Recognition of Basic Facial Expressions: A Combined Eye Tracking and Gaze Contingency Study.

Uncertainties and discrepant results in identifying crucial areas for emotional facial expression recognition may stem from the eye tracking data analysis methods used. Many studies employ parameters of analysis that predominantly prioritize the examination of the foveal vision angle, ignoring the potential influences of simultaneous parafoveal and peripheral information. To explore the possible underlying causes of these discrepancies, we investigated the role of the visual field aperture in emotional facial expression recognition with 163 volunteers randomly assigned to three groups: no visual restriction (NVR), parafoveal and foveal vision (PFFV), and foveal vision (FV). Employing eye tracking and gaze contingency, we collected visual inspection and judgment data over 30 frontal face images, equally distributed among five emotions. Raw eye tracking data underwent Eye Movements Metrics and Visualizations (EyeMMV) processing. Accordingly, the visual inspection time, number of fixations, and fixation duration increased with the visual field restriction. Nevertheless, the accuracy showed significant differences among the NVR/FV and PFFV/FV groups, despite there being no difference in NVR/PFFV. The findings underscore the impact of specific visual field areas on facial expression recognition, highlighting the importance of parafoveal vision. The results suggest that eye tracking data analysis methods should incorporate projection angles extending to at least the parafoveal level.

Compact Series-fed Circularly-polarized Patch Array basedon Microstrip Line

A compact single-layer circularly polarized (CP) antenna array is proposed in this paper for 5G/6G applications. The conventional microstrip line is modified as a feeding network by periodically and alternatively loading field blocking stubs, producing a linearly polarized in-phase radiative field aperture. By adding CP corner-truncated patches beside these in-phase fields, a linear high-gain CP antenna array excited by a single feed is obtained. The feasibility of the proposed design is demonstrated through the fabrication and measurement of a 16-element linear array. The results indicate that the 3 dB axial ratio bandwidth is 3.5% (19.60∼20.30 GHz), the -10 dB impedance bandwidth totally covers the 3 dB axial ratio bandwidth, and the peak realized gain is 14.9 dBi under an antenna length of 5.69λ0. This proposed strategy provides a very compact antenna structure to achieve high-gain CP radiation without the requirement of impedance transformers, phase shifters, and open-stop-band suppressing measures. Moreover, the antenna has a per-unit-length CP gain of 5.5/λ0, which is superior to many single-layer high-gain CPantennas.

A Quick Calculation Method for Radiation Pattern of Submillimeter Telescope with Deformation and Displacement

Radiation pattern captures the electromagnetic performance of reflector antennas, which is significantly affected by the deformation of the primary reflector due to gravity and the displacement of the secondary reflector. During the design process of large reflector antennas, a substantial amount of time is often dedicated to iteratively adjusting structural parameters and validating electromagnetic performance. To improve the efficiency of the design process, we first propose an approximate calculation method of optical path difference (OPD) for the deformation of the primary reflector under gravity and the displacement of the secondary reflector. Then an OPD fitting function based on the modified Zernike polynomials is proposed to capture the phase difference of radiation over the aperture plane, based on which the radiation pattern will be obtained quickly by the aperture field integration method. Numerical experiments demonstrate the effectiveness of the proposed quick calculation method for analyzing the radiation pattern of a 10.4 m submillimeter telescope antenna at its highest operating frequency of 856 GHz. In comparison with the numerical simulation method based on GRASP (which is an antenna electromagnetic analysis tool combining physical optics (PO) and physical theory of diffraction (PTD)), the quick calculation method reduces the time for radiation pattern analysis from more than one hour to less than two minutes. Furthermore, the quick calculation method exhibits excellent accuracy for the figure of merit (FOM) of the radiation pattern. Therefore, the proposed quick calculation method can obtain the radiation pattern with high speed and accuracy. Compared to the time-consuming numerical simulation method (PO and PTD), it can be employed for quick analysis of the radiation pattern for the lateral displacement of the secondary reflector and the deformation of the primary reflector under gravity in the design process of a reflector antenna.

Determining Aperture Field for Arbitrary Phaseless Far-Field Utilizing Inverse Design Method Based on Spectral Analysis

Determining Aperture Field for Arbitrary Phaseless Far-Field Utilizing Inverse Design Method Based on Spectral Analysis

Simultaneous sensing profiles of beam attenuation coefficient and volume scattering function at 180° using a single-photon underwater elastic-Raman lidar.

Lidar has emerged as a promising technique for vertically profiling optical parameters in water. The application of single-photon technology has enabled the development of compact oceanic lidar systems, facilitating their deployment underwater. This is crucial for conducting ocean observations that are free from interference at the air-sea interface. However, simultaneous inversion of the volume scattering function at 180° at 532 nm (βm) and the lidar attenuation coefficient at 532 nm (K l i d a r m) from the elastic backscattered signals remains challenging, especially in the case of near-field signals affected by the geometric overlap factor (GOF). To address this challenge, this work proposes adding a Raman channel, obtaining Raman backscattered profiles using single-photon detection. By normalizing the elastic backscattered signals with the Raman signals, the sensitivity of the normalized signal to variations in the lidar attenuation coefficient is significantly reduced. This allows for the application of a perturbation method to invert βm and subsequently obtain the K l i d a r m. Moreover, the influence of GOF and fluctuations in laser power on the inversion can be reduced. To further improve the accuracy of the inversion algorithm for stratified water bodies, an iterative algorithm is proposed. Additionally, since the optical telescope of the lidar adopts a small aperture and narrow field of view design, K l i d a r m tends to the beam attenuation coefficient at 532 nm (cm). Using Monte Carlo simulation, a relationship between cm and K l i d a r m is established, allowing cm derivation from K l i d a r m. Finally, the feasibility of the algorithm is verified through inversion error analysis. The robustness of the lidar system and the effectiveness of the algorithm are validated through a preliminary experiment conducted in a water tank. These results demonstrate that the lidar can accurately profile optical parameters of water, contributing to the study of particulate organic carbon (POC) in the ocean.