Estimation of near-surface density based on gravity Bayesian analysis and its application in Yunnan area
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摘要:
基于布格重力异常相对于地形起伏光滑分布的约束条件，从一维自由空气重力异常数据出发，采用贝叶斯方法估算近地表岩石密度，同时采用三次B样条函数拟合布格重力异常，获取光滑分布的布格重力异常.数据拟合和光滑约束之间的权重采用Akaike贝叶斯准则（ABIC准则）自动确定.均匀剖分模型和不均匀剖分模型数据试验都验证了该方法的有效性.相关参数评价表明，足够多的样条系数可以提高估计结果的准确性，样条系数的个数接近测点数时可获得较稳定的估计结果.增大异常的噪声水平时，ABIC准则可有效地自动增大先验光滑约束的权重.云南地区两条重力剖面应用结果表明，剖面沿线的近地表密度值起伏变化明显（达2.45~2.8 g·cm-3），前寒武纪和古生代地层密度相对较高（主要为2.53~2.75 g·cm-3），而中生代密度较低（2.45~2.73 g·cm-3）；本文估计的近地表密度结果与区域物性资料及地表地质特征较吻合；估计的剖面布格重力异常具有光滑性；红河断裂两侧近地表密度差异较大，可达0.4 g·cm-3.本文获得的两条剖面近地表密度结构和布格重力异常为该区深部结构与构造研究提供更可靠的重力基础数据.
Abstract:Bouguer gravity anomalies are calculated by terrain correction and Bouguer correction to free-air gravity anomaly data. Near-surface density is an important parameter in these two corrections. Assuming that Bouguer gravity anomalies vary smoothly with surficial topography, we estimate the near-surface density from 1-D free-air gravity anomalies by using the Bayesian method and simultaneously obtain the smooth Bouguer anomalies fitted by the cubic B-spline function. We determine the trade-off parameters between the data misfit and prior constraints automatically by the Akaike's Bayesian Information Criterion (ABIC). Synthetic data tests by using uniform and non-uniform subdivisions verify the effectiveness of the presented method. Relevant parameter evaluations show that more of the spline coefficients are involved in the method, better results will be produced. When the number of spline coefficients are close to the number of observed stations, a more stable estimation can be obtained. More noise in the data, higher weight for smooth constraints will be determined automatically by the ABIC algorithm. The application of this method to two gravity profiles in the Yunnan area shows that near-surface density along the profiles varies significantly (2.45~2.80 g·cm-3). The Proterozoic and Paleozoic strata have relatively high density (mainly 2.53~2.75 g·cm-3), and the Mesozoic strata have relatively low density (2.45~2.73 g·cm-3). The estimated near-surface density in this paper is in a good agreement with regional physical data and surface geological characteristics, and the estimated Bouguer gravity anomalies have good smoothness. The density differences between both sides of the Honghe fault are as large as 0.4 g·cm-3. The near-surface density structure and Bouguer gravity anomalies obtained in this paper provide reliable basic data for the study of deep structure in this area.
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Key words:
- Gravity anomaly /
- Near-surface density /
- Bayesian analysis /
- ABIC
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图 2
均匀剖分模型试验的超参数搜索图
Figure 2.
The search path of hyperparameters in uniform partition model test (The hyperparameters are 8.78×10-5 and 4.11×10-1, and the minimum ABIC value was 244.31)
图 6
(a) 最小ABIC值随M的变化情况；(b)估计标准差随M的变化情况
Figure 6.
(a) The changes of the minimum ABIC value with the increase of M value; (b) The changes of the estimated standard deviation of data residual with the increase of M value
图 7
各个子区块的估计密度值(A)及估计密度误差随M的变化情况(B)(黑色实心方形：估计值；黑色实线：理论值)
Figure 7.
With the increase of M value, the changes of estimated density in each subdomain (A; black line with square: estimated value; black solid line: theoretical value) and estimated density error (B)
图 8
不同噪声水平的原始自由空气异常对应的估计结果
Figure 8.
Different estimated results of original Free-air anomaly with different noise level
图 9
(a) 研究区地形图及(b)研究区地质构造简图
Figure 9.
(a) The topography map of research area; (b) The geological structure sketch of research area
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