Inversion Algorithm Research Articles

A sequence decomposition genetic algorithm for petrophysical inversion with spatial correlation

Predicting petrophysical properties based on seismic attributes is essential for accurate subsurface characterization. Typically, a forward model is first established to relate petrophysical properties to geophysical measurements, and then the petrophysical properties are inverted from actual measurements. Imposing prior constraints of spatial relationship is also desirable to regularize the ill-posed inverse problem. However, petrophysical inversion involving spatial correlation presents a high-dimensional optimization problem with multiple local extrema. This problem can be challenging to solve, particularly when discrete variables (such as lithofacies) and continuous variables (such as porosity and fluid saturation) are considered together. Therefore, we propose a global optimization algorithm that utilizes Markov chain decomposition and a genetic algorithm for joint discrete-continuous petrophysical inversion with spatial correlation. The innovation of this algorithm is to spatially decouple the sequence optimization problem into multiple low-dimensional sub-problems and overcome the initial value dependence to converge to the global optimal solution. Furthermore, an approximation operation is introduced to expedite the optimization algorithm. Numerical experiments demonstrate that after algorithmic acceleration, the spatially correlated inversion requires the same computational time as a simple spatially uncorrelated inversion and achieves significantly better accuracy than the latter. Finally, we apply the method to a case study in East China, where lithofacies, clay content, porosity, and water saturation are inferred from the data of wave velocities and density. The inversion results around the wells generally match the well logging data, verifying the feasibility of the new method.

3-D imaging of whole-space environments with electromagnetic induction sensors based on linear approximation

Accurate mapping of the periphery of tunnel has become an essential step in underground mining and engineering. Because of high sensitivity to electric conductivity and magnetic permeability, the whole-space electromagnetic (EM) method has played an important role in geological forecast of groundwater and exploration of mineral ore. However, obtaining a three-dimensional (3-D) image of the whole-space EM method by 3-D inversion is challenging due to the limited observation space and inefficiencies in 3-D forward modeling algorithms. While 1-D inversion algorithms have long been used to map the periphery of the tunnel, various 3-D inversion algorithms have been successfully applied in other scenarios. Recently, the portable frequency domain loop-loop EM induction (EMI) measurement has been considered as an active source magnetic method in near surface surveys, because of the dominance of magnetic permeability in the in-phase (IP) response. The 3-D linear forward modeling method is developed based on the location-specific magnetic sensitivity function, and the 3-D inversion algorithm has been effectively employed for mapping magnetic anomalies in large-scale area. In this study, we intend to demonstrate that the EMI measurement can give 3-D image of the periphery of the tunnel by theory and numerical experiments. The IP response of EMI in whole-space is separated into three parts, and the 3-D linear forward modeling method is examined by analytical solution. The 1-D Fourier transform is used to accelerate the 3-D forward modeling, and the 3-D inversion show a good performance of mapping the magnetic abnormal bodies in underground space.

Accurate detection method of traveling wave shape based on EEMD and L1 norm regularization

Aiming at the problem of waveform distortion of the secondary traveling wave obtained from the primary traveling wave signal transmitted by the voltage traveling wave sensor, an accurate detection method of voltage traveling wave based on ensemble empirical mode decomposition (EEMD) and L1 norm least squares regularization is proposed in this paper. Firstly, the forward transfer function model of the specialized voltage traveling wave sensor is established, and the inversion model is derived to analyze the phase frequency and amplitude frequency characteristics of the secondary traveling wave after transmission. EEMD is used to decompose the secondary traveling wave into the intrinsic modal function (IMF) components of different frequency bands. The L1 norm least square regularization inversion algorithm was used to invert each IMF component. Finally, the IMF' components after inversion are synthesized to obtain the primary traveling wave. Simulation and experimental results demonstrate that the proposed method is not affected by noise, mode aliasing effect and regularization parameter accuracy, and the obtained waveform has high similarity to the simulated waveform, which enables precise identification of fault traveling wave.

Ammonia coverage ratio control of a novel two-cell SCR-DeNOX system configuration based on IA-ISMC

To respond the China’s “14th Five-Year Plan” on the control of nitrogen oxides (NOX) emission, urea-based selective catalytic reduction (SCR) system has been widely applied to reduce the NOX emission from the diesel engine. NO2 is no longer a factor to be ignored while refining the SCR-DeNOX system model because of the ship diesel engine's long-term low temperature and oxygen-rich condition, which provides abundant conditions for the creation of NO2. Therefore, a refined eight-state two-cell SCR-DeNOX model is established in this paper. Meanwhile, the trade-off between NOX emission and tailpipe ammonia (NH3) slip is one of the major challenges which SCR-DeNOX system is facing. While meeting NOX emission standards, the requirement of limiting NH3 slip to prevent secondary pollution is becoming increasingly urgent, which needs a better structure or controller. Therefore, a two-cell SCR-DeNOX system with a by-pass valve in front of the NH3 injection is designed, integral sliding mode control based on inversion algorithm (IA_ISMC) is proposed for each cell. Based on the FTP-75 test cycle, there are three points of view are presented. Firstly, compared with the traditional six-state model, simulation results from the refined eight-state SCR-DeNOX model are closer to the experimental data. Secondly, the introduction of the by-pass structure has a mild impact on the NOX conversion efficiency, but can largely limit the NH3 slip. Finally, the controller based on IA_ISMC effectively improves the tracking performance of NH3 coverage ratio and reduces the cost of NH3 injection. To sum up, the refined two-cell SCR-DeNOX system with a by-pass valve based on IA_ISMC can enhance SCR performance and lower costs.

Hybrid watermarking and encryption techniques for securing three-dimensional information

A hybrid digital watermarking and encryption technique based on the Computer Generated Holography (CGH) and fractional Fourier transform (FRFT) combined with singular value decomposition (SVD) algorithm is proposed for securing three-dimensional (3D) information. Initially, hierarchical 3D information is encrypted using the angular spectrum diffraction method and a random phase key. This process yields a binary real valued CGH, where incorporating a random phase key broadens the key space and adds complexity, effectively scrambling and concealing the 3D information. Subsequently, the encrypted binary real valued CGH is embedded into the host image as a watermark using the FRFT-SVD algorithm. This hybrid approach enhances the security of the watermarking process. In the final step, the CGH watermark is extracted using the inverse operation of the embedding algorithm. Applying the correct optical key and angular spectrum inverse algorithm successfully reconstructs the 3D information. The watermark algorithm’s efficiency significantly improves by leveraging the rapid computational speed and high focusing capabilities of the FRFT. Additionally, integrating SVD enhances the image’s resistance to geometric attacks, thereby improving the algorithm’s invisibility and robustness. The proposed scheme effectively achieves the encryption and digital watermarking of 3D information. Simulation results substantiate the presented watermarking scheme’s efficacy and robustness.

Inverse primitive path analysis

The primitive-path analysis (PPA) [R. Everaers et al. Science 303, 823, (2004)] is an algorithm that transforms a model polymer melt into its topologically equivalent mesh by removing excess contour length stored in thermal fluctuations. Here we present an inverse PPA algorithm (iPPA) that gradually reintroduces contour length in a PPA mesh. We validate the method preserves topology by performing 100 cycles of PPA-iPPA transformations on a ring polymer melt. We show how a parametric curve can be used as a synthetic mesh to generate model materials of rings with entanglements forming a regular 2D cubic lattice. This shows how iPPA can be used to generate model polymer materials with well controlled topology. Finally we show how PPA-iPPA can be used to accelerate stress relaxation approximately by an order of magnitude in simulation time. This reduces the computational cost of computational studies of structure-property relations for polymer materials.

Exploring the Effects of Topography on Leaf Area Index Retrieved from Remote Sensing Data at Various Spatial Scales over Rugged Terrains

Topography significantly affects remotely sensed reflectance data and subsequently impacts the retrieval of the leaf area index (LAI) from surface reflectance data over rugged terrains. However, most LAI inversion algorithms ignore the influence of terrain. This paper quantitatively analyzes the topographic effects on LAI values retrieved from remote sensing data at various spatial scales (30, 90, 270, 540, 1080, and 5400 m) over rugged terrains. The PRO4SAILT (PROSPECT + 4SAILT) model and the Proy algorithm were used to simulate multiscale surface reflectance for different LAI values over rugged terrains. Based on Gaussian process regression (GPR), an LAI inversion algorithm that ignores terrain effects was first developed. The simulated multiscale reflectance data were subsequently input into the inversion algorithm to retrieve LAI values. Finally, the retrieved LAI values were compared with the corresponding reference LAI values. The results demonstrate that the finer the spatial resolution is, the more significant the topographic effects on the retrieved LAI values are. When the reference LAI is five, as the spatial resolution increases from 5400 m to 30 m, the mean percentage error (MPE) of the retrieved LAI increases from 10.46% to 13.72%, and the root mean square error (RMSE) increases from 0.5376 to 1.005. Regardless of the spatial resolution, the error in the retrieved LAI values increases with an increasing terrain slope. When the reference LAI is five and the spatial resolution is 30 m, the MPE at a slope of 15°–30° is close to 5%, and the RMSE is close to 0.3. The MPE at a slope of 30°–45° is close to 20%, and the RMSE is close to one. In addition, the accuracy of the retrieved LAI values is closely related to the sky view factor (SVF). In general, the larger the SVF is, the smaller the error in the retrieved LAI values. In addition, the conversion relationships between the retrieved LAI values using the algorithm that ignores terrain effects and the true LAI values are provided in this study.

A defect opening profile reconstruction method based on multidirectional magnetic flux leakage detection

Magnetic flux leakage (MFL) is a popular technique for detecting defects. The opening profile reconstruction is one of the most popular concerns. The commonly used unidirectional magnetization-based methods easily lead to incomplete MFL information to reconstruct the opening profile. The superimposition of MFL signals from different directions would cause information cancellation, making it difficult for the existing data processing methods to reconstruct. To solve the issues, this study constructs a model-based method to inverse defect opening profiles. It builds the forward equations from one magnetic permeability to multidirectional MFL fields. Then the pseudo-inversion with Tikhonov regularization is applied as the inversion algorithm. The algorithm associates the forward equations and finds the solution that can fulfill them simultaneously. Such a method can combine multidirectional MFL information without cancellation. It reduces the ill-posed problems that exist in unidirectional inversion and makes the reconstructed profile complete and accurate. The comparison experiments have been carried out, and the results have proved the high accuracy of the proposed method.

Two-dimensional imaging of elastic properties of rock core samples from measurements of angle-dependent ultrasonic reflection coefficients

Laboratory and field measurements often fail to identify small-scale variations in rock elastic properties. Due to limited spatial resolution, conventional laboratory methods cannot properly describe rock formations exhibiting a high degree of heterogeneity, thereby masking differences between stiff and compliant layers. Continuous sample measurements can mitigate this problem but are not widely used by the industry. We build upon our previous work and apply laboratory angle-dependent ultrasonic reflection coefficient (ADURC) measurements to achieve detailed two-dimensional descriptions of the elastic properties of complex rock samples. This method successfully yields high-resolution information on P- and S-wave velocities, as well as bulk density, across the surface of rock samples. Elastic properties are estimated using a nonlinear inversion algorithm that matches laboratory measurements with numerical simulations. ADURC data acquired at various sample locations enable detailed rock descriptions, where the effective measurement area is determined by the size of the receiver, measurement frequency, and incidence angle. Consequently, the sampling area is smaller compared with triaxial loading and acoustic transmission tests, for which the resolution is controlled by sample size. Measurements conducted on samples exhibiting different levels of spatial complexity validate the capability of the ADURC method to identify small-scale heterogeneities. For the reported experiments, variations in angle-dependent reflectivity give rise to corresponding variations in the estimated P- and S-wave velocities and density, which can exceed 60%. These small-scale variations across heterogeneous rock samples often are overlooked by conventional laboratory methods.

Performance of two semi-analytical algorithms in deriving water inherent optical properties in the Southern Ocean

Remotely sensed inherent optical properties (IOPs) are key proxies for synoptic mapping of primary production and carbon export in the global ocean. However, the IOPs inversion algorithms are scarcely evaluated in the Southern Ocean (SO) because of limited field observations. In this study, the performance of two widely used semi-analytical algorithms (SAAs), i.e., the quasi-analytical algorithm (QAA) and the generalized IOP model (GIOP), were evaluated using a compiled in situ bio-optical dataset in SO, as well as measurements from the Visible Infrared Imaging Radiometer Suite (VIIRS). Evaluations with in situ data show that QAA and GIOP have comparable performance in retrieving the total absorption coefficient (a(λ)), absorption coefficients of phytoplankton (aph(λ)), and that of detritus and colored dissolved organic matter (adg(λ)). Overall, it was found that remotely sensed a(λ) and aph(λ) by both SAAs agreed well with field measurements, with the mean absolute percentage difference (MAPD) of derived a(λ) and aph(λ) in the blue-green bands being ∼20% and ∼40%, respectively. However, derived adg(λ) by both SAAs were higher than the measured values at the lower end (adg(443) < ∼0.01 m-1), but lower at the higher end (adg(443) > ∼0.02 m-1), with MAPD of ∼60%. Results of this effort suggest confident products of a(λ) and aph(λ) from VIIRS in SO, but more dedicated efforts on the measurements and evaluation of adg(λ) in SO would be desired.

Shedding light on the MRI-driven dynamo in a stratified shearing box

ABSTRACT We study the magneto-rotational instability (MRI) dynamo in a geometrically thin disc (H/R ≪ 1) using stratified zero net (vertical) flux shearing box simulations. We find that mean fields and electromotive forces (EMFs) oscillate with a primary frequency fdyn = 0.017 Ω (approximately nine orbital period), but also have higher harmonics at 3fdyn. Correspondingly, the current helicity has two frequencies 2fdyn and 4fdyn, which appear to be the beat frequencies of mean fields and EMFs, respectively, as expected from the magnetic helicity density evolution equation. Further, we adopt a novel inversion algorithm called the ‘Iterative Removal Of Sources’, to extract the turbulent dynamo coefficients in the mean-field closure using the mean magnetic fields and EMFs obtained from the shearing box simulation. We show that an α-effect (αyy) is predominantly responsible for the creation of the poloidal field from the toroidal field, while shear generates back a toroidal field from the poloidal field, indicating that an α–Ω-type dynamo is operative in MRI-driven accretion discs. We also find that both strong outflow ($\bar{v}_z$) and turbulent pumping (γz) transport mean fields away from the mid-plane. Instead of turbulent diffusivity, they are the principal sink terms in the mean magnetic energy evolution equation. We find encouraging evidence that a generative helicity flux is responsible for the effective α-effect. Finally, we point out potential limitations of horizontal (x − y) averaging in defining the ‘mean’ on the extraction of dynamo coefficients and their physical interpretations.

A Concrete Core Void Imaging Approach and Parameter Analysis of Concrete-Filled Steel Tube Members Using Travel Time Tomography: Multi-Physics Simulations and Experimental Studies.

Concrete-filled steel tube (CFST) members have been widely used in civil engineering due to their advanced mechanical properties. However, internal defects such as the concrete core voids and interface debonding in CFST structures are likely to weaken their load-carrying capacity and stiffness, which affects the safety and serviceability. Visualizing the inner defects of the concrete cores in CFST members is a critical requirement and a challenging task due to the obvious difference in the material mechanical parameters of the concrete core and steel tube in CFST members. In this study, a curved ray theory-based travel time tomography (TTT) with a least square iterative linear inversion algorithm is first introduced to quantitatively identify and visualize the sizes and positions of the concrete core voids in CFST members. Secondly, a numerical investigation of the influence of different parameters on the inversion algorithm for the defect imaging of CFST members, including the effects of the model weighting matrix, weighting factor and grid size on the void's imaging quality and accuracy, is carried out. Finally, an experimental study on six CFST specimens with mimicked concrete core void defects is performed in a laboratory and the mimicked defects are visualized. The results demonstrate that TTT can identify the sizes and positions of the concrete core void defects in CFST members efficiently with the use of optimal parameters.

Spatiotemporal Land Use/Land Cover Changes and Impact on Urban Thermal Environments: Analyzing Cool Island Intensity Variations

This study pioneers the comprehensive evaluation of the spatiotemporal evolution of land use/land cover (LULC) in Hangzhou city, introducing the novel water body shape index (WBSI) to analyze its seasonal impacts on the urban thermal environment and urban cool island (UCI) effects, uncovering distinct patterns of thermal regulation. It particularly investigates how distance gradients and the water body shape index (WBSI) influence land surface temperature (LST) in the urban core. The region’s climate, featuring hot summers and cold winters, highlights significant seasonal LST variations. Addressing a gap in existing UCI research, the analysis extends beyond the typical large-scale planning focus to include small-scale, high-resolution aspects. Employing remote sensing and geographic information system (GIS) analysis techniques, this study analyzes the seasonal dynamics in Hangzhou’s central urban area. High-resolution LST data, obtained through single-channel inversion and resolution enhancement algorithms, are crucial to this analysis. This study employs the maximum likelihood classification method to analyze land use and land cover changes from 1990 to 2020. This analysis reveals potential drivers of urban thermal environment changes, such as the expansion of residential and commercial areas and the reduction in green spaces. Different regions in LST data are delineated to assess the cool island effect, and the complexity of water body boundaries is quantified using the water body shape index. Spatial and temporal patterns of LST changes are investigated using multivariate regression and time-series analysis models. We identified significant changes in LULC over the past 30 years in Hangzhou, closely correlating with a continuous rise in LST. This observation underscores a clear finding: the strategic importance of blue–green infrastructure in mitigating urban heat, a novel insight that extends the current understanding of urban thermal dynamics. A clear and novel finding of this study is that the intensity of the cool island effect from large water bodies not only diminishes with distance but is intricately influenced by the complexity of their shapes, as quantified by the WBSI, whereas the complexity of their boundaries enhances this effect. Additionally, the regulatory role of the cool island effect is observed to vary seasonally, being most pronounced in summer and less so in autumn and winter, thereby demonstrating a positive impact. In conclusion, our findings innovatively highlight how the specific shapes of water bodies, quantified through the water body shape index (WBSI), emerge as critical, yet previously underappreciated, drivers in modulating the urban thermal environment. This underscores a new avenue for urban planning, advocating for the strategic design of water bodies within urban landscapes. It also finds that spatial factors and seasonal variations significantly affect the intensity of the cool island effect. These findings offer valuable evidence for urban planning and climate change adaptation, emphasizing balancing natural elements with the built environment in urban design.

Simulation of a synchronized methodology for MR-based electromechanical property imaging during transcranial electrical stimulation

Introduction: Recent investigations into the biomechanics of the brain have unveiled alteration in tissue stiffness triggered by external stimuli. For instance, visual stimulation effects can be measured in elasticity images of the cortex generated by functional magnetic resonance elastography (MRE). Such a mechanical characterization method combined with non-invasive brain stimulation (NIBS), a technique that seeks to selectively modulate particular parts of the brain using weak electrical currents, has the potential to influence research on various neurological disorders. In this in silico study, we aimed to elucidate individual and interdependent aspects related to a synchronized biomechanical imaging and non-invasive brain stimulation methodology. Magnetic resonance electrical impedance tomography (MREIT) was incorporated to the pipeline, providing a promising way of evaluating NIBS-induced electrical current patterns in the brain while leveraging MRE and transcranial alternating current stimulation (tACS) experimental settings.Methods: A mouse head model was assembled using open-access atlases to include five anatomical structures: skin/subcutaneous tissue, skull, cerebrospinal fluid (CSF), brain white and grey matters. MRE, tACS, and MREIT experiments were simulated using Comsol Multiphysics with Matlab Livelink. Synthetic MRE and MREIT data were processed using the subzone non-linear inversion and harmonic Bz algorithm, respectively, to reconstruct images of the distributed complex shear modulus and electrical conductivity.Results and Discussion: Lorentz body forces arising from simultaneous MRE and tACS elicited elastic waves of negligible amplitude compared with the extrinsic actuation levels reported in the literature, which allowed accurate reconstructions of the complex shear modulus. Qualitative electrical conductivity maps retrieved by MREIT accurately delineated anatomical regions of the brain model and could be used to recover reasonably accurate distributions of tACS-induced currents. This multi-physics approach has potential for translation to human brain imaging, and may provide more possibilities for the characterization of brain function together than in isolation.

Enhancing damping estimation accuracy of exponential windowed responses of a GFRP plate through Finite Element Model Updating approach

Fibre reinforced polymer (FRP) panels are widely employed in ship and marine structures due to their better specific stiffness and strength when compared to metals. Therefore, an accurate estimation of the dynamic behaviour of such panels is necessary from its operational and serviceability point of view. In this study, the influence of exponential window functions and the associated decay rates on the damped dynamic responses of a Glass Fibre Reinforced Plastic (GFRP) plate has been investigated experimentally, using impact hammer testing. In a standard experimental modal testing of a structure, exponential window functions are commonly employed to prevent spectral leakage of the signal and achieve a good signal-to-noise ratio. However, this exercise modifies the Frequency Response Functions (FRFs) and introduces numerical damping into the measurements. A novel technique involving a Finite Element Model Updating using Inverse Eigen-Sensitivity algorithm is employed to estimate the unbiased FRFs and identify the induced numerical damping. The model updating is carried out in two stages: updating stiffness parameters first, followed by updating damping parameters in the second stage. The updating algorithm and the two-stage strategy adopted therein is found to be effective in identifying the induced numerical damping along with the unbiased FRF expressions.

Hybrid Newton-like Inverse Free Algorithms for Solving Nonlinear Equations

Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines.

A time-domain SGFD-FK hybrid method for 2D teleseismic elastic wave modeling and inversion

AbstractFull waveform inversion (FWI) has proved to be a reliable tool for high-resolution imaging of lithospheric structures at various depths down to the upper mantle. However, when the size of the model is large, the computational burden is significative and applications are restricted to low frequencies. To tackle this issue, we developed a new 2D time-domain hybrid method to simulate high-frequency teleseismic body waves propagating through a local heterogeneous elastic Earth model: The frequency-wavenumber (FK) integration method is coupled with the staggered grid finite difference method (SGFD). The FK method is used to compute the wavefield due to obliquely incident plane P and SV waves in a 1D multilayered half space that excites a local heterogeneous region. Inside this region, the velocity-stress staggered grid FD method (SGFD) is used to accurately deal with wave propagation in heterogeneous media. Spurious waves that might be generated at the boundaries of the local region are avoided using convolutional perfectly matched layers (CPML). This new hybrid method inherits the low-memory requirements of the FK method and the accuracy, efficiency and easy implementation of the SGFD. The new hybrid method is benchmarked against the analytical FK method for some canonical models and shows good agreement with analytical solutions. Subsequently, our modeling tool is incorporated into a full waveform inversion algorithm adapted for teleseismic configurations to invert the incident P wave and its coda. The inversion is carried out using a gradient approach that is efficiently implemented via the adjoint-state method. The results suggest that our hybrid method and FWI algorithm represent a valuable tool for 2D forward and inverse regional applications using teleseismic data sets.

Polarization Characterization of Porous Particles Based on DDA Simulation and Multi-Angle Polarization Measurements.

Porous suspended particles are hazardous to human health due to their strong absorption capacity for toxic substances. A fast, accurate, in situ and high-throughput method to characterize the microporous structure of porous particles has extensive application value. The polarization changes during the light scattering of aerosol particles are highly sensitive to their microstructural properties, such as pore size and porosity. In this study, we propose an overlapping sphere model based on the discrete dipole approximation (DDA) to calculate the polarization scattering characteristics of porous particles. By combining scattering calculations with multi-dimensional polarization indexes measured by a multi-angle polarized scattering vector detection system, we achieve the identification and classification of pore-type components in suspended particles. The maximum deviation based on multiple indexes is less than 0.16% for the proportion analysis of mixed particles. Simultaneously, we develop a quantitative inversion algorithm on pore size and porosity. The inversion results of the three porous polymer particles support the validity and feasibility of our method, where the inversion error of partial particles is less than 4% for pore size and less than 6% for porosity. The study demonstrates the potential of polarization measurements and index systems applied in characterizing the micropore structure of suspended particles.

On the Two-sided Permutation Inversion Problem

In the permutation inversion problem, the task is to find the preimage of some challenge value, given oracle access to the permutation. This fundamental problem in query complexity appears in many contexts, particularly cryptography. In this work, we examine the setting in which the oracle allows for quantum queries to both the forward and the inverse direction of the permutation—except that the challenge value cannot be submitted to the latter. Within that setting, we consider three options for the inversion algorithm: whether it can get quantum advice about the permutation, whether the query algorithm can restrict the distribution with which the challenge input is sampled, and whether it must produce the entire preimage (search) or only the first bit (decision). We prove several theorems connecting the hardness of the resulting variations of the permutation inversion problem and establish lower bounds for them. Our results show that, perhaps surprisingly, the permutation inversion problem does not become significantly easier when the adversary is granted oracle access to the inverse—provided it cannot query the challenge itself.

Eddy detection inverted from Argo profiles to surface altimetry

Abstract Argo floats are widely used to characterize vertical structures of ocean eddies, yet their capability to invert sea-surface features of eddies, especially those overlooked by available altimeters, has not been explored. In this paper, we propose an “interior-to-surface” inversion algorithm to effectively expand the capacity of eddy detection by estimating altimeter-missed eddies’ surface attributes from their Argo-derived potential density anomaly profiles, given that interior property and surface signature of eddies are highly correlated. An altimeter-calibrated machine learning ensemble is employed for the inversion training based on the joint altimeter-Argo eddy data and shows promising performance with mean absolute errors of 5.4 km, 0.5 cm, and 14.3 cm2/s2 for eddy radius, amplitude, and kinetic energy. Then, the trained ensemble model is applied to independently invert the properties of eddies captured by an Argo-alone detection scheme, which yields a high spatiotemporal consistency with their altimeter-captured counterparts. In particular, a portion of Argo-alone eddies is ~25% smaller than altimeter-derived ones, indicating Argo’s unique capability of profiling weaker submesoscale eddies. Sea surface temperature and chlorophyll data are further applied to validate the reliability of eddies identified and characterized by the Argo-only algorithm. This new methodology effectively complements that of altimetry in eddy detecting and can be expanded to estimate other physical/biochemical eddy variables from a variety of in-situ observations.