For a given {\it misfit function}, a specified optimality measure of a model, its gradient describes the manner in which one may alter properties of the system to march towards a stationary point. The adjoint method, arising from partial-differential-equation-constrained optimization, describes a means of extracting derivatives of a misfit function with respect to model parameters through finite computation. It relies on the accurate calculation of wavefields that are driven by two types of sources, namely the average wave-excitation spectrum, resulting in the {\it forward wavefield}, and differences between predictions and observations, resulting in an {\it adjoint wavefield}. All sensitivity kernels relevant to a given measurement emerge directly from the evaluation of an interaction integral involving these wavefields. The technique facilitates computation of sensitivity kernels (Fréchet derivatives) relative to three-dimensional heterogeneous background models, thereby paving the way for non-linear iterative inversions. An algorithm to perform such inversions using as many observations as desired is discussed.
Time-distance helioseismology is a set of powerful tools to study features below the Sun's surface. Inverse methods are needed to interpret time-distance measurements, with many examples in the literature. However, techniques that utilize a more statistical approach to inferences, and broadly used in the astronomical community, are less-commonly found in helioseismology. This article aims to introduce a potentially powerful inversion scheme based on Bayesian probability theory and Monte Carlo sampling that is suitable for local helioseismology. We describe the probabilistic method and how it i…
A time-distance helioseismic technique, similar to the one used by Ilonidis et al (2011), is applied to two independent numerical models of subsurface sound-speed perturbations to determine the spatial resolution and accuracy of phase travel time shift measurements. The technique is also used to examine pre-emergence signatures of several active regions observed by the Michelson Doppler Imager (MDI) and the Helioseismic Magnetic Imager (HMI). In the context of similar measurements of quiet sun regions, three of the five studied active regions show strong phase travel time shifts several hours …
A key component of solar interior dynamics is the meridional circulation (MC), whose poleward component in the surface layers has been well observed. Time-distance helioseismic studies of the deep structure of MC, however, have yielded conflicting inferences. Here, following a summary of existing results we show how a large center-to-limb systematics (CLS) in the measured travel times of acoustic waves affect the inferences through an analysis of frequency dependence of CLS, using data from the Helioseismic and Doppler Imager (HMI) onboard Solar Dynamics Observatory (SDO). Our results point to…
Time--Distance Helioseismology Data Analysis Pipeline for Helioseismic and Magnetic Imager onboard Solar Dynamics Observatory (SDO/HMI) and Its Initial Results
The study of solar oscillations (helioseismology) has been a very successful method of researching the Sun. Helioseismology teaches us about the structure and mean properties of the Sun. Together with mid-resolution data, the local properties were uncovered in quiet-Sun regions. However, magnetic fields affect the oscillations and prevent us from studying the properties of magnetically active regions with helioseismology. We aim to create a new methodology to suppress the negative effects of magnetic fields on solar oscillations and measure plasma properties close to active regions. The method…
Understanding the Travel-time Asymmetry of Acoustic Waves in Sunspots With Time-distance Helioseismology
Peking University(北京大学);National Space Science Center, Chinese Academy of Sciences(中国科学院国家空间科学中心);Instituto de Astrofísica de Canarias(加那利天体物理研究所);Universidad de La Laguna(拉古纳大学);Indian Institute of Astrophysics(印度天体物理研究所);KU Leuven(荷语鲁汶大学)
Context. Solar Rossby waves (r modes) have recently been discovered in the near-surface horizontal flow field using the techniques of granulation-tracking and ring-diagram analysis applied to six years of SDO/HMI data. Aims. Here we apply time-distance helioseismology to the combined SOHO/MDI and SDO/HMI data sets, which cover 21 years of observations from May 1996 to April 2017. The goal of this study is to provide an independent confirmation over two solar cycles and in deeper layers of the Sun. Methods. We have measured south-north helioseismic travel times along the equator, which are sens…
Sensitivity Kernels for Flows in Time-Distance Helioseismology: Extension to Spherical Geometry
我们扩展了现有的玻恩近似方法计算的线性灵敏度的日震走时流从笛卡尔球面几何。这一发展是必要的使用玻恩近似推断大规模的流动在太阳内部深处。在第一个健全检查,我们比较两个$f-$模式内核从我们的球形方法和现有的笛卡尔方法。水平积分和总积分在0.3%以内。作为第二个一致性检验,我们考虑一个匀速旋转的太阳和42度的旅行距离。分析旅行时的差异同意与正演模拟旅行时的差异在2%以内。此外,我们评估了不同的选择的过滤器功能的内核的42度的椭圆形的旅行距离的影响。对于所有的过滤器,灵敏度被发现分布在对流区的一个大的分数。我们表明,内核依赖于在数据分析过程中采用的过滤器功能。如果允许更高谐波度($90\lesssim l \lesssim 170$)的模式,则在表面附近出现对应于$l\approx 260$的空间尺度的噪声图案。当主要使用低阶模式($l\lesssim70$)时,灵敏度集中在最深的区域,并且在视觉上类似于射线路径状结构。在使用的不同的低阶滤波器中,我们发现相位速度滤波测量的内核在深度上是最好的本地化。
Helioseismic Signature of Chromospheric Downflows in Acoustic Travel-Time Measurements from Hinode
我们报告的一个签名的色球下降流在两个新兴的通量地区检测的时间距离日震学分析。我们使用Hinode/SOT获得的Ca II H线的色球强度振荡数据和Fe I 557.6nm线的光球多普勒数据进行分析。通过互相关的钙II振荡信号,我们已经检测到了一个旅行时间异常的plage地区,向外旅行时间比向内旅行时间短0.5-1分钟。然而,这样的异常是不存在的Fe I数据。这些结果可以解释为低色球层下行流的证据。下降速度估计低于10 km/s。这一结果表明,一个新的可能性研究色球流的时距分析。
The south-north travel-time differences are measured by applying time-distance helioseismology to the MDI and HMI medium-degree Dopplergrams covering May 1996-April 2017. Our data analysis corrects for several sources of systematic effects: P-angle error, surface magnetic field effects, and center-to-limb variations. An interpretation of the travel-time measurements is obtained using a forward-modeling approach in the ray approximation. The travel-time differences are similar in the southern hemisphere for cycles 23 and 24. However, they differ in the northern hemisphere between cycles 23 and …