Long-Period Variations of the Eccentricity Vector Valid also for Near Circular Orbits around a Non-Spherical Body

This paper studies the long period variations of the eccentricity vector of the orbit of an artificial satellite, under the influence of the gravity field of a central body. We use modified orbital elements which are non-singular at zero eccentricity. We expand the long periodic part of the corresponding Lagrange equations as power series of the eccentricity. The coefficients characterizing the differential system depend on the zonal coefficients of the geopotential, and on initial semi-major axis, inclination, and eccentricity. The differential equations for the components of the eccentricity vector are then integrated analytically, with a definition of the period of the perigee based on the notion of “free eccentricity”, and which is also valid for circular orbits. The analytical solution is compared to a numerical integration. This study is a generalization of (Cook, Planet. Space Sci., 14, 1966): first, the coefficients involved in the differential equations depend on all zonal coefficients (and not only on the very first ones); second, our method applies to nearly circular orbits as well as to not too eccentric orbits. Except for the critical inclination, our solution is valid for all kinds of long period motions of the perigee, i.e., circulations or librations around an equilibrium point.     

对月日潮汐摩擦耗散的估计

月日潮汐摩擦和地球惯量矩变化是日长长期变化的主要原因．在本文中，利用最新的地球物理和古生物钟数据，对过去15亿年以来的月日潮汐摩擦、地球惯量矩变化和日长长期变化等作了数值对比研究．由此得到二个重要结论：一是仅利用地球的自转形变不能解释J2的变化，这说明地球的重力分异现象至今仍存在着；其二是在几亿年前的潮汐摩擦比现在大得多，若取潮汐耗散与距离的立方成反比时，理论结果与由古生物钟得到的回归年日数和朔望月日数数据较为符合。     

Waveform Shaping of Sonar Transducers for Improving the Vertical Resolution in Sub-bottom Sediments Profiling

Vertical resolution is of fundamental importance in sonar exploration and is directly related to the duration of the acoustic pulse generated by the transducer. The shorter the radiated pulse, the higher the vertical resolution. Many sub-bottom profiling sonar systems use piezoelectric transducers because they are reversible and well understood. Piezoelectric projectors are normally resonant transducers, which are intrinsically narrowband. A piezoelectric transducer is usually driven by a tone-burst. However, it is possible to use Fourier techniques to find a pre-compensated electrical driving function so that the transducer radiates a prescribed wider band acoustic waveform. This technique can be applied to synthesize zero-phase cosine-magnitude, Gaussian, and bionic pulses, with a conventional sandwich transducer. Zero-phase cosine-magnitude waveforms provide minimum length pulses (and therefore maximum resolution) within a prescribed frequency band.The aim of this paper is to illustrate the synthesis of wideband acoustic pulses using an underwater piezoelectric projector. The conventional acoustic waveform radiated when a Tonpiltz transducer is transiently excited using a “click” and allows its frequency response function to be measured. This function is used to design the electrical signal which then drives the transducer so that it radiates the shortest pulse compatible with its mechanical response. The significant resolution enhancement of the waveform shaping process is illustrated by its application to a sediment wedge model.     

Estimation of Sea Ice Thickness from SARAL/AltiKa in Drifting Orbit Phase

Abstract

Intra and inter-annual variations in the sea ice thickness are highly sensitive indicators of climatic variations undergoing in the earth’s atmosphere and oceans. This paper describes the method of estimating sea ice thickness using radar waveforms data acquired by SARAL/Altika mission during its drifting orbit phase from July 2016 onwards yielding spatially dense data coverage. Based on statistical analysis of return echoes, classification of the surface has been carried out in three different types, viz. floe, lead and mixed. Time delay correction methods were suitably selected and implemented to make corrections in altimetric range measurements and thereby freeboard. By assuming hydrostatic equilibrium, freeboard data were converted into sea ice thickness. Results show that sea ice thickness varies from 4 to 5?m near ice shelves and 1 to 2.5?m in the marginal sea ice regions. Freeboard and sea ice thickness estimates were also validated using NASA’s Operation Ice Bridge (OIB) datasets. Freeboard measurements show very high correlation (0.97) having RMSE of 0.13. Overestimation of approximately 1–2?m observed in the sea ice thickness, which could be attributed to distance between AltiKa footprint and OIB locations. Moreover, sensitivity analysis shows that snow depth and snow density over sea ice play crucial role in the estimation of sea ice thickness.     

雄安新区地热地质模型探究：来自地球物理的证据

雄安新区内地热资源丰富，区内有牛驼镇地热田、容城地热田和高阳地热田，地热资源开发利用较早，但是对其深部热源机制仍未形成统一观点。为了研究雄安新区内地热田深部热源机制，在新区及外围进行了深反射地震和长周期大地电磁探测，对取得的同剖面的深反射地震和大地电磁数据进行处理和综合解释，探明了研究区从地表至莫霍面范围内地质构造和电性结构。下地壳结构在深反射地震剖面与大地电磁剖面上有很好的对应关系。电阻率低值区对应着在深反射地震剖面上存在一系列反射同相轴，且同相轴可以延续到莫霍面，电阻率高值区对应着在深反射地震剖面上无明显连续反射同相轴，尤其是在莫霍面之上呈现地震反射近似"空白区"。结合区域地热资料构建了研究区深部地热地质模型，对新区内深部地热机制进行了解释。该模型为"二元"生热模型，其热源包含两个部分，深部地幔热源和地壳放射性元素衰变生热。放射性元素衰变生热占地表热流的接近30%，而幔源热流在地表热流中的占比可达约70%。在牛驼镇下方，莫霍面以上，由于地幔热物质上涌造成下地壳上隆，幔源岩浆底侵作用于下地壳形成了局部热异常，该热异常具有低速高导的地球物理特征，认为是牛驼镇地热田和容城地热田的深部热源；以区域断裂为热通道，大地热流由深部向上传导、扩散到牛驼镇凸起和容城凸起顶部，对碳酸盐岩储水层进行加热，形成地热储层；上覆新近系沉积地层是良好的热盖层。     

Re-evaluation of focal depths and source mechanisms of selected earthquakes in the Afar depression

We present a stepwise inversion procedure to assess the focal depth and model earthquake source complexity of seven moderate-sized earthquakes  (6.2 > M _w > 5.1)  that occurred in the Afar depression and the surrounding region. The Afar depression is a region of highly extended and intruded lithosphere, and zones of incipient seafloor spreading. A time-domain inversion of full moment tensor was performed to model direct P and SH waves of teleseismic data. Waveform inversion of the selected events estimated focal depths in the range of 17–22 km, deeper than previously published results. This suggests that the brittle–ductile transition zone beneath parts of the Afar depression extends more than 22 km. The effect of near-source velocity structure on the moment tensor elements was also investigated and was found to respond little to the models considered. Synthetic tests indicate that the size of the estimated, non-physical, non-isotropic source component is rather sensitive to incorrect depth estimation. The dominant double couple part of the moment tensor solutions for most of the events indicates that their occurrence is mainly due to shearing. Parameters associated with source directivity (rupture velocity and azimuth) were also investigated. Re-evaluation of the analysed events shows predominantly normal faulting consistent with the relative plate motions in the region.