Multi-parameter reflection waveform inversion for acoustic transversely isotropic media with a vertical symmetry axis

Full waveform inversion in transversely isotropic media with a vertical symmetry axis provides an opportunity to better match the data at the near and far offsets. However, multi-parameter full waveform inversion, in general, suffers from serious cycle-skipping and trade-off problems. Reflection waveform inversion can help us recover a background model by projecting the residuals of the reflected wavefield along the reflection wavepath. Thus, we extend reflection waveform inversion to acoustic transversely isotropic media with a vertical symmetry axis utilizing the proper parameterization for reduced parameter trade-off. From a radiation patterns analysis, an acoustic transversely isotropic media with a vertical symmetry axis is better described by a combination of the normal-moveout velocity and the anisotropic parameters η and δ for reflection waveform inversion applications. We design a three-stage inversion strategy to construct the optimal resulting model. In the first stage, we only invert for the background by matching the simulated reflected wavefield from the perturbations of and δ with the observed reflected wavefield. In the second stage, the background and η are optimized simultaneously and the far-offset reflected wavefield mainly contribute to their updates. We perform Born modelling to compute the reflected wavefield for the two stages of reflection waveform inversion. In the third stage, we perform full waveform inversion for the acoustic transversely isotropic media with a vertical symmetry axis to delineate the high-wavenumber structures. For this stage, the medium is described by a combination of the horizontal velocity , η and ε instead of , η and δ. The acoustic multi-parameter full waveform inversion utilizes the diving waves to improve the background as well as utilizes reflection for high-resolution information. Finally, we test our inversion algorithm on the modified Sigsbee 2A model (a salt free part) and a two-dimensional line from a three-dimensional ocean bottom cable dataset. The results demonstrate that the proposed reflection waveform inversion approach can recover the background model for acoustic transversely isotropic media with a vertical symmetry axis starting from an isotropic model. This recovered background model can mitigate the cycle skipping of full waveform inversion and help the inversion recover higher resolution structures.     

地理国情监测质量抽查常见问题及关键点分析

随着地理国情监测进入常态化阶段,监测成果在自然资源调查和统计等领域发挥了重要作用,保障监测成果质量显得尤为重要。为保证地理国情监测过程质量符合技术设计要求,本文从质量管理和生产过程质量控制出发,结合检查过程中的常见问题,分析确定过程质量抽查的关键点,并最终保障监测成果真实、准确、可靠,为今后地理国情监测生产和质量控制提供有益参考。     

弹性静力学问题的边界积分形式的数值流形法

传统的数值流形法（NMM）一般均采用区域积分形式。结合边界单元法（BEM），提出了一种边界积分形式的数值流形法。该方法既能发挥NMM的可以灵活选取局部基的优势，又具有BEM降低问题求解维数的特点。针对二维的弹性静力学问题，对3个具有解析解的不同基准算例进行了数值应用，验证了所提方法的有效性和效率。计算结果表明，提高局部基的阶次可有效提高方法的计算精度。     

One to One Resonance at High Inclination

We report results from long term numerical integrations and analytical studies of particular orbits in the circular restricted three-body problem. These are mostly high-inclination trajectories in 1 : 1 resonance starting at or near the triangular Lagrangian L₅ point. In some intervals of inclination these orbits have short Lyapunov times, from 100 to a few hundred periods, yet the osculating semi-major axis shows only relatively small fluctuations and there are no escapes from the 1 : 1 resonance. The eccentricity of these chaotic orbits varies in an erratic manner, some of the orbits becoming temporarily almost rectilinear. Similarly the inclination experiences large variations due to the conservation of the Jacobi constant. We studied such orbits for up to 10⁹ periods in two cases and for 10⁶ periods in all others, for inclinations varying from 0° to 180°. Thus our integrations extend from thousands to 10 million Lyapunov times without escapes of the massless particle. Since there are no zero-velocity curves restricting the motion this opens questions concerning the reason for the persistence of the 1 : 1 resonant motion. In the theory sections we consider the mechanism responsible for the observed behavior. We derive the averaged 1 : 1 resonance disturbing function, to second order in eccentricity, to calculate a critical inclination found in the numerical experiment, and examine motion close to this inclination. The cause of the chaos observed in the numerical experiments appears to be the emergence of saddle points in the averaged disturbing potential. We determine the location of several such saddle points in the (, ) plane, with being the mean longitude difference and the argument of pericentre. Some of the saddle points are illustrated with the aid of contour plots of the disturbing function. Motion close to these saddles is sensitive to initial conditions, thus causing chaos.This revised version was published online in October 2005 with corrections to the Cover Date.     

A Note on Second Species Solutions Generated from p–q Resonant Orbits

The first image under the flow of the restricted three-body problem of the p—q resonant strips — that appear in the study of the p—q resonant orbits — do not have, in general, intersection with the strip. In this paper we show some particular situations in which the above intersections exist for some very simple p—q resonant orbits which, at the same time, are periodic second species solutions.This revised version was published online in October 2005 with corrections to the Cover Date.     

Mode analysis of structures using the Fourier p-element method

The Fourier p-element method is an improvement to the finite element method, and is particularly suitable for vibration analysis due to the well-behaved Fourier series. In this paper, an iteration procedure is presented for solving the resulting nonlinear eigenvalue problem. Three types of Fourier version shape functions are constructed for analyzing the circular shaft torsional vibration, the plate in-plane vibration and annular plate flexural vibration modes, respectively.The numerical results show that this method can achieve higher accuracy and converge much faster than the FEM based on polynomial interpolation, especially for higher mode analysis.     

Central Configurations of the Symmetric Restricted 4-Body Problem

We consider the symmetric planar (3 + 1)-body problem with finite masses m ₁ = m ₂ = 1, m ₃ = µ and one small mass m ₄ = . We count the number of central configurations of the restricted case = 0, where the finite masses remain in an equilateral triangle configuration, by means of the bifurcation diagram with as the parameter. The diagram shows a folding bifurcation at a value consistent with that found numerically by Meyer [9] and it is shown that for small > 0 the bifurcation diagram persists, thus leading to an exact count of central configurations and a folding bifurcation for small m ₄ > 0.     

Optimization of Time Data Codification and Transmission Schemes: Application to Gaia

Gaia is an ambitious space observatory devoted to obtain the largest and most precise astrometric catalogue of astronomical objects from our Galaxy and beyond. On-board processing and transmission of the huge amount of data generated by the instruments is one of its several technological challenges. The measurement time tags are critical for the scientific results of the mission, so they must be measured and transmitted with the highest precision – leading to an important telemetry channel occupation. In this paper we present the optimization of time data, which has resulted in a useful software tool. We also present how time data is adapted to the packet telemetry standard. The several communication layers are illustrated and a method for coding and transmitting the relevant data is described as well. Although our work is focused on Gaia, the timing scheme and the corresponding tools can be applied to any other instrument or mission with similar operational principles.