Thermal Diagnostics with the Atmospheric Imaging Assembly onboard the Solar Dynamics Observatory: A Validated Method for Differential Emission Measure Inversions

We present a new method for performing differential emission measure (DEM) inversions on narrow-band EUV images from the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). The method yields positive definite DEM solutions by solving a linear program. This method has been validated against a diverse set of thermal models of varying complexity and realism. These include (1) idealized gaussian DEM distributions, (2) 3D models of NOAA Active Region 11158 comprising quasi-steady loop atmospheres in a non-linear force-free field, and (3) thermodynamic models from a fully-compressible, 3D MHD simulation of AR corona formation following magnetic flux emergence. We then present results from the application of the method to AIA observations of Active Region 11158, comparing the region's thermal structure on two successive solar rotations. Additionally, we show how the DEM inversion method can be adapted to simultaneously invert AIA and XRT data, and how supplementing AIA data with the latter improves the inversion result. The speed of the method allows for routine production of DEM maps, thus facilitating science studies that require tracking of the thermal structure of the solar corona in time and space.Comment: 21 pages, 18 figures, accepted for publication in Ap

IMPLEMENTATION OF A FAST MATRIX INVERSION METHOD IN THE ELECTRODYNAMIC SIMULATION PROGRAM

This paper describes the imple!llentation of a fast matrix inversion algorithm that can be used efficiently in the electric network analysis. The ElectroDynamic Simulation (EDS) is an IBM PC based computer program for studying short and middle term dynamics of the electric power system. The electric network is modelled by quasi-stationary representation. EDS has an interactive menu system. The user can change the operating conditions like sending telecommands from a control center-or initiate simulation of disturbances. Simulation of some events requires changing the network matrices. The admittance matrix Y can be modified directly while the impedance matrix Z is updated by inverting the new Y. The conventional inversion is very time consuming and freezes the simulation for unacceptably long intervals. A new, faster method has been developed which takes into account that the change in the matrices due to the events is small and well-defined. In these cases the complete inversion is not needed, the impedance matrix can be updated directly, by the aid of the Sherman-IvIorrison theorem. The new method has been implemented in recent EDS versions and performs significantly faster than the conventional inversion

Hulladéklerakók és környezetük állapotfelmérése geofizikai módszereinek fejlesztése = State qualification of waste sites and their surroundings and geophysical methods development for this purpose

Kutatásokat végeztünk a függvényinverziós módszerek fejlesztésére. Ennek egyik része az 1D előremodellezésen alapuló ún. 1.5D geoelektromos függvényinverziós vizsgálatok geológiai struktúrák esetére Módszert dolgoztunk ki az inverzióban a sorfejtési együtthatók számának meghatározására. Megállapítottuk, hogy a 1.5D inverzió változékony(tipikusan 2D) szerkezetek kimutatásánál nagy hibákat okozhat, ezért erre a közelítést alkalmazó módszerre annak folytatásaként ráépítettük az un. kombinált 2D (2.5D) inverziós módszert. Ezzel a módszerrel 2D/3D-véges differencia előremodellezést alkalmazva bonyolult szerkezetek is megfelelő pontossággal kimutathatók. Függvényinverziós módszert fejlesztettünk ki a szeizmikus refrakciós adatok és a geoelektromos adatok együttes kiértékelésére. Új felszíni geoelektromos módszert fejlesztettünk ki a hulladéklerakók természetes és mesterséges aljzatszigetelésének vizsgálatára. 3D véges differencia programmal végeztünk olyan számítógépes modellvizsgálatokat, amely alapján az új módszer mérési rendszere kialakítható és a mérési adatok kiértékelhetők a szigetelési sérülések kimutatására. A mérési módszer lényege, hogy az egyik áramelektródát a hulladéklerakó felszínére kell elhelyezni (szóba jöhet ennek speciális területi vagy vonalszerű kialakítása), a mérőelektródát/elektródákat a felszínen elhelyezve az elektromos potenciál vagy potenciálkülönbség eloszlásából lehet a sérülés helyére következtetni. | Our function inversion method developments concentrate on the evaluation of resistivity data . The 1.5D geoelectric function inversion - which based on 1D forward modeling - is suitable for examing the geological structures. We developed method to determined the optimum number of coefficients in the inversion. We established that the 1.5D inversion can cause significant errors in case of changeable structures that's why we added the combined 2D (2.5) inversion method for the 1.5D one. With this procedure if we use finite difference method for forward modeling we can determine the geoelectric parameters of the complicated structures with adequate accuracy. We developed function inversion method to evaluate the refraction and resistivity data together. After the development of the algorithm and the program we test them on synthetic and field data. We developed a new surface geoelectric method to study the natural and artificial impermeable layers of waste sites. We made studies with 3D finite difference program. By the results of the study the new measurement system can be developed and the faults of the impermeable layers can be detected. The essence of the method is that the current electrodes are placed on the surface (along the line, or regional configuration) of the waste deposit and using surface measuring electrodes and we are able to infer the place of faults from the electric potential or potential difference distribution

Snp_blup_rel: software for calculating individual animal SNP-BLUP model reliabilities

The snp_blup_rel program computes model reliabilities for genomic breeding values. The program assumes a single trait SNP-BLUP model where the breeding value can include a residual polygenic (RPG) effect. The reliability calculation requires elements of the inverse of the mixed model equations (MME). The calculation has three steps: 1) MME calculation, 2) MME coefficient matrix inversion, and 3) reliability computation. When needed, the inverted matrix can be saved after step 2. Step 3 can be used separately to new genotypes which do not contribute information to Step 2. When an RPG effect is included, an approximate method based on Monte Carlo sampling is applied. This reduces the MME matrix size and allows including many genotyped individuals. The program is written in Fortran 90/95, and uses LAPACK subroutines which enable multi-threaded parallel computing. The program is efficient in terms of computing time and memory requirements, and can be used to analyze even large genomic data. Thus, the program can be used in calculating model reliabilities for large national genomic evaluations

Regularization strategy for the layered inversion of airborne TEM data: application to VTEM data acquired over the basin of Franceville (Gabon)

Airborne transient electromagnetic (TEM) is a cost-effective method to image the distribution of electrical conductivity in the ground. We consider layered earth inversion to interpret large data sets of hundreds of kilometre. Different strategies can be used to solve this inverse problem. This consists in managing the a priori information to avoid the mathematical instability and provide the most plausible model of conductivity in depth. In order to obtain fast and realistic inversion program, we tested three kinds of regularization: two are based on standard Tikhonov procedure which consist in minimizing not only the data misfit function but a balanced optimization function with additional terms constraining the lateral and the vertical smoothness of the conductivity; another kind of regularization is based on reducing the condition number of the kernel by changing the layout of layers before minimizing the data misfit function. Finally, in order to get a more realistic distribution of conductivity, notably by removing negative conductivity values, we suggest an additional recursive filter based upon the inversion of the logarithm of the conductivity. All these methods are tested on synthetic and real data sets. Synthetic data have been calculated by 2.5D modelling; they are used to demonstrate that these methods provide equivalent quality in terms of data misfit and accuracy of the resulting image; the limit essentially comes on special targets with sharp 2D geometries. The real data case is from Helicopter-borne TEM data acquired in the basin of Franceville (Gabon) where borehole conductivity loggings are used to show the good accuracy of the inverted models in most areas, and some biased depths in areas where strong lateral changes may occur

Inversion of acoustical data from the SW06 experiment, using a statistical method for signal characterization

his paper presents an application of an acoustic signal characterization scheme for ocean acoustic tomography and geoacoustic inversions proposed by Taroudakis et al., using real data. The work is the first attempt to validate the proposed scheme with data taken from sea experiments. The data have been collected during the SW06 experiment held in the New Jersey Continental Shelf and the inversion results (sea-bed geoacoustic parameters and source range) are compared with those reported by Bonnel and Chapman. The comparison and the signal reconstruction using estimated values of the model parameters is satisfactory being an indication that the new signal characterization method can be used in practical applications of acoustical oceanography

A systematization of the saddle point method. Application to the Airy and Hankel functions

AbstractThe standard saddle point method of asymptotic expansions of integrals requires to show the existence of the steepest descent paths of the phase function and the computation of the coefficients of the expansion from a function implicitly defined by solving an inversion problem. This means that the method is not systematic because the steepest descent paths depend on the phase function on hand and there is not a general and explicit formula for the coefficients of the expansion (like in Watson's Lemma for example). We propose a more systematic variant of the method in which the computation of the steepest descent paths is trivial and almost universal: it only depends on the location and the order of the saddle points of the phase function. Moreover, this variant of the method generates an asymptotic expansion given in terms of a generalized (and universal) asymptotic sequence that avoids the computation of the standard coefficients, giving an explicit and systematic formula for the expansion that may be easily implemented on a symbolic manipulation program. As an illustrative example, the well-known asymptotic expansion of the Airy function is rederived almost trivially using this method. New asymptotic expansions of the Hankel function Hn(z) for large n and z are given as non-trivial examples