A new Bayesian formulation to locate earthquakes from body-wave direction of arrival
A new Bayesian formulation to locate earthquakes from body-wave direction of arrival
复制标题
从体波到达方向定位地震的新贝叶斯公式
DOI：
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发表时间：
2016
期刊：
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通讯作者：
M. Noble
中科院分区：
文献类型：
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作者：
E. Gaucher;A. Gesret;M. Noble
地震定位大多数时候是利用监测网络上观测到的地震波的到达时间计算的。然而，三分量传感器的广泛使用也可以获得波的到达方向，这可以用于更好地约束事件震源。这在单站监测或水力压裂监测中是众所周知的，其中一串三分量传感器通常部署在单个垂直井中，并且其中P波偏振测量是定位诱发地震活动性所必需的。然而，其他地震网络，特别是覆盖面较低的地震网络，可以从这一现有信息中受益。
我们提出了一个新的贝叶斯公式，定义了一个概率密度函数的地震震源的地震体波偏振的函数。似然函数采用三分量传感器视角，并使用协方差矩阵来量化P波或S波的偏振，该协方差矩阵包含包括不确定性在内的所有必要信息。它与方向统计一致，并将建模的到达向量与在传感器处观察到的分布进行比较，假设角中心高斯概率。这种非线性方法也可用于定向来自已知震源的三分量传感器。
与现有的高斯公式不同，角中心高斯公式不会将偏振减少到一对方位角和倾斜角，并且避免了对角度不确定性的近似估计。相反，它取代了其球形数据空间中的偏振信息。如在一维速度模型中的合成试验所示，新的公式可以导致更多的受限位置，并给出适当的归一化概率密度函数。因此，地震震源具有现实的不确定性域，并且到达方向信息与到达时间信息在联合概率密度函数中的组合是直接的。
Earthquake location is most of the time computed using arrival times of seismic waves observed on monitoring networks. However, the widespread use of three-component sensors gives also access to wave arrival direction, which can be used to better constrain the event hypocenter. This is well-known in single station monitoring or in hydraulic fracturing monitoring, where a string of three-component sensors is typically deployed in a single vertical well and where the P-wave polarization measurement is necessary to locate the induced seismicity. However, other seismic networks, especially with low coverage, could benefit from this available information.
We propose a new Bayesian formulation that defines a probability density function of the earthquake hypocenter as a function of the seismic body wave polarization. The likelihood function takes a three-component sensor perspective and uses the covariance matrix, which contains all necessary information including uncertainties, to quantify the polarization of the P- or the S-wave. It is consistent with directional statistics and compares a modeled arrival vector with the distribution observed at the sensor, assuming angular central Gaussian probabilities. This non-linear approach can also be used to orient three-component sensors from known seismic sources.
Unlike existing Gaussian formulations, the angular central Gaussian one does not reduce the polarization to a couple of azimuth and inclination angles and avoids approximate estimate of angular uncertainties. On the contrary, it replaces the polarization information in its spherical dataspace. As illustrated by synthetic tests in a 1D velocity model, the new formulation can lead to more confined locations and gives properly normalized probability density functions. Hence, earthquake hypocenters are provided with realistic uncertainty domains and the combination of the direction of arrival information with the arrival time information in a joint probability density function is straight forward.