Mathematical Inversion Research Articles

Variations of the East Asian monsoon over the past 800 kyr constrained by the boron isotope composition of paleo-rainwater inferred from loess-paleosol deposits in NE China

Based on a study of the boron (B) isotope geochemistry of the loess-paleosol sequence of the Niuyangzigou section (NYZG) in Northeast (NE) China, the boron isotopic composition of paleo-rainwater (δ11Bpr) is used for the first time as a potential proxy for tracing changes in the East Asian summer monsoon (EASM) since the mid-Pleistocene. The acid-soluble phase of loess in NE China, which is characteristically a sandy loess, has lower boron concentrations (0.26 to 0.89 μg/g) and more positive δ11B values, from −12.1‰ to +9.4‰, compared to the loess of the Chinese Loess Plateau (CLP). According to the mass balance of boron accumulation from three distinct sources, a mathematical inversion calculation is used to quantify the proportion of boron from each source and to capture the original δ11Bpr signature. The resulting δ11Bpr values range from +6.8 ± 0.95‰ in loess layers to +17.3 ± 3.32‰ in paleosol layers, and the boron accumulated in loess-paleosol layers is shown to be mainly from atmospheric precipitation and silicate weathering. Synchronous variations of reconstructed δ11Bpr and other loess-based proxies, both in NE China and in the CLP, are observed over a large spatial range and on several temporal scales. The linkage of δ11Bpr to the intensity of the EASM is attributed to the kinetic boron isotope fractionation associated with vapor-precipitate phase separation along the transport path of moisture-bearing air masses. A Rayleigh fractionation model is proposed to interpret δ11Bpr in terms of the proportion of water vapor loss after multi-step fractionation processes, which is independent of temperature. The monsoon record based on δ11Bpr shows a significant shift at ∼430 ka, implying an abrupt weakening of the EASM after the Mid-Brunhes Event (MBE), which provides evidence for regional disparities in monsoon evolution in response to the MBE. The ice volume in Northern Hemisphere is a possible factor controlling changes in the EASM in NE China over the past 800 kyr.

Stress Drop Analysis on Banda Sea

Stress drop is a fundamental parameter of earthquake source that describes stress before and after an earthquake. The purpose of this study was to determine the tectonic characteristics of the Banda sea region. The research method used is a mathematical analysis and Nelder Mead Simplex nonlinear inversion methods. The results show that the Banda Sea is the area with complex tectonic conditions and large earthquake impacts. The Banda sea earthquake generated a stress drop of between 2 MPa -10 MPa from small to medium, it can be concluded that the rocks in the Banda Sea are relatively harder because the Banda Sea has a complex and varied oceanographic profile. The Banda Sea contains many continental fragments and has very deep ocean basins in the North Banda and Weber Deep, as well as plate rollbacks that form geometry in the shape of a spoon. The strength of rocks in the Banda Sea is also strengthened by the results of gravitational anomalies, there are significant differences in the gravity anomalies around the Banda ocean which indicate high density. This information is very important to know the amount of pressure released shortly after the earthquake which has a very large impact as a disaster mitigation measure.          Â

Bayesian Probabilistic Analysis of DEER Spectroscopy Data Using Parametric Distance Distribution Models.

Double electron-electron resonance (DEER) spectroscopy measures distance distributions between spin labels in proteins, yielding important structural and energetic information about conformational landscapes. Analysis of an experimental DEER signal in terms of a distance distribution is a nontrivial task due to the ill-posed nature of the underlying mathematical inversion problem. This work introduces a Bayesian probabilistic inference approach to analyze DEER data, using a multi-Gauss mixture model for the distance distribution. The method uses Markov chain Monte Carlo (MCMC) sampling to determine a posterior probability distribution over model parameter space. This distribution contains all the information available from the data, including a full quantification of the uncertainty about the parameters. The corresponding uncertainty about the distance distribution is captured via an ensemble of posterior predictive distributions. Several synthetic examples illustrate the method. An experimental example shows the importance of model checking and comparison using residual analysis and Bayes factors. Overall, the Bayesian approach allows for more robust inference about protein conformations from DEER spectroscopy.

DLT-Net: deep learning transmittance network for single image haze removal

Outdoor images taken in inclement weather conditions are often contaminated with colloidal particles and droplet in the atmosphere. These captured images are susceptible to low contrast, poor visibility, and color distortion, which is the reason for serious errors in digital image vision systems. Therefore, defogging research has material significance for practical applications. In this paper, image dehazing is regarded as a mathematical inversion and image restoration process on the basis of fog image degradation model. The global atmospheric light A can be approximately estimated by combining Gaussian low-pass filtering with the single-threshold segmentation and binary tree method. And a deep learning transmittance network is adopted to modify transmittance. Comparison experimental results show that our method is effective in dealing with thick fog, complex scenes and multicolor images. In addition, our method is superior to four other state-of-the-art defogging methods in visual impact, universality and running speed. The overall framework of our method

A practical guide to the double-spike technique for calcium isotope measurements by thermal ionization mass spectrometry (TIMS)

The double spike technique is the most reliable method for calibrating instrumental and chemical mass-dependent fractionation, which has been widely applied in isotopic analysis of many elements such as Mo, Sn, Ru, Ca, etc. However, practical use of double spiking is possibly hindered by the perceived difficulties in proper double spike calibration, mathematical inversion and data reduction. In this study, we will refer to Ca double spike on how to yield excellent isotopic data on TIMS. A detailed description on how to choose and calibrate an optimal double spike is presented. Our main aim is to provide a practical guide when working with double spike, especially for researchers in new isotopic systems.

Triple oxygen isotope investigation of fine-grained sediments from major world's rivers: Insights into weathering processes and global fluxes into the hydrosphere

Continental weathering is accompanied by formation of clays and other secondary minerals and their δ18O and Δ17O values should hence reflect to some extent signatures of meteoric water (δ18OMW) and mean annual temperatures (MAT). Our ability to extract climate information from weathered products across the geologic history relies on analytical methods tested and calibrated against modern climate conditions. We here present triple-oxygen isotope analyses of clay-size sediments from 45 rivers worldwide, as well as δ18O analyses of corresponding silt- and sand-rich detrital fractions, which altogether cover about 25% of the continental area that drained into the oceans, extending from the tropics to polar regions. The majority of studied clays closely approximate weathering products, always having high-δ18O signatures regardless of the bedrock type, and in equilibrium with local meteoric waters. Silts are only ∼1.9‰ lighter on average due to greater detrital dilution. Overall, bulk clays from across different climatic regions do not vary much isotopically; an observation which we attribute to opposing effects of temperature on clay-water fractionation and hydrologic relationship between temperature and δ18OMW. Mathematical inversion of measured clay δ18O and Δ17O values (corrected for detrital contribution) into MAT and δ18OMW, compiled for each studied watershed, returns satisfactory estimates. Globally, triple O isotopes in clays appear to be water-dominated, being controlled almost exclusively by δ18OMW at respective temperature of weathering, with minor effects related to evaporation. Using sand from rivers, correlation of δ18O silts with detrital proportions, and estimated surface outcrop of different rock types, we additionally arrive at a +11.5‰ estimate for the exposed silicate crust undergoing weathering.Globally-averaged, sediment-flux weighted clay δ18O and Δ17O values are +14.80‰ and −0.164‰, respectively. These values are significantly skewed toward O isotope signatures for the southeast Asia and western Pacific regions, characterized by very high sediment fluxes to the ocean. Using both clay- and silt-size fractions, the total weighted silicate weathering δ18O signature exported to the world's ocean is −2.59‰, almost 50% higher the previous estimate, yielding an ice-free world hydrosphere estimate of −0.78‰.Overall, the modern river clays represent a snapshot of modern weathering conditions on continents, and associated first-order climatic signatures related to MAT and δ18O of the hydrosphere. This implies that measured increase in δ18O and stepwise decrease in Δ17O in shales in the geologic record capture: evolving global hydrologic cycle upon continental emergence, decrease in global MAT or diagenetic conditions, and decreasing ocean mass via rehydrating of the mantle by subduction of hydrated low-δ18O, high-Δ17O slabs.

GInSAR: A cGPS Correction for Enhanced InSAR Time Series

Earth surface displacements from interferometric synthetic aperture radar (InSAR) have long been used to study deformation from a wide range of geophysical processes. Whereas deformation rates can be robustly estimated from InSAR by averaging many individual deformation observations, noise in these observations has limited their utility for generating deformation time series. In this article, we introduce a novel combination of InSAR and Global Positioning System (GPS) data that align InSAR displacements to an absolute reference and reduces long-wavelength spatial errors prior to InSAR time series construction. We test our GInSAR (GPS-enhanced InSAR) methodology on Sentinel-1 data over the southern Central Valley, CA, USA, comparing GInSAR displacement velocities and time series with those from three other referencing techniques. We find that the GInSAR approach outperforms alternative methods, yielding mm-level displacement differences with respect to collocated cGPS. By contrast, other referencing methods can overestimate peak subsidence velocities in the Central Valley by upwards of 10%, deviate by tens of millimeters relative to cGPS validation time series, and contain spatial biases absent in the GInSAR methodology. We also present a modification to the widely used small baseline subset (SBAS) technique for time series estimation, whereby we use a temporal connectedness constraint to regularize the mathematical inversion and increase the number of InSAR pixels with valid time series estimates.

Tomographic inversion of gravity gradient field for a synthetic Itokawa model

This article investigates reconstructing the internal mass density of a numerical asteroid model using the gradient of a simulated gravity field as synthetic measurement data. Our goal is to advance the mathematical inversion methodology and find feasibility constraints for the resolution, noise and orbit selection for future space missions. We base our model on the shape of the asteroid Itokawa as well as on the recent observations and simulation studies which suggest that the internal density varies, increasing towards the center, and that the asteroid may have a detailed structure. We introduce randomized multiresolution scan algorithm which might provide a robust way to cancel out bias and artifact effects related to the measurement noise and numerical discretization. In this scheme, the inverse algorithm can reconstruct details of various sizes without fixing the exact resolution a priori, and the randomization minimizes the effect of discretization on the solution. We show that the adopted methodology provides an advantageous way to diminish the surface bias of the inverse solution. The results also suggest that a noise level below 80 Eotvos will be sufficient for the detection of internal voids and high density anomalies, if a sparse set of measurements can be obtained from a close-enough distance to the target.

Volumetric Imaging with a Single Projection Enabled by Deep Learning

Traditionally, a tomographic image is obtained by mathematical inversion of the encoding function of the imaging wave for a given set of measured data from different angular positions. While continuous effort has been made in imaging with reduced angular measurements over the years, tomographic imaging with ultra-sparse sampling has yet to be realized. In this work, we push the sparsity to the limit of a single projection and demonstrate what seemingly unlikely scenario of a single-view tomographic imaging is readily achievable by leveraging from the state-of-the-art deep learning technique and seamless integration of prior knowledge in the deep learning-based image reconstruction process. We develop a hierarchical neural network for X-ray CT imaging with ultra-sparse views and develop a structured training process for deep learning to bridge the dimensionality in X-ray imaging. The essences of our approach are the introduction of a novel feature domain transformation between a 2D projection and 3D volumetric CT image, and the construction of a robust encoding/decoding framework. To evaluate the feasibility of the proposed approach, the trained network is deployed on our generated dataset. We collect 3D CT dataset from clinical patient’s database, and digitally produce projection images from CT images using the geometry consistent with a clinical on-board cone-beam CT system for radiation therapy. Data augmentation with a series of translation, rotation, and organ deformation to the 3D CT are used to produce annotated data pairs that mimic different imaging situations. After adequate training, we deploy the deep learning model inference for single-view 3D volumetric reconstruction on two cases. The reconstructed results are compared with ground truth both qualitatively and quantitatively. From results’ illustration, we observe the deep learning-derived images closely resemble the target images, indicating the potential of the proposed model for volumetric imaging. For quantized computation, the averaged MAE/RMSE/SSIM/PSNR values over all testing samples for single-view reconstruction are 0.018, 0.177, 0.929, and 30.523, respectively, for case 1. The indices for case 2 are found to be 0.025, 0.385, 0.838, and 27.157, respectively. The qualitative and quantitative results demonstrate that our model is capable of achieving high-quality 3D image reconstruction even with only a single or few 2D projection. We have presented a novel deep learning framework for volumetric imaging with ultra-sparse data sampling. The mechanism here is fundamentally different from the traditional approaches in that the image formation is driven by prior knowledge casted in the deep learning model. This work pushes the boundary of tomographic imaging to the single-view limit. Practically, the single-view imaging may present a useful solution in some image-guided interventional procedures with simplified imaging system design.

Putting force laws to the test

Force Microscopy In frequency-modulated atomic force microscopy, force is not measured directly. The resonant frequency amplitude and phase of the vibrating cantilever are converted into force through mathematical inversion algorithms. The resolution of this approach now extends to measuring the force between individual atoms, but Sader et al. show that the underlying interatomic forces can also vary rapidly. These conditions can make the inversion of the frequency shifts mathematically ill-posed and lead to unphysical results. They formulate a simple inflection point test of the changes in force with distance of the tip from the surface that ensures that the inversion algorithm problem will yield an accurate force measurement. Nat. Nanotechnol. 13 , 1088 (2018).

Spatial representativeness evaluation of air quality monitoring sites by point-centred variography

We propose a geostatistical technique based on point-centred semi-variograms that can be used to derive valuable information about the spatial representativeness of air quality monitoring sites. Whereas classical geostatistics describes the spatial correlation structure of a concentration field in terms of the variogram, point-centred variography is based on the average of squared concentration differences observed in pairs formed from a particular central point and the set of all other points in the domain. It thereby places a monitoring station in the context of the local or regional air quality pattern. We demonstrate how a mathematical inversion of the point-centred variogram can provide estimates of the extent of the representativeness area of a monitoring site. The application of this approach is tested on a set of modelling data from the city of Antwerp, which was used for the FAIRMODE/AQUILA intercomparison exercise of methods for the assessment of spatial representativeness.

Scene-Awareness Based Single Image Dehazing Technique via Automatic Estimation of Sky Area

The occurrence of fog, mist, smog, or haze significantly reduces the visibility of the scenes and images, resulting in limited recognition of computer vision and computer graphics. So, removing haze from images is a must. In this paper, we regard image dehazing as a mathematical inversion process and image restoration based on atmospheric scattering models. The atmospheric light can be accurately estimated by combining the gray threshold segmentation and the skyline method. The improved least squares filtering method is used to optimize the transmittance map so that the edge details can be highlighted and the halo effect can be alleviated. A large number of test images show that our algorithm can achieve better experimental results than the other seven most advanced dehazing strategies.

Geophysical analysis of natural caves in iron lithotypes in the region of Mariana, Southeastern Quadrilátero Ferrífero, Brazil

Abstract In Brazil, natural caves in iron lithotypes have increasingly been discovered in iron mining areas and its surroundings. Mining companies attempt to study them according to the Federal Decree 6640/2008 and the Normative Instruction 2/2009 of the Ministry of the Environment, which is concerned with the preservation of the Brazilian Speleological Heritage. This research is within one of those studies in which a geophysical campaign methodology is established for an attempted prospection of caves, in an area located on the north flank of Mariana's Anticlinal, Quadrilatero Ferrifero. The flank, which is sustained by iron formations from the Itabira Group and covered by the product of alteration and sedimentary redistribution, experienced extensive and compressive tectonics, generating, respectively, the main structuration in the NW-SE direction and schist thrust slices from the Nova Lima Group. Caves are mainly developed in the lithological contacts and in fault zones. In the regional stage, the methodology uses aeromagnetometric (identification of iron lithotypes, structural and statistical analysis of magnetic lineaments) and aeroradiometric (structural-geological mapping and setting of lithological contacts) methods. Results have shown some caves in lateral contact zones between lithologies, and the structural control imposed by a shear zone in the area. At the local stage, the electrical resistivity method - EL was used, dipole-dipole array, data mathematical inversion, presentation of pseudo-depth sections and tridimensional modeling. The results, in accordance with the topographic data, show the possible limits of the geometric contour and the tendency for cave deepening. However, studies of the moisture, of similar caves with different spacings, and the use of Ground Penetration Radar - GPR are suggested.

Towards reproducible measurement of nanoparticle size using dynamic light scattering: Important controls and considerations

The characterization of nanoparticles in dispersions, in particular measuring their size and size distribution, is a prerequisite before they can be used in toxicological testing. Such characterization requires reliable methods with good reproducibility. The aim of this study was to evaluate the reproducibility, and thus the potential of Dynamic Light Scattering (DLS) for nanoparticle size determination. DLS is easy to use and well established in most nanotoxicology laboratories. However, reproducibility and in particular variability between measurements done using different instrumental setups have not been addressed systematically before. Here we performed initial experiments with rather monodisperse dispersions of spherical particles in water. Significant discrepancies in the measured distributions were obtained with different DLS instruments, especially when fitting the data using mathematical inversion methods. Significant errors can be made due to different settings being used for fitting the data. These were even more prominent when working with dilute dispersions of very small particles. Our study has identified several important points to be taken into consideration in order to overcome possible issues in measurement and analysis of nanoparticles using DLS.In practice, however, nanoparticles may have significant polydispersities and/or can be non-spherical. We extend the comparative work on spherical particles, to show how to characterize polydisperse and/or high aspect ratio particles using DLS instruments.

Performance of some numerical Laplace inversion methods on American put option formula

Numerical inversion approaches of Laplace transform is used to obtain a semianalytic solution. Some of the mathematical inversion methods such as Durbin-Crump, Widder, and Papoulis can be used to calculate American put options through the optimal exercise price in the Laplace space. The comparison of methods on some simple functions is aimed to know the accuracy and parameters which used in the calculation of American put options. The result obtained is the performance of each method regarding accuracy and computational speed. The Durbin-Crump method has an average error relative of 2.006e-004 with computational speed of 0.04871 seconds, the Widder method has an average error relative of 0.0048 with computational speed of 3.100181 seconds, and the Papoulis method has an average error relative of 9.8558e-004 with computational speed of 0.020793 seconds.

Traceable X,Y self-calibration at single nm level of an optical microscope used for coherence scanning interferometry

Coherence scanning interferometry used in optical profilers are typically good for Z-calibration at nm-levels, but the X,Y accuracy is often left without further notice than typical resolution limits of the optics, i.e. of the order of ~1 µm. For the calibration of metrology tools we rely on traceable artefacts, e.g. gauge blocks for traditional coordinate measurement machines, and lithographically mask made artefacts for microscope calibrations. In situations where the repeatability and accuracy of the measurement tool is much better than the uncertainty of the traceable artefact, we are bound to specify the uncertainty based on the calibration artefact rather than on the measurement tool. This is a big drawback as the specified uncertainty of a calibrated measurement may shrink the available manufacturing tolerance. To improve the uncertainty in X,Y we can use self-calibration. Then, we do not need to know anything more than that the artefact contains a pattern with some nominal grid. This also gives the opportunity to manufacture the artefact in-house, rather than buying a calibrated and expensive artefact. The self-calibration approach we present here is based on an iteration algorithm, rather than the traditional mathematical inversion, and it leads to much more relaxed constrains on the input measurements.In this paper we show how the X,Y errors, primarily optical distortions, within the field of view (FOV) of an optical coherence scanning interferometry microscope, can be reduced with a large factor. By self-calibration we achieve an X,Y consistency in the 175 × 175 µm2 FOV of ~2.3 nm (1σ) using the 50× objective. Besides the calibrated coordinate X,Y system of the microscope we also receive, as a bonus, the absolute positions of the pattern in the artefact with a combined uncertainty of 6 nm (1σ) by relying on a traceable 1D linear measurement of a twin artefact at NIST.

Emission of Gas and $$\hbox {Al}_{2}\hbox {O}_{3}$$ Al 2 O 3 Smoke in Gas–Al Particle Deflagration: Experiments and Emission Modeling for Explosive Fireballs

Emission of gas and $$\hbox {Al}_{2}\hbox {O}_{3}$$ smoke within the deflagration of $$\hbox {H}_{2}{-}\hbox {O}_{2}$$ –{ $$\hbox {N}_{2}{-}\hbox {CO}_{2}$$ }–Al particles has been studied in a closed combustion chamber at pressures of up to 18 bar and at gas temperatures of up to 3700 K. Measurements of radiance intensity were taken using a five wavelength pyrometer (0.660 $$\upmu \hbox {m}$$ , 0.850 $$\upmu \hbox {m}$$ , 1.083 $$\upmu \hbox {m}$$ , 1.260 $$\upmu \hbox {m}$$ , 1.481 $$\upmu \hbox {m}$$ ) and a grating spectrometer in the range (4.10 $$\upmu \hbox {m}$$ to 4.30 $$\upmu \hbox {m}$$ ). In order to characterize the aluminum oxide smoke size and temperature, an inversion method has been developed based on the radiation transfer equation and using pyrometer measurements and thermochemical calculations of $$\hbox {Al}_{2}\hbox {O}_{3}$$ smoke volume fractions. Temperatures in combustion gas have been determined using a method based on the assumed blackbody head of the 4.26 $$\upmu \hbox {m}$$ $$\hbox {CO}_{2}$$ emission line and on its spectral shift with pressure and temperature. For validation purpose, this method has been applied to measurements obtained when calibrated alumina particles are injected in a combustion chamber prior to gaseous deflagrations. This mathematical inversion method was developed to investigate explosive fireballs.

Determination of the bottom deformation from space- and time-resolved water wave measurements

In this paper we study both theoretically and experimentally the inverse problem of indirectly measuring the shape of a localized bottom deformation with a non-instantaneous time evolution, from either an instantaneous global state (space-based inversion) or a local time-history record (time-based inversion) of the free-surface evolution. Firstly, the mathematical inversion problem is explicitly defined and uniqueness of its solution is established. We then show that this problem is ill-posed in the sense of Hadamard, rendering its solution unstable. In order to overcome this difficulty, we introduce a regularization scheme as well as a strategy for choosing the optimal value of the associated regularization parameter. We then conduct a series of laboratory experiments in which an axisymmetric three-dimensional bottom deformation of controlled shape and time evolution is imposed on a layer of water of constant depth, initially at rest. The detailed evolution of the air–liquid interface is measured by means of a free-surface profilometry technique providing space- and time-resolved data. Based on these experimental data and employing our regularization scheme, we are able to show that it is indeed possible to reconstruct the seabed profile responsible for the linear free-surface dynamics either by space- or time-based inversions. Furthermore, we discuss the different relative advantages of each type of reconstruction, their associated errors and the limitations of the inverse determination.

Automatic Recognition Method of Layer Paths in the Ionogram Based on Mathematical Morphology Method and Inversion Technology

The automatic recognition of layer paths in the ionogram can get the key parameters of ionogram which are very important and necessary to the research of space exploration. This paper describes a new automatic recognition method and its application to automatically recognize layer paths from ionogram based on morphological operator and inversion technology. This method is verified through the comparison of actual detecting data with statistical analysis. Results show more than 90% automatic recognition results accord with the people analysis. This automatic recognition method has high acceptable rate and is suitable for recognition ionogram with different high angle wave states. It can accurately recognize the parameters in the ionogram with a fast and precise approach. This method meets the real-time requirements of ionosphere sounding detection in practice.

Dynamic Recurrent Neural Network Based Indirect Adaptive Control for Nonlinear Systems

In this study, an indirect adaptive controller based on dynamic recurrent neural network (DRNN) is developed in the form of the internal model control structure. This control method includes two learning phases, i.e., off-line and on-line learning. In the offline learning, the DRNN is learned by the epoch wise back propagation through time (BPTT) method to represent the forward dynamics of the system to be controlled. In the online phase, the DRNN is used as the internal model of the controlled system and its parameters can be trained by the Truncated BPTT to cope with the possible change in the system dynamics. Hence, the mathematical inversion of the DRNN internal model is computed online to act as the forward controller. Finally, the controller is then obtained by cascading this inverse model with a robust filter and a linear compensator to improve the closed loop performance. The proposed method is applied to a continuous stirred tank reactor (CSTR) with time varying behavior to evaluate the performance of controller.