面向剖面重力异常转换的等效源优化策略

Equivalent source optimization strategy for gravity anomaly profile transformations

在本文中,我们基于模型试验讨论了利用等效源实现剖面重力异常转换的可靠性,并针对发现的问题提出了一套场源设置优化策略:(1)沿剖面两侧对等效源层和观测数据扩边;(2)通过局部异常单调变化区间个数的整倍数控制等效源层中线质量的数量;(3)利用Tikhonov正则化确保反演的稳定性,并在迭代计算过程中维持条件数不变.合成模型试验表明:(1)单独对等效源层扩边可以消除异常导数在剖面边界附近的振荡,同时对等效源和数据扩边则可以进一步抑制垂向一阶导数和向上延拓计算值与理论值之间的剪刀差;(2)以深度偏移量、倍数、单侧扩边距离以及条件数为控制参数的等效源设置方式具有良好的可操作性.最后,我们将这些优化措施应用在了一条实测重力剖面上,并取得了与模型试验类似的结果.

In this paper we discussed, based on model tests, the reliability of gravity anomaly profile transformations through equivalent sources, and proposed a set of optimization schemes for source layout to overcome the defects found:(1)both the source layer and data are extended outward from each end of the profile;(2)the number of line masses within the equivalent source layer is controlled by the product of a multiplier and the number of segments on which the residual anomalies vary monotonically;(3)stabilization of inversion is maintained through Tikhonov regularization, with condition numbers unchanged during iterative computing processes. Synthetic model tests verify that:(1)Extending the equivalent source layer alone could eliminate oscillations of the derivatives, and extending source layer and data simultaneously could further depress the scissors differentials between calculated and theoretical values of the first vertical derivatives and upward continuation;(2)Using depth offset, multiplier, unilateral extension distance, and condition number as controlling parameters for equivalent source layout is of good feasibility. At the end, we applied these optimization measures to a gravity profile collected above a mining tunnel, and acquired transformation results similar to those of the model tests.