Multi-frequency Data Research Articles

Direct and inverse scattering in an optical waveguide*

Abstract In this paper, we study the direct and inverse scattering of the Schrödinger equation in a three-dimensional optical planar waveguide. For the direct problem, we derive a resonance-free region and resolvent estimates for the resolvent of the Schrödinger operator in such a geometry. Based on the analysis of the resolvent, several inverse problems are investigated. First, given the potential function, we prove the uniqueness of the inverse source problem with multi-frequency data. We also develop a Fourier-based method to reconstruct the source function. The capability of this method is numerically illustrated by examples. Second, the uniqueness and increased stability of an inverse potential problem from data generated by incident waves are achieved in the absence of the source function. To derive the stability estimate, we use an argument of quantitative analytic continuation in complex theory. Third, we prove the uniqueness of simultaneously determining the source and potential by active boundary data generated by incident waves. In these inverse problems, we only use the limited lateral Dirichlet boundary data at multiple wavenumbers within a finite interval.

VODCA v2: multi-sensor, multi-frequency vegetation optical depth data for long-term canopy dynamics and biomass monitoring

VODCA v2: multi-sensor, multi-frequency vegetation optical depth data for long-term canopy dynamics and biomass monitoring

A Multifrequency Data Fusion Deep Learning Model for Carbon Price Prediction

ABSTRACTIn response to the global need for effective management of carbon emissions and alignment with sustainable development goals, predicting carbon trading prices accurately is critical. This study introduces a multifrequency data fusion carbon price prediction model (MFF‐CPPM), addressing the nonlinear characteristics of carbon trading prices and inconsistent feature factor frequencies. The MFF‐CPPM consists of a feature‐extraction frontend, a multifrequency data fusion transformer, and a fusion regression layer, offering a novel methodological approach in forecasting studies. The model's validity was tested in Guangdong, China's largest carbon trading pilot market. The results demonstrated that the MFF‐CPPM outperformed baseline models in terms of carbon price‐prediction accuracy and trend forecasting. Additional trials conducted in Hubei and Beijing confirmed the model's robustness and generalization capabilities, providing valuable evidence of its effectiveness and reliability across varying market contexts. This study presents a novel predictive model for carbon trading prices, with a unique capability to harness data at differing frequencies. The MFF‐CPPM not only enhances forecasting accuracy but also offers an innovative approach to effectively incorporate multifrequency information. This advancement paves the way for flexible forecasting models in any scenario where data arrive at differing frequencies.

Satellite’s differential code bias conversion model between different IGS clock products using uncombined BDS-3 multi-frequency data

Satellite’s differential code bias conversion model between different IGS clock products using uncombined BDS-3 multi-frequency data

Lung Ultrasound Spectroscopy Applied to the Differential Diagnosis of Pulmonary Diseases: An In Vivo Multicenter Clinical Study.

Lung ultrasound (LUS) is an important imaging modality to assess the state of the lung surface. However, current LUS approaches are based on subjective interpretation of imaging artifacts, which results in poor specificity as quantitative evaluation lacks. The latter could be improved by adopting LUS spectroscopy of vertical artifacts. Indeed, parameterizing these artifacts with native frequency, bandwidth, and total intensity ( [Formula: see text]) already showed potentials in differentiating pulmonary fibrosis (PF). In this study, we acquired radio frequency (RF) data from 114 patients. These data (representing the largest LUS RF dataset worldwide) were acquired by utilizing a multifrequency approach, implemented with an ULtrasound Advanced Open Platform (ULA-OP). Convex (CA631) and linear (LA533) probes (Esaote, Florence, Italy) were utilized to acquire RF data at three (2, 3, and 4 MHz), and four (3, 4, 5, and 6 MHz) imaging frequencies. A multifrequency analysis was conducted on vertical artifacts detected in patients having cardiogenic pulmonary edema (CPE), pneumonia, or PF. These artifacts were characterized by the three abovementioned parameters, and their mean values were used to project each patient into a feature space having up to three dimensions. Binary classifiers were used to evaluate the performance of these three mean features in differentiating patients affected by CPE, pneumonia, and PF. Acquisitions of multifrequency data performed with linear probe lead to accuracies up to 85.43% in the differential diagnosis of these diseases (convex probes' maximum accuracy was 74.51%). Moreover, the results showed high potentials of mean [Formula: see text] (by itself or combined with other features) in improving LUS specificity.

CSEM Optimization Using the Correspondence Principle

Traditionally, 3D modeling of marine controlled-source electromagnetic (CSEM) data (in the frequency domain) involves high-memory demand, requiring solving a large linear system for each frequency. To address this problem, we propose to solve Maxwell’s equations in a fictitious dielectric medium with time-domain finite-difference methods, with the support of the correspondence principle. As an advantage of this approach, we highlight the possibility of its implementation for execution with GPU accelerators, in addition to multi-frequency data modeling with a single simulation. Furthermore, we explore using the correspondence principle to the inversion of CSEM data by calculating the gradient of the least-squares objective function employing the adjoint-state method to establish the relationship between adjoint fields in a conductive medium and their counterparts in the fictitious dielectric medium, similar to the approach used in forward modeling. We validate this method through 2D inversions of three synthetic CSEM datasets, computed for a simple model consisting of two resistors in a conductive medium, a model adapted from a CSEM modeling and inversion package, and the last one based on a reference model of turbidite reservoirs on the Brazilian continental margin. We also evaluate the differences between the results of inversions using the steepest descent method and our proposed momentum method, comparing them with the limited-memory BFGS (Broyden–Fletcher–Goldfarb–Shanno) algorithm (L-BFGS-B). In all experiments, we use smoothing by model reparameterization as a strategy for regularizing and stabilizing the iterations throughout the inversions. The results indicate that, although it requires more iterations, our modified momentum method produces the best models, which are consistent with results from the L-BFGS-B algorithm and require less storage per iteration.

A Long Short-Term Memory Approach to Incorporating Multifrequency Data Into Deep-Learning-Based Microwave Imaging

A Long Short-Term Memory Approach to Incorporating Multifrequency Data Into Deep-Learning-Based Microwave Imaging

Multiview Multistatic vs. Multimonostatic Three-Dimensional Ground-Penetrating Radar Imaging: A Comparison

The availability of multichannel ground-penetrating radar systems capable of gathering multiview, multistatic, multifrequency data provides novel chances to improve subsurface imaging results. However, customized data processing techniques and smart choices of the measurement setup are needed to find a trade-off between image quality and acquisition time. In this paper, we adopt a Born Approximation-based full 3D approach, which can manage multiview-multistatic, multifrequency data and faces the imaging as a linear inverse scattering problem. The inverse problem is solved by exploiting the truncated singular value decomposition as a regularization scheme. The paper presents a theoretical study aimed at assessing how the reconstruction capabilities of the imaging approach depend on the adopted measurement configuration. In detail, the performance achievable in the standard case of multimonostatic, multifrequency data is compared with that provided by a multiview-multistatic, multifrequency configuration, where the data are gathered by considering a progressively increasing number of transmitting antennas. The comparison of the achievable imaging performance is carried out by exploiting the spectral content and the point spread function, which are general tools to foresee the achievable reconstruction capabilities. Reconstruction results related to a numerical experiment based on full-wave data are also provided.

Improvement of BDS-3 inter-frequency clock bias estimation and its application in multi-frequency precise point positioning

BDS-3 broadcasts five civilian signals, establishing a fundamental basis for multi-frequency real-time precise point positioning (RT PPP). Nevertheless, the existence of inter-frequency clock bias (IFCB) renders the current satellite clock error product unsuitable for multi-frequency PPP processing. Consequently, there is a critical need to conduct a thorough analysis of BDS-3 IFCBs and propose real-time service methods for RT PPP users. In this study, 8-day BDS-3 multi-frequency data obtained from 130 International GNSS Service (IGS) stations are employed to scrutinize the characteristics of BDS-3 IFCBs and validate the proposed real-time service method. The results disclose a noticeable disparity between the constant part of IFCBs computed using the differential code bias (DCB) product and those estimated from observations. The time-varying parts of different IFCBs, estimated using various combinations, are examined using the Fast Fourier Transform (FFT). The outcomes indicate that these IFCBs exhibit identical periods of 12, 6, and 4 h, although their fourth-period terms differ. To model the sequences of IFCBs, a polynomial with a fourth-order harmonic model is utilized, and the coefficients of the fitted model are subsequently transmitted for RT PPP processing. Experimental results show that the predicted accuracies of IFCBs for most satellites exceed 90 %, albeit with a noticeable decline as the prediction time increases. When applied in RT PPP for 20 IGS stations, the method significantly shortens the convergence time in dual-frequency and triple-frequency RT PPP when predicted IFCBs are provided. In the B1C/B2a, B1C/B3I, and B1I/B2a dual-frequency combinations, the average convergence times for RT PPP are reduced by 58 %, 46 %, and 59 %, respectively. In the B1I/B2a/B3I triple-frequency combinations, it is reduced by 48 %.

Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Points (Part II): Near-Field Case in 3D

Imaging a Moving Point Source from Multifrequency Data Measured at One and Sparse Observation Points (Part II): Near-Field Case in 3D

Flux dependence of redshift distribution and clustering of LOFAR radio sources

We study the flux density dependence of the redshift distribution of low-frequency radio sources observed in the LOFAR Two-metre Sky Survey (LoTSS) deep fields and apply it to estimate the clustering length of the large-scale structure of the Universe, examining flux density limited samples (1 mJy, 2 mJy, 4 mJy and 8 mJy) of LoTSS wide field radio sources. We utilise and combine the posterior probability distributions of photometric redshift determinations for LoTSS deep field observations from three different fields (Boötes, Lockman hole and ELAIS-N1, together about $26$ square degrees of sky), which are available for between $91<!PCT!>$ to $96<!PCT!>$ of all sources above the studied flux density thresholds and observed in the area covered by multi-frequency data. We estimate uncertainties by a bootstrap method. We apply the inferred redshift distribution on the LoTSS wide area radio sources from the HETDEX field (LoTSS-DR1; about $424$ square degrees) and make use of the Limber approximation and a power-law model of three dimensional clustering to measure the clustering length, $r_0$, for various models of the evolution of clustering. We find that the redshift distributions from all three LoTSS deep fields agree within expected uncertainties. We show that the radio source population probed by LoTSS at flux densities above $1$ mJy has a median redshift of at least $0.9$. At $2$ mJy, we measure the clustering length of LoTSS radio sources to be $r_0 = (10.1 $Mpc in the context of the comoving clustering model. Our findings are in agreement with measurements at higher flux density thresholds at the same frequency and with measurements at higher frequencies in the context of the comoving clustering model. Based on the inferred flux density limited redshift distribution of LoTSS deep field radio sources, the full wide area LoTSS will eventually cover an effective (source weighted) comoving volume of about $10\ $ Gpc$^3$.

The time-variable ultraviolet sky: Active galactic nuclei, stars, and white dwarfs

Here, we present the first catalog of Ultraviolet time-VAriable sources (1UVA). We describe a new analysis pipeline called VAriable Source Clustering Analysis (VASCA). We applied this pipeline to ten years of data from the Galaxy Evolution Explorer (GALEX) satellite. We analyzed a sky area $ deg ^2$, and detected 4,202 time-variable ultraviolet (UV) sources. We cross-correlated these sources with multi-frequency data from the Gaia satellite and the Set of Identifications, Measurements and Bibliography for Astronomical Data (SIMBAD) database, finding an association for 3,655 sources. The source sample was dominated by active galactic nuclei ( percent ) and stars ( percent ). We examined the UV and multi-frequency properties of these sources, focusing on the stellar population. We found UV variability for four white dwarfs (WDs). One of them, WD J004917.14-252556.81, was recently found to be the most massive pulsating WD. Its spectral energy distribution shows no sign of a stellar companion. The observed flux variability was unexpected and difficult to explain.

A “MeerKAT-meets-LOFAR” study of the complex multi-component (mini-)halo in the extreme sloshing cluster Abell 2142

Context. Clusters of galaxies are known to be turbulent environments, whether they are merging systems where turbulence is injected via the conversion of gravitational potential energy into the intracluster medium (ICM), or whether they are relaxed systems in which small-scale core sloshing is occurring within the potential well. In many such systems, diffuse radio sources associated with the ICM are found: radio haloes and mini-haloes. Aims. Abell 2142 is a rich cluster undergoing an extreme episode of core sloshing, which has given rise to four cold fronts and a complex multi-component radio halo. Recent work revealed that there are three primary components to the halo that spans a distance of up to around 2.4 Mpc. The underlying physics of particle acceleration on these scales is poorly explored, and requires high-quality multi-frequency data with which to perform precision spectral investigation. We aim to perform such an investigation. Methods. We used new deep MeerKAT L-band (1283 MHz) observations in conjunction with LOFAR HBA (143 MHz) data as well as X-ray data from XMM-Newton and Chandra to study the spectrum of the halo and the connection between the thermal and non-thermal components of the ICM. Results. We confirm the presence of the third halo component, detecting it for the first time at 1283 MHz and confirming its ultra-steep spectrum nature, as we recovered an integrated spectrum of αH3, total = −1.68 ± 0.10. All halo components follow power-law spectra with increasingly steep spectra moving towards the cluster outskirts. We profiled the halo in three directions, finding evidence of asymmetry and spectral steepening along an axis perpendicular to the main axis of the cluster. Our investigation of the thermal non-thermal connection shows sub-linear correlations that are steeper at 1283 MHz than 143 MHz, and we find evidence of different connections in different components of the halo. In particular, we find both a moderate anti-correlation (H1, the core) and positive correlation (H2, the ridge) between the radio spectral index and X-ray temperature. Conclusions. Our results are broadly consistent with an interpretation of turbulent (re-)acceleration following an historic minor cluster merger scenario in which we must invoke some inhomogeneities. However, the anti-correlation between the radio spectral index and X-ray temperature in the cluster core is more challenging to explain; the presence of three cold fronts and a generally lower temperature may provide the foundations of an explanation, but detailed modelling is required to study this further.

Inverse modeling of frequency domain-based one-dimensional soil water flow in layered soils

Soils are heterogeneous at multiple scales. Estimates of spatially varying saturated hydraulic conductivity (Ks) of soils dictate the resolution of modeling water flux based on the Richardson-Richards equation (RRE), but direct measurements of Ks everywhere in a field are practically impossible. As a result, this study develops an inverse approach to estimate spatially varying Ks utilizing soil moisture observations driven by periodic weather variability at different frequencies. Using a numerical solution to vertical, one-dimensional RRE based on Gardner-Kozeny (GK) model in a heterogeneous soil with periodic flux, we investigate the spatial cross-correlation between Ks and observations (the amplitude or phase shift) of soil moisture fluctuation at different frequencies without high computational cost in the conventional time-domain model. These correlation patterns vary with the spatial location and frequency, suggesting that soil moisture fluctuations at different frequencies at one monitoring location carry non-redundant information about the heterogeneous distribution of Ks. Guided by cross-correlation maps, several inverse experiments reveal the effectiveness of multi-frequency data of soil moisture fluctuation for mapping the heterogeneous distribution of Ks. Monte Carlo simulations suggest that multi-frequency data can provide non-redundant and useful information about the estimation of heterogeneous Ks. Synthetic data based on a commonly-applied nonlinear van Genuchten-Mualem (VG) model is then tested in our inversion algorithm. The results indicate that the spatial pattern of the inverted GK Ks is very similar to that of the VG Ks, although these two parameters are inherently not identical since they are used in two different models. In addition, the inverted GK Ks can successfully predict the soil moisture fluctuation of frequencies that were not used in the inversion. Despite having no field experiments to validate this model, we believe this is the first attempt to conduct frequency-domain inverse modeling in vadose zone hydrology using soil moisture fluctuation.

Estimating above-ground biomass of trees outside forests using multi-frequency SAR data in the semi-arid regional landscape of southern India

Estimating above-ground biomass of trees outside forests using multi-frequency SAR data in the semi-arid regional landscape of southern India

Land cover mapping of mixed classes using 2D CNN with multi-frequency SAR data

Synthetic aperture radar (SAR) data obtained at multiple frequencies and polarizations offers valuable complementary information for classifying mixed classes that exhibit similar backscattering response. Although deep learning-based convolutional neural networks (CNNs) effectively extract features from multi-frequency SAR data, the arbitrary ordering of SAR features may hinder optimal convolution of the best feature sub-space for a specific class and underutilize available multi-frequency data. To address this, a novel CNN transforming SAR feature-space from 1-D to 2-D and employing varied dilation-rate convolutions is introduced. This transformation maximizes unique and localized feature combinations, efficiently utilizing the available feature sub-spaces and extracting discriminative features for accurate classifications, addressing the challenge of arbitrary band neighborhoods. Utilizing dual-polarization SAR data from ALOS-2 PALSAR-2 and Sentinel-1 sensors, the proposed CNN achieves an average f-score of 0.97 and a kappa coefficient of 0.97, an improvement of 11 %, 7 % and 3 % in OA compared to the 1-D, 2-D and 3-D CNN classifiers, without feature transformation. The classifier's generalization ability is evaluated using ground truth knowledge of various heterogeneous classes, and the proposed CNN classifier outperforms others in terms of accuracy metrics and generalization ability.

Multi-Frequency GPR Data Fusion through a Joint Sliding Window and Wavelet Transform-Weighting Method for Top-Coal Structure Detection

Top-coal structure detection is an important basis for realizing effective mining in fully mechanized cave faces. However, the top-coal structure is very complex and often contains multi-layer gangues, which seriously influence the level of effective mining. For these reasons, this paper proposes a novel multi-frequency ground-penetrating radar (GPR) data-fusing method through a joint sliding window and wavelet transform weighting method to accurately detect the top-coal structure. It possesses the advantages of both high resolution and great detection depth, and it can also integrate multi-frequency GPR data into one composite profile to interpret the internal structure information of top coal in detail. The detection procedure is implemented following several steps: First of all, the multi-frequency GPR data are preprocessed and aligned through a band-pass filter and a zero offset elimination method to establish their spatial correspondences. Secondly, the proposed method is used to determine the time-varying weight values of each frequency GPR signal according to the wavelet energy proportion within the sliding window; also, the edge detection algorithm is introduced to improve the fusion efficiency of the wavelet transform so as to realize the effective fusion of the multi-frequency GPR data. Thirdly, a reflection intensity model of multi-frequency GPR signals traveling in the top-coal is established by using the stratified identification method, and then, the detailed top-coal structure can be inversely interpreted. Finally, the quantitative evaluation criteria, information entropy (IE), space–frequency (SF) and Laplacian gradient (LG), are used to evaluate the multi-frequency GPR data fusion’s effectiveness in laboratory and field environments. The experimental results show that, compared with the genetic, time-varying and wavelet transform fusion method, the fusion performance of the presented method possesses higher values in the IE, SF and LG evaluation criteria, and it also has both the merits of high resolution and great detection depth.

Ordered magnetic fields around the 3C 84 central black hole

Context. 3C 84 is a nearby radio source with a complex total intensity structure, showing linear polarisation and spectral patterns. A detailed investigation of the central engine region necessitates the use of very-long-baseline interferometry (VLBI) above the hitherto available maximum frequency of 86 GHz. Aims. Using ultrahigh resolution VLBI observations at the currently highest available frequency of 228 GHz, we aim to perform a direct detection of compact structures and understand the physical conditions in the compact region of 3C 84. Methods. We used Event Horizon Telescope (EHT) 228 GHz observations and, given the limited (u, v)-coverage, applied geometric model fitting to the data. Furthermore, we employed quasi-simultaneously observed, ancillary multi-frequency VLBI data for the source in order to carry out a comprehensive analysis of the core structure. Results. We report the detection of a highly ordered, strong magnetic field around the central, supermassive black hole of 3C 84. The brightness temperature analysis suggests that the system is in equipartition. We also determined a turnover frequency of νm = (113 ± 4) GHz, a corresponding synchrotron self-absorbed magnetic field of BSSA = (2.9 ± 1.6) G, and an equipartition magnetic field of Beq = (5.2 ± 0.6) G. Three components are resolved with the highest fractional polarisation detected for this object (mnet = (17.0 ± 3.9)%). The positions of the components are compatible with those seen in low-frequency VLBI observations since 2017–2018. We report a steeply negative slope of the spectrum at 228 GHz. We used these findings to test existing models of jet formation, propagation, and Faraday rotation in 3C 84. Conclusions. The findings of our investigation into different flow geometries and black hole spins support an advection-dominated accretion flow in a magnetically arrested state around a rapidly rotating supermassive black hole as a model of the jet-launching system in the core of 3C 84. However, systematic uncertainties due to the limited (u, v)-coverage, however, cannot be ignored. Our upcoming work using new EHT data, which offer full imaging capabilities, will shed more light on the compact region of 3C 84.

Studies of the NGC315 galaxy and the distribution of extragalactic objects around it

Studies of extended extragalactic radio sources have an important feature and significance for forming an opinion about the distribution of matter in the Universe. The galaxy NGC 315 is an extended radio source within which there are many compact radio sources that form its intensity. Studies of this galaxy and its surroundings assume that although there are many sources in the NGC 315 immediate vicinity, in its wider 6° circumferences, there is a deficiency of extragalactic sources, and this deficiency is more clearly expressed at distances between 0.8 and 2.2 redshifts. Considering the distribution of extragalactic sources in this region, we can state that this does not give grounds to consider the distribution in the Universe to be uniform, which indicates the heterogeneity of the Universe, although some doubts remain here. To solve this problem, it is necessary to carry out non-standard, more sensitive, and targeted multi-frequency observations, which will allow obtaining such results that will make the identification of the obtained multi-frequency data more reliable. One of the possible promising directions for solving this problem is, in particular, the possibility of using microchannel plates (MCPs) as radiation detectors, the technology of which has begun to develop rapidly in recent years.

Error estimation to the direct sampling method for the inverse acoustic source problem with multi-frequency data

Error estimation to the direct sampling method for the inverse acoustic source problem with multi-frequency data