瑞雷波辐射方向图的假设检验：理想源屏蔽的理论评估
Hypothesis Tests on Rayleigh Wave Radiation Pattern Shapes: A Theoretical Assessment of Idealized Source Screening
摘要：
浅层震源激发瑞利波地面运动，其辐射模式与方位角有关。我们把二元假设检验的理论模型，这样的辐射模式筛选圆柱对称源（如爆炸）从非对称源（如非垂直倾滑，或非VDS故障）。这些数据模型包括具有几个未知参数的源，被高斯噪声污染并嵌入分层半空间中。广义极大似然比测试，我们从这些数据模型产生的筛选统计和决策规则，依赖于测量，嘈杂的地面运动在离散传感器位置。我们明确量化这些统计数据的筛选能力如何随着源的任何倾滑和走滑分量的大小而增加，相对于噪声（断层信号强度），以及它们如何随网络几何形状而变化。作为我们的理论的应用，我们应用这些测试来（1）找到最佳的传感器位置，最大限度地提高筛选非圆形辐射图案的概率，以及（2）在特定的归因概率下，反演可能被错误地归因于爆炸的最大非VDS故障信号。最后，我们量化了某些错误是如何来源于开放裂缝增加筛选率错误。虽然这种理论解决方案是理想的，需要未来的验证，他们仍然是重要的地下爆炸监测方案，因为他们提供了基本的物理限制的鉴别能力的测试，从非VDS断层源屏幕爆炸。
英文摘要：
Shallow seismic sources excite Rayleigh wave ground motion with azimuthally dependent radiation patterns. We place binary hypothesis tests on theoretical models of such radiation patterns to screen cylindrically symmetric sources (like explosions) from non-symmetric sources (like non-vertical dip-slip, or non-VDS faults). These models for data include sources with several unknown parameters, contaminated by Gaussian noise and embedded in a layered half-space. The generalized maximum likelihood ratio tests that we derive from these data models produce screening statistics and decision rules that depend on measured, noisy ground motion at discrete sensor locations. We explicitly quantify how the screening power of these statistics increase with the size of any dip-slip and strike-slip components of the source, relative to noise (faulting signal strength), and how they vary with network geometry. As applications of our theory, we apply these tests to (1) find optimal sensor locations that maximize the probability of screening non-circular radiation patterns, and (2) invert for the largest non-VDS faulting signal that could be mistakenly attributed to an explosion with damage, at a particular attribution probability. Lastly, we quantify how certain errors that are sourced by opening cracks increase screening rate errors. While such theoretical solutions are ideal and require future validation, they remain important in underground explosion monitoring scenarios because they provide fundamental physical limits on the discrimination power of tests that screen explosive from non-VDS faulting sources.
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