The InSight mission to Mars is well underway and will be the first mission to acquire seismic data from a planet other than Earth. In order to maximise the science return of the InSight data, a multifaceted approach will be needed that seeks to investigate the seismic data from a series of different frequency windows, including body waves, surface waves, and normal modes. Here, we present a methodology based on globally-averaged models that employs the long-period information encoded in the seismic data by looking for fundamental-mode spheroidal oscillations. From a preliminary analysis of the expected signal-to-noise ratio, we find that normal modes should be detectable during nighttime in the frequency range 5–15 mHz. For improved picking of (fundamental) normal modes, we show first that those are equally spaced between 5–15 mHz and then show how this spectral spacing, obtained through autocorrelation of the Fourier-transformed time series can be further employed to select normal mode peaks more consistently. Based on this set of normal-mode spectral frequencies, we proceed to show how this data set can be inverted for globally-averaged models of interior structure (to a depth of ∼250km$\sim 250~\mbox{km}$), while simultaneously using the resultant synthetically-approximated normal mode peaks to verify the initial peak selection. This procedure can be applied iteratively to produce a “cleaned-up” set of spectral peaks that are ultimately inverted for a “final” interior-structure model. To investigate the effect of three-dimensional (3D) structure on normal mode spectra, we constructed a 3D model of Mars that includes variations in surface and Moho topography and lateral variations in mantle structure and employed this model to compute full 3D waveforms. The resultant time series are converted to spectra and the inter-station variation hereof is compared to the variation in spectra computed using different 1D models. The comparison shows that 3D effects are less significant than the variation incurred by the difference in radial models, which suggests that our 1D approach represents an adequate approximation of the global average structure of Mars.

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关于确定火星内部结构的正常模式的可探测性和使用

InSight 火星任务正在进行中，这将是第一个从地球以外的行星获取地震数据的任务。为了最大限度地提高洞察力数据的科学回报，将需要一种多方面的方法来研究来自一系列不同频率窗口的地震数据，包括体波、表面波和正常模式。在这里，我们提出了一种基于全局平均模型的方法，该方法通过寻找基本模式球体振荡来利用地震数据中编码的长周期信息。通过对预期信噪比的初步分析，我们发现在夜间 5-15 mHz 的频率范围内应该可以检测到正常模式。为了改进（基本）正常模式的选择，我们首先展示那些在 5-15 mHz 之间等距间隔，然后展示如何进一步利用通过傅立叶变换时间序列的自相关获得的光谱间隔来更一致地选择正常模式峰值。基于这组正常模式频谱频率，我们继续展示如何将这个数据集反转为内部结构的全局平均模型（深度约为 250km$\sim 250~\mbox{km}$），同时使用合成近似的正常模式峰来验证初始峰选择。这个过程可以迭代地应用以产生一组“清理过的”光谱峰，这些峰最终被反转为“最终的”内部结构模型。为了研究三维 (3D) 结构对常模光谱的影响，我们构建了一个火星的 3D 模型，其中包括表面和莫霍面地形的变化以及地幔结构的横向变化，并使用该模型计算完整的 3D 波形。所得时间序列被转换为光谱，并将其站间变化与使用不同一维模型计算的光谱变化进行比较。比较表明，3D 效应不如径向模型差异引起的变化显着，这表明我们的 1D 方法代表了火星全球平均结构的充分近似。所得时间序列被转换为频谱，并将其站间变化与使用不同一维模型计算的频谱变化进行比较。比较表明，3D 效应不如径向模型差异引起的变化显着，这表明我们的 1D 方法代表了火星全球平均结构的充分近似。所得时间序列被转换为光谱，并将其站间变化与使用不同一维模型计算的光谱变化进行比较。比较表明，3D 效应不如径向模型差异引起的变化显着，这表明我们的 1D 方法代表了火星全球平均结构的充分近似。