基于三维构造张量的位场边界识别滤波器

地质体构造边界位置的确定是位场数据解释中的一项重要工作，现有很多基于位场梯度张量数据的边界检测滤波器，但存在识别边界位置模糊且无法均衡深浅地质体异常的缺点.本文定义了位场数据的三维构造张量，并提出基于位场构造张量的边界滤波器.为了同时显示不同振幅异常的边界位置，对新定义的滤波器进行归一化处理.在高阶均衡滤波器的计算中需要计算位场的垂向高阶导数，本文引入一种计算的稳定算法，基于拉普拉斯方程利用位场水平导数求解垂向导数，可减小垂向导数计算中产生的误差.将定义的滤波器应用到合成的重磁数据中证明了新方法相比传统的滤波器能更加清晰、准确地圈定边界位置，而且针对同时含有正负异常的地质情况，可避免产生额外的错误边界.最后将新的滤波器应用到实测的重磁数据的解释中，结果显示基于构造张量的滤波器可更准确清晰地划分出断裂的边界位置，发现更多的构造细节.

A filter to detect edge of potential field data based on three-dimensional structural tensors

To detect the edge of potential field is an important task in identifying the horizontal position of geological structure. Although there are many methods based on potential field gradient tensors used to edge detection, the resolved edges remain blurred and inaccurate. This paper defines the structural tensors of a potential field and develops the related edge detectors to outline sources edges. In order to display different-amplitude anomalies simultaneously, we purpose two normalization strategies. When we calculate the new edge detectors, high-order vertical derivatives of potential field computation can increase the noise effect. The new calculation algorithm using horizontal derivatives to calculate vertical derivatives based on Laplace equation is applied to solve this problem. The presented filters tested on a synthetic potential field model show that they can outline the source edges clearly and accurately compared with traditional detectors. For complex situations with positive and negative anomalies, the new methods will not cause extra false edges. At last, we apply these new detectors to the real measured gravity and magnetic data. The results indicate that the new methods have ability to display edges of geological structures clearly and accurately and to discover more subtle information.