Tectonic stress field in Shandong region inferred from small earthquake focal mechanism solutions
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摘要: 基于山东地区1970—2012年5月387次中小地震震源机制解数据,使用Gephart和Forsyth的 FMSI方法计算了该区的平均构造应力方向； 使用区域应力张量阻尼反演方法,结合共轭梯度法求解了应力张量的阻尼最小二乘最优化问题,并根据Lund和Townend推导给出的由构造应力张量计算最大水平主应力方向的公式,反演计算了山东地区构造应力场的空间分布特征,并讨论了该区构造应力场的变化及其与郯庐断裂带的关系．Abstract: Based on 387 focal mechanism solutions of middle and small earthquakes occurred from 1970 to 2012,this paper studies the stress field in Shandong region by using damped regional-scale stress inversion. We adapted the conjugate gradient method to solve the damped optimization problem of stress tensors. According to the formulae derived by Lund and Townend we calculated the maximum horizontal principal stress orientations in this region. We also discussed the relationship between spatial variation of regional stress field and the Tancheng-Lujiang fault zone.
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图 1 本文使用的小震资料空间分布(a)及震源机制解分类(b)图
Figure 1. Locations of 387ML≥2.0 earthquakes used in this paper (a) and classification of focal mechanisms on the octant equal-area projection according to Frohlich (2001) (b)
图 2 本文使用的小震震源机制解的P轴(a)、T轴(b)下半球极射投影图
Figure 2. Lower hemisphere projection ofPaxes (a) andTaxes (b) used in this study
图 3 本文使用的小震震源机制解的归一化P轴方位(a)与T轴方位(b)统计直方图
Figure 3. Histogram of normalized azimuths ofPaxes (a) andTaxes (b) of the focal mechanism solutions used in this study
图 4 山东地区主应力轴及其置信区间的下半球等面积投影
Figure 4. Lower-hemisphere equal-area projections of principle stress axesσ1， σ2andσ3， and their confidence regions
图 5 模型长度与数据拟合误差之间的折中曲线图虚曲线旁所标数字是阻尼参数e的取值(见式(11))
Figure 5. Trade-off between model length and misfit Numbers along the dashed line are values of damping parameterse
图 6 山东地区背景应力场反演结果(0.5°网格， 阻尼系数e=0.5)(a) 最大水平主压应力方向； (b) 最大水平主张应力方向； (c) 最大水平主压应力方向误差
Figure 6. Inverted stress results for Shandong region with damping parametere=0.5, on a 0.5°×0.5° grid (a) The maximum horizontal principal compressive stress orientation; (b) The maximum horizontal principal extensive stress orientation; (c) Errors in estimated principal stress orientations
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