球壳形磁性层磁异常正反演方法

DIRECT AND INVERSE METHODS OF MAGNETIC ANOMALY ENGENDERED BY MAGNETIC LAYER WITH SPHERICAL SHELL SHAPE

为了适应卫星磁测资料解释的需要,作者在磁性界面和磁性层磁异常正反演方法研究的基础上,首次提出了球壳形磁性层磁异常正反演理论和方法。 作者首先阐述了垂直磁化球壳型磁性层模型,导出了场垂直分量Z_(λο)的球谐系数正演公式。然后,给出了磁性层上,下层面埋深变化值与磁化强度变化值的球谐系数反演公式。进而导出了迭代反演收敛条件。本文的磁化强度反演方法不同于目前国内外已有的方法,其反演对象是磁化强度变化值△J_(λθ),磁化强度平均值J是必须给定的定解条件。这种反演方法能给出尽可能满足人们解释要求的解,克服了前人反演方法总存在负值的困难。 为了增加球壳形磁性层反演方法的实用性,作者还在类似平面频率城反演方法所作假设的前提下,把这种利用球谐分析理论在全球面导出的方法,严格地推广应用于局部区域。这也是球谐分析理论在局部区域应用的一个实例,在理沦上具有一定的意义。

<ABSTRACT> In order to interpret Magsat data the authors advanced the theory and methods used for solving the direct and inverse problems of the magnetic anomaly of magnetic layer with spherical shell shape. Firstly, the authors give the model of magmetic layer with spherical shell shape and vertical magnetization, derive the direction expression of spherical harmonic coefficient of the field Z engendered by this magnetic layer. Secondly, the authors derive the inversion expression of the spherical harmonic coefficients of its , A in the order of varied values of the top surface depth, bottom surface depth and magnetization. It shoud be pointed out: In order to determine the solutions of and from , it is necessary to give the conditions for determining solutions and to extract from the fields to be used in solving inversion problems. Based on the principle of external field equavalence the important condition for determining the solution of is that' the average value J of magnetization must be given'. Further, the authors give a stable algorithm of inversion problem solutions and a convergence condition of iteration inversion. Finally, on the basis of certain assumptions the authors extend strictly this theory and methods used for the whole earth's surface to that for the partial earth's surface. This may be served as an example for applying the spherical harmonic analysis theory on the partial earth's surface.