We present a Bayesian model for the estimation of ground-motion models that allows one to account for truncated data. Truncated data occurs in ground-motion model development because instruments do not record continuously, but only when triggered. The model is formulated as a multi-level model and incorporates event and station terms. The model considers truncation on one variable [e.g., peak ground acceleration (PGA)], and models the joint occurrence of PGA and other ground-motion intensity measures, while conditioning on the truncation for PGA. Initially, we perform numerical experiments on simulated data sets and show that not taking data truncation into account leads to biased models. Regressions using the proposed truncated model can recapture the functions used in the simulation well, and perform comparable to alternative approaches used in the past. Subsequently, we show the impact of the truncated model on observed ground-motion data representing moderate and high trigger levels, 2–4 gal and 10 gal, respectively. Differences to a model that does not take truncation into account occur at larger distances, and are more severe for the high trigger level data. For untruncated regression, the values of the standard deviations are underestimated.

我们提出了一种估计地面运动模型的贝叶斯模型，该模型可以解决截断的数据。在地面运动模型开发中会出现截断的数据，因为仪器不会连续记录，而是仅在触发时才记录。该模型被表述为多级模型，并结合了事件和站点项。该模型考虑了一个变量的截断[例如，峰值地面加速度（PGA）]，并对PGA和其他地面运动强度度量的联合出现进行了建模，同时以PGA的截断为条件。最初，我们在模拟数据集上进行数值实验，结果表明，不考虑数据截断会导致模型产生偏差。使用建议的截断模型进行回归可以很好地捕获仿真中使用的功能，并具有与过去使用的替代方法相当的性能。随后，我们显示了截断模型对观察到的地面运动数据的影响，这些数据分别代表中度和高触发水平（分别为2–4 gal和10 gal）。与不考虑截断的模型的差异发生在较大的距离处，并且对于高触发电平数据而言更严重。对于不截断的回归，标准偏差的值被低估了。