用格点尝试法求解P波初动震源机制解及解的质量评价

P-wave first-motion focal mechanism solutions and their quality evaluation

P波初动符号物理图像明确,是稳定的地震波信息.在资料充分时,可以较好地确定震源机制解.网格搜索法是目前流行的利用P波初动符号求解地震震源机制解的方法.不过,在实际观测资料不充分时,虽然较迭代算法优越,但网格搜索法依然有较大的不确定性.到目前为止,人们还没有找到合理的解决方案,极大地制约了这一类方法的应用.针对这一现状,本文在许忠淮提出的格点尝试法的基础上对网格搜索法进行了几个方面的改进.首先,采用新的加权方法计算加权矛盾比:权重因子包括反映初动符号质量的权重以体现资料质量的影响;不包括反映观测点与节面距离的权重以避免因节面附近资料权重的双重减小带来的系统偏差;通过减小震源球上密集资料点的权重以部分地抵消震源球上P波初动符号资料分布不均匀对可能解的影响.在通过加权矛盾比筛选可能的震源机制解时,把震源球分为面积相对均匀的网格进行解的搜索,避免了因网格划分不均匀所导致的平均解的计算偏差.针对资料不足情况下震源机制解会受控于个别观测点P波初动符号的情况,我们借鉴杰克刀(jackknife)技术,在可选解中增加了那些一个观测点被去除后的可选解,既对解的质量有了更好的把握,又增加了找到真解的可能性.进一步地,针对可选解存在多个解簇的情况,本文提出了通过聚类提供多组可选解的做法.最后,针对目前缺乏对解的合理评价体系的现状,提出了主要基于解的离散度并参考加权最小矛盾比对震源机制解质量进行评价的新方案.

P-wave first motion, an unambiguous physical quantity, is a kind of steady seismic information. When enough data were available, it could be used to ideally determine focal mechanism solutions. The most popular method for employing P-wave first motion to determine focal mechanism solutions is the grid search method. However, when applied to earthquakes with few data points, grid search method still has great uncertainty, although it is believed to be better than the it restricts th grid search Here, the erative method. By now, no satisfactory settlement has been found, which greatly e application of this method. In this paper, we focus on the improvement of former methods. Firstly, possible solutions are selected by weighted inconsistency ratio. weighting scheme retains the data-quality weighting factor so as to consider the influence of data quality, omits the weighting factor reflecting the distance between data points and nodal planes for avoiding over-reducing the weights of the observations near nodal planes, and adds another weighting factor which gives more power to sparse data points on the focal sphere for partly canceling out the influence of uneven distribution of the employed data points. Meanwhile, we divide the focal sphere into several roughly equal-square areas, which prevent deviation from real mean solution by artificial concentration of test solutions. We improve our inversion quality by employing jackknife technique, which enlarges the solution set by adding those possible solutions for one observation being ignored. This technique, along with clustering analysis, not only increases the possibility of finding out true solutions, but also makes us comprehend the quality of focal mechanism solutions unambiguously. Finally, we provide a new scheme for evaluating the quality of focal mechanism solutions based on the dispersion of selected solutions as well as the minimum weighted inconsistency ratio.