Models for postseismic transient displacements can be formulated using logarithmic and exponential decay formulas with single or multiple timescales. The logarithmic form is associated with rate and state friction theory and afterslip, while the exponential form is associated with bulk viscoelastic relaxation of coseismic stresses. It is now quite widely understood that one can model GPS/GNSS time series manifesting postseismic transient displacements almost equally well using trajectory models constructed using logarithmic or exponential transients. This is consistent with the consensus established by the late 1970s that it is difficult to use geodetic observations to distinguish between deep aseismic afterslip and more diffuse viscoelastic relaxation as the primary mechanism of postseismic deformation. In this paper, we assess the relative explanatory value of both logarithmic and exponential forms by focusing on GNSS time series measured with better than typical signal-to-noise ratios. We find that the double logarithmic transient typically provides much better fits than double exponential transient, when both models are given equal degrees of freedom. We also discuss the relative utility of the hybrid transient formulas in which the logarithmic component is assigned shorter decay timescale parameters than the exponential component. These models fit observed postseismic displacements almost as well as double logarithmic transients.

中文翻译：

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GNSS 轨迹模型中的对数和指数瞬变作为震后变形主要过程的指标

可以使用具有单个或多个时间尺度的对数和指数衰减公式来制定震后瞬态位移模型。对数形式与速率和状态摩擦理论以及后滑相关，而指数形式与同震应力的体积粘弹性松弛相关。现在已经很广泛地理解，人们可以使用使用对数或指数瞬态构建的轨迹模型几乎同样好地对显示震后瞬态位移的 GPS/GNSS 时间序列进行建模。这与 1970 年代后期建立的共识一致，即难以使用大地观测来区分深地震后滑和更弥散的粘弹性松弛作为震后变形的主要机制。在本文中，我们通过关注以优于典型信噪比的方式测量的 GNSS 时间序列来评估对数和指数形式的相对解释值。我们发现，当两个模型具有相同的自由度时，双对数瞬态通常比双指数瞬态提供更好的拟合。我们还讨论了混合瞬态公式的相对效用，其中对数分量分配的衰减时间尺度参数比指数分量更短。这些模型几乎符合观测到的震后位移以及双对数瞬变。我们发现，当两个模型具有相同的自由度时，双对数瞬态通常比双指数瞬态提供更好的拟合。我们还讨论了混合瞬态公式的相对效用，其中对数分量分配的衰减时间尺度参数比指数分量更短。这些模型几乎符合观测到的震后位移以及双对数瞬变。我们发现，当两个模型具有相同的自由度时，双对数瞬态通常比双指数瞬态提供更好的拟合。我们还讨论了混合瞬态公式的相对效用，其中对数分量被分配比指数分量更短的衰减时间尺度参数。这些模型几乎符合观测到的震后位移以及双对数瞬变。