Joint inversion of multi-station receiver functions and gravity data for imaging Moho variations and average crustal vP/vS ratios
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摘要: 地壳厚度和波速比是研究地壳结构和组分的两个重要参数，可为区域构造研究提供重要约束。接收函数被广泛地用于确定地壳厚度和波速比，例如H-κ方法或H-κ-c方法，但是该方法只能确定台站下方的地壳厚度和速度比，当地震台站分布稀疏时，很难约束台站间的横向不均匀性。另一方面，重力数据也可用于莫霍面的起伏变化研究，它在横向上覆盖很好，有较高的分辨率，但在纵向上分辨率相对较低。为此，本研究提出了一种联合反演算法求解莫霍面深度和地壳波速比参数。联合反演算法综合考虑了接收函数在纵向上的较高分辨率和重力数据在横向上的较高分辨率，同时拟合区域内所有台站上的接收函数和区域重力数据。模型测试表明联合反演算法较单一的接收函数反演更精确，特别是对于地壳厚度的确定。Abstract: Crustal thickness and vP/vS ratio are two important parameters for understanding crustal structure and composition, which can help to study regional tectonics. Receiver function analysis has been widely used for determining crustal thickness and vP/vS ratio by the H-κ method or the H-κ-c method. However, it can only acquire average crustal thickness and vP/vS ratio beneath each seismic station, but cannot constrain their lateral variations among seisimic stations due to their sparse and irregular distribution. On the other hand, the gravity data has been widely used to derive the Moho variaitons, which has a good coverage and resolution laterally but poor resolution vertically. Therefore, in this study we have developed a new joint inversion method of receiver functions and gravity data to simultaneously invert for variations of Moho depths and average crustal vP/vS ratios in a region. The method takes advantage of complementary strengths of receiver functions and gravity data, and can simultaneously fit all receiver functions and gravity data in the region. The synthetic tests show that the proposed joint inversion method produces more reliable results than only receiver function analysis, especially for the crustal thickness.
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Key words:
- joint inversion /
- receiver function /
- gravity /
- Moho /
- vP/vS ratio
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图 1 莫霍面起伏模型（a）和地壳平均波速比模型（b），其中三角形表示虚拟台站
Figure 1. Synthetic Moho model （a） and the average crustal vP/vS model （b） where the black triangles indicate virtual seismic stations
图 2 虚拟台站（东向坐标x＝350 km，北向坐标y＝250 km）下方的简单P波速度结构（a）和根据该模型正演出的对应不同射线参数的理论接收函数（b），以及图1a中莫霍面起伏所引起的重力异常（c）
Figure 2. The simple crustal P-wave velocity structure beneath one virtual seismic station at x＝350 km in the east direction and y＝250 km in the north direction （a），and the theoretical receiver functions for different ray parameters （b），and gravity anomalies caused by Moho variations in Fig.1a （c）
图 3 联合反演L-曲线分析
（a，b，c）通过接收函数确定的不同平滑参数和阻尼参数下的归一化模型与数据残差的关系，最优参数$ {\varpi }_{H}＝300 $，$ {\lambda }_{H}＝300 $，$ {\lambda }_{k}＝8\;000 $；（d） 接收函数与重力之间权重关系曲线，重力的最优参数$ \gamma ＝25 $
Figure 3. L-curve analysis for the joint inversion
（a，b，c） Trade-off between the normalized model residuals and data residuals for different smoothing or damping parameters used in receiver function inversion （$ {\varpi }_{H}＝300 $，$ {\lambda }_{H}＝300 $，${\lambda }_{\kappa}＝8\;000$）； （d） Tradeoff analysis between the normalized model residuals and data residuals for different weights between receiver function and gravity data，and the optimal weight $ \gamma ＝25 $
图 4 （a） 接收函数的RMS迭代收敛曲线；（b） 重力异常的RMS迭代收敛曲线
图中黑色圆点为只采用接收函数到时数据，红色方块为采用接收函数和重力异常两种数据联合反演的结果
Figure 4. （a） The RMS residuals of receiver function；（b） The RMS residuals of gravity data
The black dots denote the results only by receiver function data，and the red diamonds denote the results by joint inversion
图 5 （a，b） 仅采用接收函数数据反演和联合反演获取的莫霍面；（c，d） 采用接收函数反演和联合反演所获取的莫霍面结果与理论模型的残差分布；（e，f） 采用接收函数和联合反演得到的地壳平均波速比；（g，h） 反演的平均地壳波速比结果与理论模型之间的残差
Figure 5. （a，b） The Moho results determined by receiver function analysis and joint inversion，respectively； （c，d） The deviations of inverted Moho models in Figs.（a） and （b） from theoretical Moho model in Fig. 1a，respectively；（e，f） The average crustal vP/vS ratios by receiver function analysis and joint inversion，respectively； （g，h） The deviations of inverted vP/vS models in Figs. （e） and （f） from the theoretical vP/vS model in Fig. 1b，respectively
图 6 虚拟台站（x＝350 km，y＝250 km）下的地壳P波速度结构（a）和正演的接收函数（b）
Figure 6. The crustal P-wave velocity structure （a） at one virtual seismic station （x＝350 km，y＝250 km） and the theoretical receiver functions （b）
图 7 复杂速度模型情况下接收函数（a）和重力异常（b）的RMS迭代收敛曲线
图中黑色圆点为只采用接收函数到时数据，红色方块为采用接收函数和重力异常两种数据联合反演的结果
Figure 7. The RMS residuals of receiver function data （a） and gravity data （b） with iterations for the complex velocity model
The black dots denote the results only by receiver function data，and the red diamonds denote the results by joint inversion
图 8 只采用接收函数反演（a）和联合反演（b）得到的莫霍面结果与原始模型的残差以及只采用接收函数反演（c）和联合反演（d）获取的速度比结果与原始模型的残差
Figure 8. Deviations between theoretical Moho model in Fig. 1a and the inverted Moho models from only receiver functions （a） and joint inversion （b），and deviations between theoretical vP/vS model in Fig. 1b and the inverted vP/vS models from only receiver functions （c） and joint inversion （d），respectively
表 1 不同P波速度对联合反演的影响
Table 1. The effect of different P-wave velocities on joint inversion
vP
/（km·s−1）联合反演RMS拟合 联合反演残差 莫霍面深度/km vP/vS 接收函数/s 重力异常/（10−5 m·s−2） 最大残差 标准差 最大残差 标准差 6.0 0.362 2.905 0.664 0.285 0.177 0.041 6.1 0.361 2.842 0.607 0.263 0.164 0.033 6.2 0.363 2.794 0.554 0.251 0.152 0.033 6.3 0.363 2.743 0.526 0.249 0.139 0.041 6.4 0.363 2.695 0.569 0.256 0.126 0.054 6.5 0.362 2.649 0.612 0.268 0.123 0.062 6.6 0.364 2.602 0.653 0.286 0.142 0.068 
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表 2 不同剩余密度参数对联合反演结果的影响
Table 2. Effect of different contrast densities on joint inversion
剩余密度
/（kg·m−3）联合反演RMS拟合 联合反演残差 莫霍面深度/km vP/vS 接收函数/s 重力异常/（10−5 m·s−2） 最大残差 标准差 最大残差 标准差 350 0.375 6.550 1.410 0.794 0.168 0.055 400 0.371 3.560 1.150 0.638 0.156 0.048 450 0.364 3.070 0.940 0.372 0.147 0.044 500 0.363 2.740 0.529 0.249 0.139 0.041 550 0.365 2.510 0.710 0.318 0.132 0.040 600 0.368 2.330 0.990 0.456 0.126 0.040 650 0.372 2.190 1.250 0.595 0.121 0.041
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表 3 不同参考界面深度对联合反演影响
Table 3. Effect of different reference interfaces on joint inversion
参考深度/km 联合反演RMS拟合 联合反演残差 莫霍面深度/km vP/vS 接收函数/s 重力异常/（10−5 m·s−2） 最大残差 标准差 最大残差 标准差 38.5 0.363 2.745 1.908 1.410 0.136 0.076 39.0 0.363 2.745 1.439 0.953 0.121 0.063 39.5 0.363 2.745 0.971 0.515 0.130 0.051 40.0 0.363 2.743 0.529 0.249 0.139 0.041 40.5 0.363 2.742 0.994 0.545 0.148 0.034 41.0 0.363 2.742 1.463 0.986 0.156 0.032 41.5 0.363 2.743 1.931 1.444 0.165 0.034
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