Abstract The interferometric synthetic aperture radar (InSAR) small baseline subset (SBAS) technique can be applied to land with varying deformation magnitudes ranging from mm/yr to tens of cm/yr. SBAS defines a network of interferograms that is limited by temporal and spatial baseline thresholds that are often applied arbitrarily, or in apparently subjective ways in the literature. We use simulated SAR data to assess (1) the influence of residual noise and SBAS network configuration on InSAR-derived deformation rates, and (2) how the number of interferograms and data gaps in the time series may further impact the estimated rates. This leads us to an approach for defining a SBAS network based on geodetic reliability theory represented by the redundancy number (r-number). Simulated InSAR datasets are generated with three subsidence signals of linear rates plus sinusoidal annual amplitudes of −2 mm/yr plus 2 mm, −20 mm/yr plus 5 mm and −100 mm/yr plus 10 mm, contaminated by Gaussian residual noise bounded within [−2; +2] mm, [−5; +5] mm and [−10; +10] mm, corresponding to standard deviations of approximately 0.5 mm, 1.5 mm and 3.0 mm, respectively. The influence of data gaps is investigated through simulations with percentages of missing data ranging from 5% to 50% that are selected (1) randomly across the 4-year time series, and (2) for three-month windows to represent the northern winter season where snow cover may cause decorrelation. These simulations show that small deformation rates are most adversely affected by residual noise. In some extreme cases, the recovered trends can be contrary to the signal (i.e., indicating uplift when there is simulated subsidence). We demonstrate through simulations that the r-number can be used to pre-determine the reliability of SBAS network design, indicating the r-values between ~0.8 and ~0.9 are optimal. r-numbers less than ~0.3 can deliver erroneous rates in the presence of noise commensurate with the magnitude of deformation. Finally, the influence of data gaps is not as significant compared to other factors such as a change in the number of interferograms used, although the blocks of “winter” gaps in the SBAS network show a larger effect on the rates than gaps at random intervals across the simulated time series.

中文翻译：

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残余噪声、网络配置和数据缺口对使用 SBAS 技术的 InSAR 衍生的陆地运动速率的破坏性影响

摘要 干涉合成孔径雷达 (InSAR) 小基线子集 (SBAS) 技术可应用于变形幅度从 mm/yr 到数十 cm/yr 的陆地。SBAS 定义了一个干涉图网络，该网络受到时间和空间基线阈值的限制，这些阈值通常被任意应用，或以文献中明显主观的方式应用。我们使用模拟 SAR 数据来评估 (1) 残余噪声和 SBAS 网络配置对 InSAR 衍生变形率的影响，以及 (2) 时间序列中干涉图和数据间隙的数量如何进一步影响估计的变形率。这使我们找到了一种基于由冗余数（r 数）表示的大地测量可靠性理论来定义 SBAS 网络的方法。模拟 InSAR 数据集由三个线性速率加上正弦年振幅 -2 毫米/年加 2 毫米、-20 毫米/年加 5 毫米和 -100 毫米/年加 10 毫米的正弦年振幅生成，受高斯残余噪声限制在 [-2; +2] 毫米，[−5; +5] 毫米和 [−10; +10] mm，分别对应于大约 0.5 mm、1.5 mm 和 3.0 mm 的标准偏差。通过模拟调查数据差距的影响，缺失数据的百分比范围为 5% 到 50%，这些数据是 (1) 在 4 年时间序列中随机选择的，以及 (2) 以三个月的窗口代表北方冬季积雪可能导致去相关的季节。这些模拟表明，残余噪声对小变形率的影响最大。在某些极端情况下，恢复的趋势可能与信号相反（即，表示模拟下沉时的隆起）。我们通过模拟证明了 r 数可用于预先确定 SBAS 网络设计的可靠性，表明 ~0.8 和 ~0.9 之间的 r 值是最佳的。在存在与变形量相称的噪声的情况下，小于 ~0.3 的 r 数可能会产生错误的速率。最后，与其他因素（例如使用的干涉图数量的变化）相比，数据间隙的影响并不那么显着，尽管 SBAS 网络中的“冬季”间隙块对速率的影响大于随机间隔的间隙在模拟的时间序列中。表明 ~0.8 和 ~0.9 之间的 r 值是最佳的。在存在与变形量相称的噪声的情况下，小于 ~0.3 的 r 数可能会产生错误的速率。最后，与其他因素（例如使用的干涉图数量的变化）相比，数据间隙的影响并不那么显着，尽管 SBAS 网络中的“冬季”间隙块对速率的影响大于随机间隔的间隙在模拟的时间序列中。表明 ~0.8 和 ~0.9 之间的 r 值是最佳的。在存在与变形量相称的噪声的情况下，小于 ~0.3 的 r 数可能会产生错误的速率。最后，与其他因素（例如使用的干涉图数量的变化）相比，数据间隙的影响并不那么显着，尽管 SBAS 网络中的“冬季”间隙块对速率的影响大于随机间隔的间隙在模拟的时间序列中。