分层介质中无线电反射的精确球面波正演模型
Exact spherical-wave forward model for radio reflection from stratified media and implications for the anomalous-polarity events observed by ANITA
AI总结：
该研究提出分层介质的精确球面波无线电反射正演模型，验证其精度后应用于ANITA异常极性事件解释，测试快速传播模型的镜面分解，重现多数HiCal-1脉冲极性反转，适用于多种介质。
AI中文摘要：
超高能粒子（$\boldsymbol{\rm \textit{>}10^{18}}$ eV）的无线电探测依赖于宽带无线电脉冲从自然介质边界的反射特性。我们将单一均匀界面的球面波（Sommerfeld–Weyl）处理方法扩展至分层介质，方法是将每个平面波分量的菲涅耳系数替换为球面局部切平面上计算得到的分层介质特征矩阵反射系数。当消除层间对比度时，该计算在机器精度下可简化为单一边界的结果；在10个HiCal-2仰角下，其与已发表的球面表面计算结果的一致性优于1.1%，平均偏差为0.6%。我们将该形式体系应用于解释ANITA异常极性事件的浅冰堆积层模型。对于实际的冰堆积层对比度，分层会改变反射振幅，但在所研究的仰角下，不会在150–850 MHz频段内反转脉冲极性。在参考的s偏振双层模型中，在局部仰角8°、15°和25°时，系数符号反转分别需要埋藏折射率$\boldsymbol{\textit{n}_2 \backsimeq2.56}$、2.04和1.79。我们还测试了快速传播模型中使用的镜面分解方法，发现其与高空气球几何结构下的全角积分一致性为0.2%，而近边界源则需要全积分计算。计算得到的反射脉冲在106对HiCal-1直射/反射脉冲对中，重现了101对的预期极性反转。由于介质通过其复折射率引入，该框架适用于冰、月球 regolith（月壤）和导电介质。
英文摘要：
Radio detection of ultra-high energy particles relies on the propagation and reflection of broadband radio pulses at boundaries between natural media. In the Sommerfeld--Weyl treatment, a spherical wave is decomposed into plane-wave components and their reflection from a single homogeneous interface is calculated exactly. We extend that treatment to an arbitrary number of laterally uniform spherical layers. Both the spherical-wave decomposition of the source and the spherical geometry of the boundary are retained, while the reflection and transmission coefficients of the plane-wave components are replaced by the exact characteristic-matrix coefficients of the layered medium, evaluated at the local incidence angle on the spherical boundary. When the layer contrast is removed, the formalism recovers the single-boundary result to machine precision, and it reproduces the published spherical-surface reflectivity calculation to better than $1.1\%$ at ten HiCal-2 elevation angles, with a mean deviation of $0.6\%$. We reproduce the measured HiCal-1 reflected pulses from their measured direct partners, with a best signed correlation of $0.83$ and a median of $0.70$ across $106$ pairs, of which $101$ show the expected polarity inversion. Applied to the six reported ANITA anomalous-polarity event geometries, the buried-layer refractive index required for a sign change of the reflection coefficient ranges from $1.68$ at the steepest event to $3.8$--$5.4$ at the four near-horizon events. The full waveform calculation gives no non-inverted reflected pulse at any of these angles, showing that shallow, laterally uniform firn layering does not account for the polarity of the anomalous ANITA events. Because the formalism depends only on the complex refractive index of the medium, it applies more generally to isotropic, nonmagnetic stratified media, including ice, lunar regolith, and conducting layers.
