TEC Compensated Inversion Method of Ionospheric Occultation

For the inversion of ionospheric occultation data, the Abel inversion method of calibrated TEC is usually adopted, but the spherical asymmetry of the real ionosphere will bring errors to the inversion result of electron densities. This paper studies a TEC compensated inversion method. By combining with a background field, this method may eliminate the effect of the horizontal variability of electron density on the TEC, and improve the applicability of the assumption of spherical symmetry as well as the inversion accuracy. Applying this method to the inversion of simulative occultation events, the result demonstrates that compared with the traditional Abel transform inversion, the TEC compensated inversion method can reduce the inversion error. Comparing the various background fields obtained in different ways, it is shown that the higher the coincidence level between the background field and the real field, the better the inversion result.     

A chromospheric temperature inversion and its implications on millimeter brightness distribution

The brightness temperature curve of the quiet Sun at millimeter wavelengths suggests a possible inversion in the mid-millimeter range. Interpreting this as a result of an actual inversion in the chromospheric temperature structure, and example of a model chromoshere is presented whose calculated temperature curve exhibits such an inversion. This model is then tested for radial brightness distribution at millimeter wavelengths. Comparing the calculated distributions at 3.2 mm and 6 mm with eclipse measurements made with parabolic cylinders at 3.2 mm and 8.6 mm shows qualitative agreement, allowing for instrumental smoothing. It is conluded that a chromospheric temperature inversion, either actual or effective, could account for the inversion suggested by millimeter data and also the complex brightness distributions measured during eclipses with parabolic cylinders.     

Site-testing at Muztagh-ata site Ⅲ:temperature inversion in surface-layer atmosphere

In this article,we present detailed seasonal,monthly and daily statistics of temperature difference in the surface layer at the Muztagh-ata site based on the temperature measurements at two heights of 2 m and6 m.We find that temperature inversion occurs frequently at our site during nighttime,especially during the cold season.Strong temperature inversion always represents stable atmospheric turbulence,which is crucial for an optical observatory.By analyzing the behavior of temperature inversion and its correlation with wind and cloud amount,one conclusion can be made that radiation inversion is the main reason for the existence of temperature inversion in the surface-layer at the Muztagh-ata site.     

GPS/LEO掩星技术中超折射效应的修正

在GPS掩星探测地球大气技术中，Abel积分变换要求大气折射指数n是折射半径a的单值函数，当大气折射率的垂直梯度达到小于一个极限值dN／dr≈-0．16N-unit m^-1上述单值性不成立，称其为超折射，此时Abel积分变换不再适用,如果还是在形式上应用经典的Abel变换，在反演结果中就会产生负大气折射率偏差．描述了低对流层中超折射现象的物理特性和数学表示；在广义Abel积分变换的基础上，讨论了超折射层内和超折射层下的大气剖面反演算法；选择了一个简单的采样间隔内等大气折射率垂直梯度假设，对英国高分辨率无线电探空观测资料进行模拟计算，验证了负超折射与大气折射率偏差的关系，并提出的广义Abel变换的合理性.     

The Inversion Problem of Phase Travel Time Perturbations in Acoustic Imaging

The three-dimensional distribution of change in phase travel time of an active region below the solar surface can be constructed with the technique of acoustic imaging. The interpretation of the distribution of measured phase travel time perturbation suffers from the finite spatial resolution of the acoustic lenses. In the ray approximation, the phase travel time perturbation measured in acoustic imaging can be expressed as an integral of the product of the relative sound-speed perturbation and a kernel. Forward computations show that the vertical resolution of phase travel time perturbation is poor even in the ray approximation. In this study, we discuss the inversion of phase travel time perturbations to estimate the relative sound-speed perturbation with a regularized least-squares inversion method. The tests with model perturbations of sound speed show that the inversion reasonably recovers the distribution of the model perturbation. We also apply the inversion method to the measured phase travel time perturbation of active region NOAA 7981.     

Analysis of stellar occultation data: Effects of photon noise and initial conditions

A new inversion technique for obtaining temperature, pressure, and number density profiles of a planetary atmosphere from an occultation light curve is described. This technique employs an improved boundary condition to begin the numerical inversion and permits the computation of errors in the profiles caused by photon noise in the light curve. We present our assumptions about the atmosphere, optics, and noise and develop the equations for temperature, pressure, and number density and their associated errors. By inverting in equal increments of altitude, Δh, rather than in equal increments of time, Δt, the inversion need not be halted at the first negative point on the light curve as required by previous methods. The importance of the boundary condition is stressed, and a new initial condition is given. Numerical results are presented for the special case of inversion of a noisy isothermal light curve. From these results, simple relations are developed which can be used to predict the noise quality of an occultation. It is found that fractional errors in temperature profiles are comparable to those of pressure and number density profiles. An example of the inversion method is shown. Finally, we discuss the validity of our assumptions. In an appendix we demonstrate that minimum fractional errors in scale height determined from the inversion are comparable to those from an isothermal fit to a noisy isothermal light curve.     

Maximum Entropy Regularization Method of Ionospheric Occultation

With the increasing of applications of Global Positioning System (GPS), the research on the factors affecting the radio signals is becoming more and more important. One of the most significant effects on ionosphere monitoring is the ionospheric radio occultation (IRO), and the IRO data is now serving as one of the most important monitoring sources for the ionospheric measurements. Meanwhile the inversion of the occultation data is a popular topic. The traditional Abel inversion process through compensated total electron content (TEC) is a linear inversion method, thus it would transfer the measurement errors directly to the inversion results. In order to improve the occultation results, we introduce in this paper two nonlinear methods, namely the regularization method and the maximum entropy regularization method. Through designed simulative experiments, we verify and compare these three methods, and conclude that the maximum entropy regularization method can reduce significantly the influence of measurement errors.     

Inversion of synchrotron spectra

The problem of synchrotron radiation spectra is treated from the viewpoint of deconvolving the spectrum of ultrarelativistic source electrons from the observed photon spectrum. It is shown that for homogeneous sources the problem amounts to inversion of a Meijer transform with a modified Bessel finction kernel. A precise analytic inversion is only possible in the complex plane but Meijer transform tables are available for a wide range of functions. More convenient inversion formulae prove possible by use of a Laplace transform approximation or by analysing the spectra in terms of their integral moments. The filtering property of the transform is also established showing that the contribution to the synchrotron spectrum of high frequency components in the electron spectrum declines exponentially with their frequency. Thus, as with other Laplace-like transforms, only a few terms in an electron spectrum expansion can be deconvolved for any plausible noise level in the synchrotron spectrum.     

Inversion of relief on Mars

Relief inversion has been invoked to explain a number of geomorphic features of the martian surface. Terrestrial relief inversion occurs when former depressions become elevated because their fill is more resistant to erosion than the surrounding terrain. It is a common product of long-term landscape evolution on Earth, especially in relatively stable intra-cratonic settings and flat, or near flat lying successions. The inverted relief will preserve relicts of former land surfaces and is therefore older than the surrounding terrain. Relief inversion can occur by a range of processes, including infill of depressions by intrinsically resistant material, selective secondary cementation via diagenesis and weathering, or surface armouring. We examine a number of possible cases of inverted relief on Mars that appear to have formed by these three processes. We suggest that the most likely cementing agents for surface induration are iron oxides, silica, and sulfates. Possible cementation mechanisms include fluid mixing during regional groundwater flow, cooling of hydrothermal or basinal fluids as they near the surface, and evaporation and sublimation of near surface water. Wind action appears the most common erosive process on Mars capable of the regional landscape lowering necessary for relief inversion to occur, unlike on Earth where both deflation and runoff are important. Preliminary crater densities of selected features show that the tops of the proposed inverted relief have considerably more craters than the surrounding plains, as is predicted by the inversion hypothesis. More accurate dating of inverted surfaces and the adjacent areas may provide a simple way of measuring the degree of erosion over time in at least some areas of Mars.     

Filaments and large-scale magnetic fields

We have used Stanford magnetic field maps to construct distributions of longitudinal magnetic field gradients in the neighbourhood of polarity inversion lines. The distributions were constructed with proper account of the type of the polarity inversion lines and of the existence or absence of dark filaments above them. It is shown that for polarity inversion lines that pass inside active regions or on their boundary, grad B_II distributions for portions of the lines with persisting filament are shifted toward lower values of gradient as compared with grad B_II distributions for portions of the lines without filaments. The influence of the spatial resolution of the magnetograms upon polarity inversion line characteristics is discussed.     

A fast Stokes inversion technique based on quadratic regression

Stokes inversion calculation is a key process in resolving polarization information on radiation from the Sun and obtaining the associated vector magnetic fields. Even in the cases of simple local thermodynamic equilibrium(LTE) and where the Milne-Eddington approximation is valid, the inversion problem may not be easy to solve. The initial values for the iterations are important in handling the case with multiple minima. In this paper, we develop a fast inversion technique without iterations. The time taken for computation is only 1/100 the time that the iterative algorithm takes. In addition, it can provide available initial values even in cases with lower spectral resolutions. This strategy is useful for a filter-type Stokes spectrograph, such as SDO/HMI and the developed two-dimensional real-time spectrograph(2DS).     

On the thermal structure of Uranus

Uranus has an effective temperature close to the solar equilibrium value and undoubtedly a thermal inversion of at least 140 K at a pressure of ～3 dyncm^?2. With the inversion and the thermal opacity provided by a HeH₂ mixture in a ratio close to solar abundance, acceptable agreement can be achieved with the available infrared observations. The cause of the inversion is, however, uncertain. The use of the HeH₂ opacity for Uranus is justified by the excellent agreement of the frequency variation of that opacity with the thermal spectrum of Jupiter.     

Inversion of Zeeman polarization for solar magnetic field diagnostics

The topic of magnetic field diagnostics with the Zeeman effect is currently vividly discussed. There are some testable inversion codes available to the spectropolarimetry community and their application allowed for a better understanding of the magnetism of the solar atmosphere. In this context, we propose an inversion technique associated with a new numerical code. The inversion procedure is promising and particularly successful for interpreting the Stokes profiles in quick and sufficiently precise way. In our inversion, we fit a part of each Stokes profile around a target wavelength, and then determine the magnetic field as a function of the wavelength which is equivalent to get the magnetic field as a function of the height of line formation.To test the performance of the new numerical code, we employed “hare and hound” approach by comparing an exact solution (called input) with the solution obtained by the code (called output). The precision of the code is also checked by comparing our results to the ones obtained with the HAO MERLIN code. The inversion code has been applied to synthetic Stokes profiles of the Na D₁ line available in the literature. We investigated the limitations in recovering the input field in case of noisy data. As an application, we applied our inversion code to the polarization profiles of the Fe i λ 6302.5 Å observed at IRSOL in Locarno.     

电离层掩星反演的正则最大熵法

电离层掩星数据现已成为电离层观测数据的重要来源,对掩星数据的反演研究一直是掩星研究的热点.传统采用的改正TEC(1btal Electron Content)的Abel变换反演法为线性反演法,它会把测量误差带入反演结果中.为改善反演效果受测量误差的影响,引入两种非线性的反演方法一正则化和正则最大熵反演法.随后设计模拟试验,对3种方法进行验证、比较,得到正则最大熵反演法可以很好地减小测量误差的影响.     

Three-Dimensional Nonlinear Force-Free Field Reconstruction of Solar Active Region 11158 by Direct Boundary Integral Equation

A three-dimensional coronal magnetic field is reconstructed for the NOAA active region 11158 on 14 February 2011. A GPU-accelerated direct boundary integral equation (DBIE) method is implemented which is approximately 1000 times faster than the original DBIE used on solar non-linear force-free field modeling. Using the SDO/HMI vector magnetogram as the bottom boundary condition, the reconstructed magnetic field lines are compared with the projected EUV loop structures as observed in the front-view (SDO/AIA) and the side-view (STEREO-A/B) images for the first time; they show very good agreement three-dimensionally. A quantitative comparison with some stereoscopically reconstructed coronal loops shows that the average misalignment angles in our model are at the same order as the state-of-the-art results obtained from reconstructed coronal loops. It is found that the observed coronal loop structures can be grouped into a number of closed and open field structures with some central bright coronal loop features around the polarity inversion line. The reconstructed highly sheared magnetic field lines agree very well with the low-lying sigmoidal filament along the polarity inversion line. This central low-lying magnetic field loop system must have played a key role in powering the flare. It should be noted that while a strand-like coronal feature along the polarity inversion line may be related to the filament, one cannot simply interpret all the coronal bright features along the polarity inversion line as manifestation of the filament without any stereoscopic information.     

VFISV: Very Fast Inversion of the Stokes Vector for the Helioseismic and Magnetic Imager

In this paper we describe in detail the implementation and main properties of a new inversion code for the polarized radiative transfer equation (VFISV: Very Fast Inversion of the Stokes Vector). VFISV will routinely analyze pipeline data from the Helioseismic and Magnetic Imager (HMI) on-board of the Solar Dynamics Observatory (SDO). It will provide full-disk maps (4096×4096 pixels) of the magnetic field vector on the Solar Photosphere every ten minutes. For this reason VFISV is optimized to achieve an inversion speed that will allow it to invert sixteen million pixels every ten minutes with a modest number (approx. 50) of CPUs. Here we focus on describing a number of important details, simplifications and tweaks that have allowed us to significantly speed up the inversion process. We also give details on tests performed with data from the spectropolarimeter on-board of the Hinode spacecraft.     

太阳NOAA6891活动区磁中性线的分析

太阳活动高产区NOAA6891是一个岛型δ黑子，它有5条中性线，表现出不同的性质．其中第3条的横场比较弱，但是由于有剪切，所以有耀斑活动．而第2条中性线的横场较大，剪切得非常厉害，所以在这个区域产生了大量的耀斑，包括2个白光耀斑．正因为如此，所以要对磁场作三维分析，其中用磁场拓扑界面来分析是一种好的途径．     

Generalization of Lagrange's implicit function theorem to N-dimensions

A theorem for the inversion of a class of implicit functions, more general than the one considered by Lagrange, is proved. The inversion is developed as a power series in a small parameter. Recursive relations for the coefficients of the series are given.     

Top layers charaterization of the Martian surface: Permittivity estimation based on geomorphology analysis

Mars Express spacecraft inserted successfully Martian orbit at the end of 2003. On board this probe, a radar instrument called MARSIS (for Mars Advanced Radar for Surface and Ionosphere Sounding) is looking for water inside the first kilometers of Martian crust. To support MARSIS planning and data inversion, Laboratoire de Planétologie de Grenoble developed a MARSIS signal simulator.We show in this paper that MARSIS can also characterize some surface features, in addition to subsurface water and ionosphere sounding. We study a Martian surface region of special interest: Nilokeras Mensae, inside Acidalia Planitia. We discuss the previous geological studies of this region, and show the geomorphologies analyze of this surface area could lead to a simple terrain model. Then, we present a possible data inversion scheme and applying the MARSIS simulator, we test a first radar data inversion.Finally, we will show that complete dielectric characteristics of surface top layers can be retrieved, at least as often Mars Express flies over some layered terrain (at wavelength scale).     

Phase inversion of one-dimensional artificial seismic data

Oscillations of an inhomogeneous one-dimensional loop have been simulated for the purpose of examining the effect of excitation and damping on the sound-speed inversion based on phase analysis. It has been demonstrated that the procedure is robust against the realization noise arising from frequent, stochastic excitation of weakly damped waves, but that strong damping can spoil the inversion.