Reconstruction Of Density Distribution Research Articles

3-D muographic inversion in the exploration of cavities and low-density fractured zones

SUMMARY Muography is an imaging tool based on the attenuation of cosmic muons for observing density anomalies associated with large objects, such as underground caves or fractured zones. Tomography based on muography measurements, that is, 3-D reconstruction of density distribution from 2-D muon flux maps, brings along special challenges. The detector field of view covering must be as balanced as possible, considering the muon flux drop at high zenith angles and the detector placement possibilities. The inversion from directional muon fluxes to a 3-D density map is usually underdetermined (more voxels than measurements). Therefore, the solution of the inversion can be unstable due to partial coverage. The instability can be solved by geologically relevant Bayesian constraints. However, the Bayesian principle results in parameter bias and artefacts. In this work, linearized (density-length based) inversion is applied by formulating the constraints associated with inversion to ensure the stability of parameter fitting. After testing the procedure on synthetic examples, an actual high-quality muography measurement data set from seven positions is used as input for the inversion. The resulting tomographic imaging provides details on the complicated internal structures of karstic fracture zone. The existence of low density zones in the imaged space was verified by samples from core drills, which consist of altered dolomite powder within the intact high density dolomite.

Gravity Data Inversion with Method of Local Corrections for Finite Elements Models

We present a new method for gravity data inversion for the linear problem (reconstruction of density distribution by given gravity field). This is an iteration algorithm based on the ideas of local minimization (also known as local corrections method). Unlike the gradient methods, it does not require a nonlinear minimization, is easier to implement and has better stability. The algorithm is based on the finite element method. The finite element approach in our study means that the medium (part of a lithosphere) is represented as a set of equal rectangular prisms, each with constant density. We also suggest a time-efficient optimization, which speeds up the inversion process. This optimization is applied on the gravity field calculation stage, which is a part of every inversion iteration. Its idea is to replace multiple calculations of the gravity field for all finite elements in all observation points with a pre-calculated set of uniform fields for all distances between finite element and observation point, which is possible for the current data set. Method is demonstrated on synthetic data and real-world cases. The case study area is located on the Timan-Pechora plate. This region is one of the promising oil- and gas-producing areas in Russia. Note that in this case we create a 3D density model using joint interpretation of seismic and gravity data.

Mesh-free free-form lensing – I. Methodology and application to mass reconstruction

Many applications and algorithms in the field of gravitational lensing make use of meshes with a finite number of nodes to analyze and manipulate data. Specific examples in lensing are astronomical CCD images in general, the reconstruction of density distributions from lensing data, lens-source plane mapping or the characterization and interpolation of a point-spread-function. We present a numerical framework to interpolate and differentiate in the mesh-free domain, defined by nodes with coordinates that follow no regular pattern. The framework is based on radial basis functions (RBFs) to smoothly represent data around the nodes. We demonstrate the performance of Gaussian RBF-based, mesh-free interpolation and differentiation, which reaches the sub-percent level in both cases. We use our newly developed framework to translate ideas of free-form mass reconstruction from lensing onto the mesh-free domain. By reconstructing a simulated mock lens we find that strong lensing only reconstructions achieve < 10% accuracy in the areas where these constraints are available but provide poorer results when departing from these regions. Weak-lensing only reconstructions give < 10% percent accuracy outside the strong lensing regime, but cannot resolve the inner core structure of the lens. Once both regimes are combined, accurate reconstructions can be achieved over the full field of view. The reconstruction of a simulated lens, using constraints that mimics real observations, yields accurate results in terms of surface-mass density, NFW parameter, Einstein radius and magnification map recovery, encouraging the application of this method to real data.

A Parallel Implementation of 3D Computed Tomography Algorithm

A computed tomography problem as a 3D reconstruction of density distribution is considered. The input data are obtained as a result of irradiations. The solution of the computed tomography problem is presented as a set of cross-section images. The reconstruction in a single cross-section is performed by algorithm of convolution and back projection. The parallelization is fulfilled over a set of cross-sections by use of the MPI technology.

An extension of quasi-one-dimensional tomography

A method for rapid limited-angle tomography is suggested thatallows the reconstruction of density distribution in hardwood sampleswith high accuracy and spatial resolution from only a few x-rayprojections. The sparsity of the experimental x-ray data iscompensated by incorporation of a priori knowledge aboutgeneric wood macrostructure, as well as some morphological informationobtainable from optical images of the sample surface, in themathematical framework of the tomographic analysis. Numerical testsof the proposed method confirm its potential as a practical techniquefor nondestructive testing of trees for scientific and industrialpurposes. It can also be useful for the analysis of other types ofobject with an underlying layered structure.