三维物性分布的位场计算

本文在连续层状模型的基础上,将Parker位场公式推广到更具一般性的两种三维物性分布模型中。此时岩石的密度ρ和磁化强度J不仅在水平方向上可以任意变化,而且在深度上可依指数或线性函数形式变化。新的位场公式仍具有严密而简明的特点。结合圣安德烈斯断层带的重力反演,介绍了它的应用、模型分解和双界面同时反演的技术。

A COMPUTATION METHOD OF POTENTIAL FIELD WITH THREE-DIMENSIONAL DENSITY AND MAGNETIZATION DISTRIBUTIONS

Based on Parker's formula of potential field valid in an uneven layer model, twokinds of extended formulas are proposed. Compared with previous methods, it can beused in more general cases where the assumed density and magnetization not only varyin horizontal direction but also in vertical by either an exponential or a linear functions.The new formulas can be expressed strictly and compactly in frequency domain as fol-lows: F[△g（r₀）]=-2πGe^-kx₀Σfrom n=1 to ∞((（k-λ）^n-1/n!)F[ρ₀（r）hⁿ（r）])or F[△g（r₀）]=-2πGe^-kx₀Σfrom n=1 to ∞((k^n-1/n!)F[ρ₀（r）hⁿ（r）]) +2πGe^-kx₀Σfrom n=2 to ∞(((（n-1）k^n-2)/n!)F[β₀（r）hⁿ（r）])It can be found that these formulas are feasible to modelling those complicated geolo-gical structures. A gravity inversion for San Andreas fault is introduced as an exam-ple. The applications of new formulas, a technique of model decomposition and simul-taneous inversion of two interfaces are briefly discussed as well.