Development of a High-Gain Rotational-Motion Seismograph

我们提出了一种方法来获得震源参数，最重要的是破裂速度，小地震的基础上停止阶段。假设破裂开始于椭圆的一个焦点，并在断层面上以恒定的破裂速度径向扩展，最终终止于椭圆边界。这个模型使我们能够调查各种各样的破裂配置，从一个圆形的单边传播破裂。在这个模型中，我们发现，两个高频停止阶段，是希尔伯特变换的对方，辐射和两个停止阶段之间的到达时间的差异是依赖于破裂速度的平均值，椭圆的长半轴的半径，和它的椭圆度。这些参数可以通过非线性最小二乘反演方法来估计。我们进行模拟测试，这使我们能够检测到一个希尔伯特变换对的到达时间与噪声数据的假设源模型预测的一致。这些模拟试验表明，我们的反演方法是有用的。由于我们的方法不需要一个先验假设的平均破裂速度，断层面的方向，和圆形裂纹模型，它为我们提供了一个工具，估计准确的震源尺寸以及破裂过程的小地震。

We propose a method to obtain source parameters, most importantly the rupture velocity, of small earthquakes based on stopping phases. It is assumed that a rupture begins at one focus of an ellipse and spreads radially at a constant rupture velocity on the fault surface, eventually terminating on the elliptical boundary. This model allows us to investigate a wide variety of rupture configurations, ranging from a circular to a unilaterally propagating rupture. In this model, we find that two high-frequency stopping phases, being Hilbert transformations of each other, are radiated and that the difference in arrival times between the two stopping phases is dependent on the average value of the rupture velocity, the radius of the major semi-axes of the ellipse, and its ellipticity. These parameters can be estimated by a nonlinear least-squares inversion method. We perform simulation tests, which allow us to detect a Hilbert transform pair whose arrival times coincide with ones predicted by an assumed source model from noisy data. These simulation tests show that our inversion method is useful. Since our method does not require an a priori assumption of the average rupture velocity, the orientation of the fault plane, and the circular crack model, it provides us with a tool for estimating accurate source dimensions as well as rupture processes of small earthquakes.