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目前,根据网格求解物理特征的反演方法中使用了两种约束:(1)绝对约束:它要求解矢量接近于一个预先给定的矢量,如近似于岭回归中的零矢量等;(2)相对约束:它要求解矢量的元素互相很接近,如该方法的平滑度要求物理特征的空间导数是连续的。只使用绝对约束可能会产生一个与真实的地质属性不相符的有偏解;反之,只使用相对约束可能使反演不够稳定。 我们提出一种稳定的反演方法。该方法只在物理特征已知的点,如露头和井等地方进行绝对约束,在其它点上,则根据物理特征空间分布的线性关系采用相对约束。该方法模拟了物理特征分布中使用的插值方法,插值函数必须满足如连续性、贯穿整个数据等特征。该方法非常灵活,它不仅结合了真实信息,还结合了如连续性、对称性及趋势等间接信息。而且,它既能应用于线性问题,又能应用于非线性问题。我们将该方法应用于合成的势场数据,得到了如下的结果:(1)只使用平滑约束和有限的地面信息、井中信息就能产生沉积盆地基底起伏的可靠图像(根据重力资料)和磁化强度区域分布的可靠图像。(2)由于解对阻尼参数不敏感,所以计算很简单。我们还将该方法应用于加利福尼亚的San Jacinto地堑的布格异常,所得的结果与原来的解释完全一致。
At present, two kinds of constraints are used in the inversion method of solving physical features based on grid: (1) Absolute constraint: it requires that the solution vector be close to a predetermined vector, such as zero vector in the ridge regression; 2) Relative Constraints: It requires elements of solution vectors to be very close to each other. For example, the smoothness of the method requires that the spatial derivatives of the physical features be continuous. Using only absolute constraints may result in a biased solution that does not correspond to the true geological attributes; on the contrary, using only relative constraints may render the inversion less stable. We propose a stable inversion method. The method is absolutely constrained only at points where physical features are known, such as outcrops and wells. At other points, the method uses relative constraints based on the linear relationship of spatial distribution of physical features. The method simulates the interpolation method used in the distribution of physical features. The interpolation function must satisfy the features such as continuity and whole data. The method is very flexible, it combines not only real information but also indirect information such as continuity, symmetry and tendency. Moreover, it can be applied to both linear and non-linear problems. We apply this method to the synthesized potential field data and obtain the following results: (1) Using only smoothing constraints and limited ground information, well-bore information produces reliable images of the basement undulations of sedimentary basins (based on gravity data) and magnetization Reliable image of intensity distribution. (2) The calculation is simple because the solution is insensitive to the damping parameters. We also apply this method to the Bouguer anomaly in the San Jacinto Rift, California, and the results obtained are fully consistent with the original interpretation.