基于方向tilt-Euler的三维磁数据快速反演

三维磁异常快速反演是磁法勘探进行地质解释的一项重要内容.本文在方向tilt梯度基础上进行导数处理，并进行合理改进，得到了6个改进的方向tilt梯度导数，丰富了不同方向上的磁异常信息.对常规欧拉反褶积方程进行三个方向求导，所构成的方程组与6个改进的方向tilt梯度导数进行结合，从而构建出了两个基于方向tilt梯度导数的快速反演方程组（方向tilt-Euler法），用于反演场源的位置参数.另外，将三个方向导数下的欧拉反褶积进行平方和及均方根处理，得到了场源构造指数的求解公式.单一模型试验表明，6个改进的方向tilt梯度导数异常基本不受磁化方向影响，可从不同方向上反映磁异常信息，方向tilt-Euler能够准确地反演出场源的位置及构造指数.叠加模型试验证实了方向tilt-Euler法相对于tilt-Euler法，具有反演解聚集度更强、连续性更好、反演准确度更高、受噪声影响更小及无虚假反演解等优点.将本文方法应用于内蒙古塔木素航磁资料处理中，获得了丰富的地下磁源分布信息，为了解该地区隐伏断裂构造及岩体分布等提供了有效依据.

Fast inversion of 3D magnetic data based on the directional tilt-Euler method

The fast inversion of 3D magnetic data is an important task of magnetic interpretation. In this paper, six improved derivatives of directional tilt-gradient are derived to obtain rich magnetic information in different directions. In addition, two linear equations (named tilt-Euler method) based on the combination of three directional derivatives of conventional Euler deconvolution and the six improved derivatives of the directional tilt-gradient, are proposed for fast estimation of magnetic source-parameters. Moreover, a formula is introduced to estimate structural index of magnetic source based upon mean square root of the sum of squares of three directional derivatives of Euler deconvolution. The single model test shows that the six improved derivatives of the directional tilt-gradient are less influenced by the magnetization direction, and can reflect the magnetic anomaly of different directions. The directional tilt-Euler method can exactly estimate the position and structural index of the source. The multisource model test demonstrates that the directional tilt-Euler method has tighter clustering and better continuity of the solutions, higher precision, less affected by noise and no spurious solutions, when compared with the tilt-Euler method. The directional tilt-Euler method is applied to aeromagnetic data over Tamusu area of Inner Mongolia, and the rich information of magnetic sources is obtained, which can provide effective evidences for hidden faulted structures and rock masses.