数据空间磁异常模量三维反演

强剩磁的存在通常导致了总磁化强度方向未知,进而影响了磁异常的反演和解释.磁异常模量是一种受磁化方向影响小的转换量,可以在强剩磁条件下通过反演三维磁化强度大小分布来推测场源分布状态.我们提出了一种数据空间磁异常模量反演算法来减少剩磁的影响.与标准的模型空间L2范数正则化反演方法相比,我们的方法有两个优点:一是无需搜索正则化参数(需要反复求解非线性反演问题),因而可以减少计算时间;二是反演结果更加聚焦,深度分辨率更高,我们对此进行了原因分析.通过模型和实测数据测试证明了该算法的有效性和更好的反演效果.

3D data-space inversion of magnetic amplitude data

3D magnetic inversion for susceptibility distribution is a powerful tool in quantitative interpretation of magnetic data and has been successfully applied to exploration of mineral and oil gas resources and to interpretation of regional geologic structure. The traditional inversion algorithms require knowledge of magnetization direction, which means that one should assume there is no remanent magnetization and self-demagnetization. Consequently, the direction of magnetization is assumed to be the same as the current geomagnetic field direction. However, strong remanent magnetization always exists and the total magnetization direction can be significantly different from that of the geomagnetic field direction due to complicated geological conditions, and in this case the traditional inversion algorithms become ineffective and the inversion result may be wrong. Magnetic amplitude data are less sensitive to the total magnetization direction and can be used to invert for 3D magnetization strength distribution to delineate the positions of causative bodies in the presence of strong remanent magnetization. We present a data-space magnetic amplitude inversion algorithm to reduce the effects of remanent magnetization. We also give a detail formula derivation of the proposed algorithm. In the data space, the matrix dimensions are equal to N×N (the number of data) rather than M×M (the number of model parameters), where N is far less than M. So the computational efficiency is improved. The computational time is further reduced because this method does not need to search for a regularization parameter by using an incomplete conjugate gradient method. Moreover, a square root operator is used to impose a positivity constraint on the effective susceptibility and likewise to focus the inversion results. Three synthetic data examples and a real data example are used to verify the proposed data-space algorithm. Tests on these examples show that the proposed method can focus the inversion results and likewise increase solution speed by up to an order of magnitude compared with the standard model-space, L₂-norm regularized inversion.