Assembly method in GIS INTEGRO and its usage for solving of gravitational inverse problem

2021 ◽  
pp. 36-47
Author(s):  
Sergey Mitsyn ◽  
Egor Bolshakov
Keyword(s):  
Inverse Problem ◽  
A Priori ◽  
Regional Scale ◽  
Original Formulation ◽  
Model Evolution ◽  
Assembly Method ◽  
Practice Methods

Various methods based on growing bodies are lately gaining attention in a context of inverse gravity problem that we call a family of “assembly methods”. A variant of method was adopted for GIS INTEGRO in original formulation that is fit for the problem of multiple bodies incorporated in an environment of varying density, in absolute densities (not density contrasts) that are however have to be a priori specified. Such formulation allowed the implementation of the method that is suitable for territory modeling in the regional scale. To workaround method’s instability a number of changes are proposed that consist of introduction of priority on atomic modifications, modification queue and assessment of model evolution instead of just the final result. The developed software allows processing of large grids (tens of millions of tiling elements) even on 5–8 year old desktops. Based on method approbation experience some insights and practice methods are presented. An application example is presented as part of work on modeling of Enisei-Khatanga regional depression territory.

scholarly journals Inverse problem for fractional diffusion equation

2011 ◽  
Vol 14 (1) ◽  
Author(s):  
Vu Tuan
Keyword(s):  
Inverse Problem ◽  
Diffusion Coefficient ◽  
Lower Bound ◽  
Diffusion Equation ◽  
Spectral Data ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
One Dimensional ◽  
Initial Distributions

AbstractWe prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.

scholarly journals SCIAMACHY tropospheric NO<sub>2</sub> over Switzerland: estimates of NO<sub>x</sub> lifetimes and impact of the complex Alpine topography on the retrieval

2007 ◽  
Vol 7 (23) ◽  
pp. 5971-5987 ◽  
Author(s):  
D. Schaub ◽  
D. Brunner ◽  
K. F. Boersma ◽  
J. Keller ◽  
D. Folini ◽  
...  
Keyword(s):  
A Priori ◽  
Regional Scale ◽  
Close Correlation ◽  
Sensitivity Study ◽  
Visible Spectral Range ◽  
Alpine Region ◽  
Emission Rates ◽  
General Ability ◽  
Swiss Plateau ◽  
Scanning Imaging

Abstract. This study evaluates NO2 vertical tropospheric column densities (VTCs) retrieved from measurements of the Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY) above Switzerland and the Alpine region. The close correlation between pixel averaged NOx emission rates from a spatially and temporally highly resolved inventory and the NO2 VTCs under anticyclonic meteorological conditions demonstrates the general ability of SCIAMACHY to detect sources of NOx pollution in Switzerland. This correlation is further used to infer seasonal mean NOx lifetimes carefully taking into account the influence of the strong diurnal cycle in NOx emissions on these estimates. Lifetimes are estimated to 3.6 (±0.8) hours in summer and 13.1 (±3.8) hours in winter, the winter value being somewhat lower than previous estimates. A comparison between the 2003-2005 mean NO2 VTC distribution over Switzerland and the corresponding 1996–2003 mean from the Global Ozone Monitoring Experiment (GOME) illustrates the much better capability of SCIAMACHY to resolve regional scale pollution features. However, the comparison of seasonal averages over the Swiss Plateau with GOME and ground based in situ observations indicates that SCIAMACHY exhibits a too weak seasonal cycle with comparatively high values in summer and low values in winter. A problem likely contributing to the reduced values in winter (not reported in earlier literature) is the use of inaccurate satellite pixel surface pressures derived from a coarse resolution global model in the retrieval. The marked topography in the Alpine region can lead to deviations of several hundred meters between the model assumed and the real pixel-averaged surface height. A sensitivity study based on selected clear sky SCIAMACHY NO2 VTCs over the Swiss Plateau and two fixed a priori NO2 profile shapes indicates that inaccurate pixel surface pressures affect retrieved NO2 columns over complex terrain by up to 40%. For retrievals in the UV-visible spectral range with a decreasing sensitivity towards the earth's surface, this effect is of major importance when the NO2 resides close to the ground, a situation most frequently observed during winter.

scholarly journals The Neuroelectromagnetic Inverse Problem and the Zero Dipole Localization Error

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Rolando Grave de Peralta ◽  
Olaf Hauk ◽  
Sara L. Gonzalez
Keyword(s):  
Inverse Problem ◽  
Unique Solution ◽  
A Priori ◽  
Inverse Solution ◽  
Localization Error ◽  
A Priori Information ◽  
Dipole Localization ◽  
Inverse Solutions ◽  
Priori Information ◽  
Additional Constraints

A tomography of neural sources could be constructed from EEG/MEG recordings once the neuroelectromagnetic inverse problem (NIP) is solved. Unfortunately the NIP lacks a unique solution and therefore additional constraints are needed to achieve uniqueness. Researchers are then confronted with the dilemma of choosing one solution on the basis of the advantages publicized by their authors. This study aims to help researchers to better guide their choices by clarifying what is hidden behind inverse solutions oversold by their apparently optimal properties to localize single sources. Here, we introduce an inverse solution (ANA) attaining perfect localization of single sources to illustrate how spurious sources emerge and destroy the reconstruction of simultaneously active sources. Although ANA is probably the simplest and robust alternative for data generated by a single dominant source plus noise, the main contribution of this manuscript is to show that zero localization error of single sources is a trivial and largely uninformative property unable to predict the performance of an inverse solution in presence of simultaneously active sources. We recommend as the most logical strategy for solving the NIP the incorporation of sound additional a priori information about neural generators that supplements the information contained in the data.

scholarly journals Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information

Algorithms ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 228
Author(s):  
Rasoul Shafipour ◽  
Gonzalo Mateos
Keyword(s):  
Inverse Problem ◽  
Covariance Matrix ◽  
A Priori ◽  
Dynamic Network ◽  
Streaming Data ◽  
Optimal Time ◽  
Time Varying ◽  
Graph Learning ◽  
Topology Inference ◽  
Diffusion Dynamics

We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup entails observations modeled as stationary graph signals generated by local diffusion dynamics on the unknown network. Moreover, we may have a priori information on the presence or absence of a few edges as in the link prediction problem. The stationarity assumption implies that the observations’ covariance matrix and the so-called graph shift operator (GSO—a matrix encoding the graph topology) commute under mild requirements. This motivates formulating the topology inference task as an inverse problem, whereby one searches for a sparse GSO that is structurally admissible and approximately commutes with the observations’ empirical covariance matrix. For streaming data, said covariance can be updated recursively, and we show online proximal gradient iterations can be brought to bear to efficiently track the time-varying solution of the inverse problem with quantifiable guarantees. Specifically, we derive conditions under which the GSO recovery cost is strongly convex and use this property to prove that the online algorithm converges to within a neighborhood of the optimal time-varying batch solution. Numerical tests illustrate the effectiveness of the proposed graph learning approach in adapting to streaming information and tracking changes in the sought dynamic network.

An approach for assessing suitability for forest management based on constraints of the physical environment at a regional scale

2015 ◽  
Vol 45 (5) ◽  
pp. 529-539 ◽  
Author(s):  
André Robitaille ◽  
Jean-Pierre Saucier ◽  
Michel Chabot ◽  
Damien Côté ◽  
Catherine Boudreault
Keyword(s):  
Forest Management ◽  
Physical Environment ◽  
A Priori ◽  
Regional Scale ◽  
Forest Growth ◽  
Sensitivity Analyses ◽  
Land Area ◽  
Forest Operations ◽  
Entire Study ◽  
Aeolian Deposits

Constraints of the physical environment affect forest growth and forest operations. At a local scale, these constraints are generally considered during forest operations. At regional or continental scales, they are often integrated to larger assessments of the potential for a given land unit to be managed. In this study, we propose an approach to analyze the integration of physical-environment constraints in forest management activities at the regional scale (482 000 km2). The land features that pose constraints to forest management (i.e., hydromorphic organic deposits, dead-ice moraines, washed till, glacial block fields, talus, and active aeolian deposits, slopes > 40%) were evaluated within 1114 land districts. To distinguish land districts that can be suitably managed from those where constraints are too important for sustainable timber production, we carried out a sensitivity analysis of physical constraints for the 1114 land districts. After analysis of two portions of the study area under management, a land district was considered suitable for management when more than 20% of its land area consists of features imposing few constraints or, for mountain-type relief districts, when more than 40% of the land area consists of features imposing few constraints. These cutoff values were defined by expert opinion, based on sensitivity analyses performed on the entire study area, on analyses of two different sectors with different types of constraints and on a strong understanding of the study area. Our results show that land districts where the physical environment posed significant constraints covered 7.5% of the study area (36 000 km2). This study shows that doing an a priori classification of land units based on permanent environmental features could facilitate the identification of areas that are not suitable for forest management activities.

The inverse problem in reducible Markov chains

1976 ◽  
Vol 13 (01) ◽  
pp. 49-56 ◽  
Author(s):  
W. D. Ray ◽  
F. Margo
Keyword(s):  
Inverse Problem ◽  
Markov Chain ◽  
Equilibrium Distribution ◽  
Probability Distributions ◽  
A Priori ◽  
Feasible Region ◽  
Numerical Examples ◽  
Transient States ◽  
Equilibrium Probability ◽  
Absorbing States

The equilibrium probability distribution over the set of absorbing states of a reducible Markov chain is specified a priori and it is required to obtain the constrained sub-space or feasible region for all possible initial probability distributions over the set of transient states. This is called the inverse problem. It is shown that a feasible region exists for the choice of equilibrium distribution. Two different cases are studied: Case I, where the number of transient states exceeds that of the absorbing states and Case II, the converse. The approach is via the use of generalised inverses and numerical examples are given.

scholarly journals Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source

2020 ◽  
Vol 28 (2) ◽  
pp. 211-235
Author(s):  
Tran Bao Ngoc ◽  
Nguyen Huy Tuan ◽  
Mokhtar Kirane
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Regularization Method ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Nonlinear Source ◽  
Numerical Example ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

AbstractIn this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.

scholarly journals Classification of Landslide Activity on a Regional Scale Using Persistent Scatterer Interferometry at the Moselle Valley (Germany)

2018 ◽  
Vol 10 (12) ◽  
pp. 1880 ◽  
Author(s):  
Andre Kalia
Keyword(s):  
A Priori ◽  
Regional Scale ◽  
Economic Loss ◽  
Data Availability ◽  
High Temporal Resolution ◽  
Persistent Scatterer Interferometry ◽  
Landslide Activity ◽  
Persistent Scatterer ◽  
Spatial Coverage ◽  
Sar Data

Landslides are a major natural hazard which can cause significant damage, economic loss, and loss of life. Between the years of 2004 and 2016, 55,997 fatalities caused by landslides were reported worldwide. Up-to-date, reliable, and comprehensive landslide inventories are mandatory for optimized disaster risk reduction (DRR). Various stakeholders recognize the potential of Earth observation techniques for an optimized DRR, and one example of this is the Sendai Framework for DRR, 2015–2030. Some of the major benefits of spaceborne interferometric Synthetic Aperture Radar (SAR) techniques, compared to terrestrial techniques, are the large spatial coverage, high temporal resolution, and cost effectiveness. Nevertheless, SAR data availability is a precondition for its operational use. From this perspective, Copernicus Sentinel-1 is a game changer, ensuring SAR data availability for almost the entire world, at least until 2030. This paper focuses on a Sentinel-1-based Persistent Scatterer Interferometry (PSI) post-processing workflow to classify landslide activity on a regional scale, to update existing landslide inventories a priori. Before classification, a Line-of-Sight (LOS) velocity conversion to slope velocity and a cluster analysis was performed. Afterwards, the classification was achieved by applying a fixed velocity threshold. The results are verified through the Global Positioning System (GPS) survey and a landslide hazard indication map.

scholarly journals Geometric and level set tomography using ensemble Kalman inversion

2019 ◽  
Vol 220 (2) ◽  
pp. 967-980
Author(s):  
Jack B Muir ◽  
Victor C Tsai
Keyword(s):  
Inverse Problem ◽  
Level Set ◽  
Large Scale ◽  
A Priori ◽  
Model Specification ◽  
A Priori Knowledge ◽  
Fast Marching ◽  
Near Surface ◽  
Derivative Free ◽  
Priori Knowledge

SUMMARY Tomography is one of the cornerstones of geophysics, enabling detailed spatial descriptions of otherwise invisible processes. However, due to the fundamental ill-posedness of tomography problems, the choice of parametrizations and regularizations for inversion significantly affect the result. Parametrizations for geophysical tomography typically reflect the mathematical structure of the inverse problem. We propose, instead, to parametrize the tomographic inverse problem using a geologically motivated approach. We build a model from explicit geological units that reflect the a priori knowledge of the problem. To solve the resulting large-scale nonlinear inverse problem, we employ the efficient Ensemble Kalman Inversion scheme, a highly parallelizable, iteratively regularizing optimizer that uses the ensemble Kalman filter to perform a derivative-free approximation of the general iteratively regularized Levenberg–Marquardt method. The combination of a model specification framework that explicitly encodes geological structure and a robust, derivative-free optimizer enables the solution of complex inverse problems involving non-differentiable forward solvers and significant a priori knowledge. We illustrate the model specification framework using synthetic and real data examples of near-surface seismic tomography using the factored eikonal fast marching method as a forward solver for first arrival traveltimes. The geometrical and level set framework allows us to describe geophysical hypotheses in concrete terms, and then optimize and test these hypotheses, helping us to answer targeted geophysical questions.

scholarly journals Atmospheric inversion of SO<sub>2</sub> and primary aerosol emissions for the year 2010

2013 ◽  
Vol 13 (13) ◽  
pp. 6555-6573 ◽  
Author(s):  
N. Huneeus ◽  
O. Boucher ◽  
F. Chevallier
Keyword(s):  
Biomass Burning ◽  
Fossil Fuel ◽  
A Priori ◽  
Regional Scale ◽  
Model Performance ◽  
So2 Emissions ◽  
Aerosol Model ◽  
Skill Scores ◽  
Emission Fluxes ◽  
Aerosol Emissions

Abstract. Natural and anthropogenic emissions of primary aerosols and sulphur dioxide (SO2) are estimated for the year 2010 by assimilating daily total and fine mode aerosol optical depth (AOD) at 550 nm from the Moderate Resolution Imaging Spectroradiometer (MODIS) satellite instrument into a global aerosol model of intermediate complexity. The system adjusts monthly emission fluxes over a set of predefined regions tiling the globe. The resulting aerosol emissions improve the model performance, as measured from usual skill scores, both against the assimilated observations and a set of independent ground-based measurements. The estimated emission fluxes are 67 Tg S yr−1 for SO2, 12 Tg yr−1 for black carbon (BC), 87 Tg yr−1 for particulate organic matter (POM), 17 000 Tg yr−1 for sea salt (SS, estimated at 80 % relative humidity) and 1206 Tg yr−1 for desert dust (DD). They represent a difference of +53, +73, +72, +1 and −8%, respectively, with respect to the first guess (FG) values. Constant errors throughout the regions and the year were assigned to the a priori emissions. The analysis errors are reduced with respect to the a priori ones for all species and throughout the year, they vary between 3 and 18% for SO2, 1 and 130% for biomass burning, 21 and 90 % for fossil fuel, 1 and 200% for DD and 1 and 5% for SS. The maximum errors on the global-yearly scale for the estimated fluxes (considering temporal error dependence) are 3% for SO2, 14% for BC, 11% for POM, 14% for DD and 2% for SS. These values represent a decrease as compared to the global-yearly errors from the FG of 7% for SO2, 40% for BC, 55% for POM, 81% for DD and 300% for SS. The largest error reduction, both monthly and yearly, is observed for SS and the smallest one for SO2. The sensitivity and robustness of the inversion system to the choice of the first guess emission inventory is investigated by using different combinations of inventories for industrial, fossil fuel and biomass burning sources. The initial difference in the emissions between the various set-ups is reduced after the inversion. Furthermore, at the global scale, the inversion is sensitive to the choice of the BB (biomass burning) inventory and not so much to the industrial and fossil fuel inventory. At the regional scale, however, the choice of the industrial and fossil fuel inventory can make a difference. The estimated baseline emission fluxes for SO2, BC and POM are within the estimated uncertainties of the four experiments. The resulting emissions were compared against projected emissions for the year 2010 for SO2, BC and POM. The new estimate presents larger emissions than the projections for all three species, with larger differences for SO2 than POM and BC. These projected SO2 emissions are outside the uncertainties of the estimated emission inventories.

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