On the relation between seismic moment and stress drop in the presence of stress and strength heterogeneity
On the relation between seismic moment and stress drop in the presence of stress and strength heterogeneity
复制标题
应力和强度不均匀存在下地震矩与应力降的关系
DOI：
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发表时间：
1979
期刊：
影响因子：
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通讯作者：
R. Madariaga
中科院分区：
文献类型：
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作者：
R. Madariaga
根据定义，地震矩与地震断层面上的平均滑动有关。在这里，我们推导出一个精确的表达地震矩的一般非均匀应力降分布和几何形状的故障的复杂事件。我们发现地震矩与断层上应力降的加权积分成正比。该线性关系中的权重是具有相同震源几何形状但均匀应力降的假设事件的滑动。地震矩和应力降之间的这种关系取决于几何形状。特别地，对于多个源，权重被减小了0/R的数量级的因子，其中0是典型子断层的半径，R是总源区域的半径。作为这些结果的结果，我们发现，对于一个给定的应力降，一个简单的故障产生一个更大的地震矩比一个多个故障相同的总表面。相反，对于给定的时刻和震源区，复杂的事件将需要更高的应力降的子断层比一个简单的光滑的故障。我们测试这些结果与三个矩形模型的故障。第一种是简单、光滑的断层，具有均匀的应力降。第二个模型是一个简单的断层，在断层的中心部分应力降为零。最后一个模型是一个复杂的事件，其中断层的中心部分保持完整。我们发现，最后两个模型是很难区分从他们的远场辐射。
The seismic moment is related by definition to the average slip on the fault plane of an earthquake. Here we derive an exact expression for the seismic moment in terms of a general heterogeneous stress drop distribution and the geometry of the fault of a complex event. We find that the seismic moment is proportional to a weighted integral of the stress drop on the fault. The weight in this linear relationship is the slip for a hypothetical event with the same source geometry but uniform stress drop. This relationship between seismic moment and stress drop depends on geometry. In particular, for multiple sources the weight is reduced by factors of the order of o/R, where 0 is the radius of a typical subfault and R is the radius of the total source area. As a consequence of these results we find that for a given stress drop, a simple fault generates a larger seismic moment than a multiple fault of the same total surface. Conversely, for a given moment and source area, a complex event would need higher stress drops on the subfaults than a simple smooth fault. We test these results with three rectangular models of faulting. The first is a simple, smooth fault with uniform stress drop. The second model is a simple fault with zero stress drop in the central section of the fault. The last model is a complex event where the central section of the fault remains unbroken. We show that the last two models are difficult to distinguish from their far-field radiation.