Aerosol size spectra from spectral extinction data: the use of a linear inversion method

1982 ◽  
Vol 21 (9) ◽  
pp. 1578 ◽  
Author(s):  
R. Rizzi ◽  
R. Guzzi ◽  
R. Legnani
Keyword(s):  
Inversion Method ◽  
Extinction Data ◽  
Linear Inversion ◽  
Size Spectra

2-D and 3-D resistivity image reconstruction using crosshole data

Geophysics ◽  
1992 ◽  
Vol 57 (10) ◽  
pp. 1270-1281 ◽  
Author(s):  
Hiromasa Shima
Keyword(s):  
Field Test ◽  
Numerical Models ◽  
Electrical Potential ◽  
Nonlinear Least Squares ◽  
Three Dimensions ◽  
Inversion Method ◽  
Good Resolution ◽  
Inversion Algorithm ◽  
Linear Inversion ◽  
Resistivity Model

Theoretical changes in the distribution of electrical potential near subsurface resistivity anomalies have been studied using two resistivity models. The results suggest that the greatest response from such anomalies can be observed with buried electrodes, and that the resistivity model of a volume between boreholes can be accurately reconstructed by using crosshole data. The distributive properties of crosshole electrical potential data obtained by the pole‐pole array method have also been examined using the calculated partial derivative of the observed apparent resistivity with respect to a small cell within a given volume. The results show that for optimum two‐dimensional (2-D) and three‐dimensional (3-D) target imaging, in‐line data and crossline data should be combined, and an area outside the zone of exploration should be included in the analysis. In this paper, the 2-D and 3-D resistivity images presented are reconstructed from crosshole data by the combination of two inversion algorithms. The first algorithm uses the alpha center method for forward modeling and reconstructs a resistivity model by a nonlinear least‐squares inversion. Alpha centers express a continuously varying resistivity model, and the distribution of the electrical potential from the model can be calculated quickly. An initial general model is determined by the resistivity backprojection technique (RBPT) prior to the first inversion step. The second process uses finite elements and a linear inversion algorithm to improve the resolution of the resistivity model created by the first step. Simple 2-D and 3-D numerical models are discussed to illustrate the inversion method used in processing. Data from several field studies are also presented to demonstrate the capabilities of using crosshole resistivity exploration techniques. The numerical experiments show that by using the combined reconstruction algorithm, thin conductive layers can be imaged with good resolution for 2-D and 3-D cases. The integration of finite‐element computations is shown to improve the image obtained by the alpha center inversion process for 3-D applications. The first field test uses horizontal galleries to evaluate complex 2-D features of a zinc mine. The second field test illustrates the use of three boreholes at a dam site to investigate base rock features and define the distribution of an altered zone in three dimensions.

Non linear inversion of gravity gradients and the GGI gradiometer

2011 ◽  
Vol 3 (4) ◽  
Author(s):  
Manik Talwani
Keyword(s):  
Iterative Procedure ◽  
Least Square ◽  
Inversion Method ◽  
Gravity Gradients ◽  
Linear Inversion ◽  
Non Linear ◽  
Best Fitting ◽  
The Difference ◽  
Differential Curvature ◽  
Fitting Model

AbstractAll gradiometers currently operating for exploration in the field are based on Lockheed Martin’s GGI gradiometer. The working of this gradiometer is described and a method for robust non linear inversion of gravity gradients is presented. The inversion method involves obtaining the gradient response of a trial body consisting of vertical rectangular prisms. The inversion adjusts the depth to the tops or bases of the prisms. In the trial model all the prisms are not required to have the same area of cross section or the same density (which can also be allowed to vary with depth). The depth to the tops and bottoms of each prism can also be different. This response is compared with the observed values of gradient and through an iterative procedure, the difference is minimized in a least square sense to arrive at a best fitting model by varying the position of the tops or bottoms of the prisms. Each gradient can be individually inverted or one or more gradients can be jointly inverted. The method is extended to invert gravity values individually or jointly with gradient values. The use of Differential Curvature, a quantity which is directly obtained by current gradiometers in use and which is an invariant under a rotation in the horizontal plane, is emphasized. Synthetic examples as well as a field example of inversion are given.

scholarly journals A Simple Quantitative Inversion Approach for Microwave Imaging in Embedded Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
M. Ambrosanio ◽  
R. Scapaticci ◽  
L. Crocco
Keyword(s):  
Real Time ◽  
Quantitative Imaging ◽  
Impedance Matching ◽  
Field Approximation ◽  
Microwave Imaging ◽  
Point Of View ◽  
Inversion Method ◽  
Linear Inversion ◽  
Imaging Results ◽  
Different Shapes

In many applications of microwave imaging, there is the need of confining the device in order to shield it from environmental noise as well as to host the targets and the medium used for impedance matching purposes. For instance, in MWI for biomedical diagnostics a coupling medium is typically adopted to improve the penetration of the probing wave into the tissues. From the point of view of quantitative imaging procedures, that is aimed at retrieving the values of the complex permittivity in the domain under test, the presence of a confining structure entails an increase of complexity of the underlying modelling. This entails a further difficulty in achieving real-time imaging results, which are obviously of interest in practice. To address this challenge, we propose the application of a recently proposed inversion method that, making use of a suitable preprocessing of the data and a scenario-oriented field approximation, allows obtaining quantitative imaging results by means of quasi-real-time linear inversion, in a range of cases which is much broader than usual linearized approximations. The assessment of the method is carried out in the scalar 2D configuration and taking into account enclosures of different shapes and, to show the method’s flexibility different shapes, embedding nonweak targets.

scholarly journals The Community Cloud retrieval for CLimate (CC4CL). Part II: The optimal estimation approach

2017 ◽  
Author(s):  
Gregory R. McGarragh ◽  
Caroline A. Poulsen ◽  
Gareth E. Thomas ◽  
Adam C. Povey ◽  
Oliver Sus ◽  
...  
Keyword(s):  
A Priori ◽  
Optimal Estimation ◽  
Forward Model ◽  
Inversion Method ◽  
Surface Model ◽  
Linear Inversion ◽  
Retrieval Method ◽  
Ice Cloud ◽  
Cloud Models ◽  
Community Cloud

Abstract. The Community Cloud retrieval for Climate (CC4CL) is a cloud property retrieval system for satellite-based multispectral imagers and is an important component of the Cloud Climate Change Initiative (Cloud_cci) project. In this paper we discuss the optimal estimation retrieval of cloud optical thickness, effective radius and cloud top pressure based on the Optimal Retrieval of Aerosol and Cloud (ORAC) algorithm. Key to this method is the forward model which, includes the clear-sky model, the liquid water and ice cloud models, the surface model including a bidirectional reflectance distribution function (BRDF), the "fast" radiative transfer solution (which includes a multiple scattering treatment) All of these components and their assumptions and limitations will be discussed in detail. The forward model provides the accuracy appropriate for our retrieval method. The errors are comparable to the instrument noise for cloud optical thicknesses greater than 10. At optical thicknesses less than 10 modelling errors become more significant. The retrieval method is then presented describing optimal estimation in general, the non-linear inversion method employed, measurement and a priori inputs, the propagation of input uncertainties and the calculation of subsidiary quantities that are derived from the retrieval results. An evaluation of the retrieval was performed using measurements simulated with noise levels appropriate for the MODIS instrument. Results show errors less than 10 % for cloud optical thicknesses greater than 10. Results for clouds of optical thicknesses less than 10 have errors ranging up to 20 %.

Inverting travel times with a triplication

1982 ◽  
Vol 72 (6A) ◽  
pp. 2147-2170
Author(s):  
Hans S. Jarosch
Keyword(s):  
Body Wave ◽  
P Wave ◽  
Inversion Method ◽  
Linear Inversion ◽  
Time Curve ◽  
Wave Travel ◽  
Data Points ◽  
A New Technique ◽  
The Right ◽  
Lunar Core

abstract A new technique has been developed to overcome difficulties which arise when body-wave data in the form of T-delta is reduced to the tau-p form in the presence of cusps. The technique uses sophisticated constrained spline fits to allow for constraints on the derivatives and thus eliminates the possibility of points of inflexion occurring as well as making sure that the curvature is in the right direction. Having arrived at a good fit to the T-delta data with a single spline, the tau-p curve can be derived which has taken the cusp properly into consideration. The tau-p curve is then inverted with a new linear inversion method, which again takes into consideration whether a particular point lies on a prograde or retrograde branch. The technique is applied to the lunar seismic data, where at least one triplication is presumed to occur for the P-wave travel-time curve. It is shown that the present analysis is not accurate enough to address itself to the problem of a possible lunar core, since there are insufficient data points for events close to the antipode of the center of the lunar network.

scholarly journals A linear inversion method to infer exhumation rates in space and time from thermochronometric data

2014 ◽  
Vol 2 (1) ◽  
pp. 47-65 ◽  
Author(s):  
M. Fox ◽  
F. Herman ◽  
S. D. Willett ◽  
D. A. May
Keyword(s):  
Linear System ◽  
Resolving Power ◽  
Inversion Method ◽  
Model Parameters ◽  
Time Interval ◽  
Time Intervals ◽  
Linear Inversion ◽  
Exhumation Rate ◽  
Space And Time ◽  
Exhumation Rates

Abstract. We present a formal inverse procedure to extract exhumation rates from spatially distributed low temperature thermochronometric data. Our method is based on a Gaussian linear inversion approach in which we define a linear problem relating exhumation rate to thermochronometric age with rates being parameterized as variable in both space and time. The basis of our linear forward model is the fact that the depth to the "closure isotherm" can be described as the integral of exhumation rate, ..., from the cooling age to the present day. For each age, a one-dimensional thermal model is used to calculate a characteristic closure temperature, and is combined with a spectral method to estimate the conductive effects of topography on the underlying isotherms. This approximation to the four-dimensional thermal problem allows us to calculate closure depths for data sets that span large spatial regions. By discretizing the integral expressions into time intervals we express the problem as a single linear system of equations. In addition, we assume that exhumation rates vary smoothly in space, and so can be described through a spatial correlation function. Therefore, exhumation rate history is discretized over a set of time intervals, but is spatially correlated over each time interval. We use an a priori estimate of the model parameters in order to invert this linear system and obtain the maximum likelihood solution for the exhumation rate history. An estimate of the resolving power of the data is also obtained by computing the a posteriori variance of the parameters and by analyzing the resolution matrix. The method is applicable when data from multiple thermochronometers and elevations/depths are available. However, it is not applicable when there has been burial and reheating. We illustrate our inversion procedure using examples from the literature.

scholarly journals Assessing the Capabilities of a New Linear Inversion Method for Quantitative Microwave Imaging

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Loreto Di Donato ◽  
Roberta Palmeri ◽  
Gino Sorbello ◽  
Tommaso Isernia ◽  
Lorenzo Crocco
Keyword(s):  
Numerical Analysis ◽  
Cross Section ◽  
Born Approximation ◽  
Circular Cross Section ◽  
Microwave Imaging ◽  
Inversion Method ◽  
Dielectric Cylinder ◽  
Quantitative Criterion ◽  
Linear Inversion ◽  
Imaging Approach

We investigate the imaging capabilities of a new linear microwave imaging approach, which allows to quantitative retrieve the complex permittivity distribution of unknown nonweak targets. To this end, we carry out a parametric numerical analysis for a canonical scatterer (a homogeneous dielectric cylinder with circular cross section) and derive a quantitative criterion to foresee the method’s applicability. The reliability of the criterion is then tested against noncanonical scatterers to show the effectiveness of the method in imaging nonweak targets and in outperforming the linearized inversion method based on the standard Born approximation.

scholarly journals PEMODELAN INVERSI DATA MAGNETOTELLURIK 1-D MENGGUNAKAN METODA GENETIC ALGORITHM (GA) DENGAN POPULASI MICRO GENETIC ALGORITHM KASUS 3 LAYER DAN 5 LAYER

2019 ◽  
Vol 8 (2) ◽  
pp. 167-180
Author(s):  
Nia Maharani
Keyword(s):  
Genetic Algorithm ◽  
Natural Selection ◽  
Selection Process ◽  
Synthetic Data ◽  
Inversion Method ◽  
Earth Model ◽  
Observation Data ◽  
Linear Inversion ◽  
Synthetic Model ◽  
Micro Genetic Algorithm

This paper discusses non-linear inversion method with Genetic Algorithm (GA) which inspired by natural selection process (survival for the fittest) and genetic using 20 populations (micro genetic algorithm). The method is applied to 1-D magnetotelluric inverted data with model parameter is resistivity as a function of depth. This research only uses synthetic data obtained from synthetic model. The model is homogeneous earth model with 3 and 5 layers. Perturbation of model is performed until minimum misfit between theoritical and observation data achieved. The 3 layers and 5 layers inversion processes are applied to 3 layers and 5 layers earth model respectively, with satisfactory results in other words it can reproduce the synthetic model.

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