复杂条件二维重力场及重力张量场空间波数域正演方法

Fast forward modelling of gravity field and gradient tensor for complex two-dimensional anomaly

随着传感器技术的发展,重力场与重力张量场测量技术发展迅速,为实现地下密度分布精细反演提供了数据保障。正演是反演的基础,解决任意密度分布复杂地质体重力场与重力张量正演高效、高精度计算问题,是实现重力高效、精细反演、人机交互反演解释的关键。针对起伏地形和任意密度分布这种复杂条件下二维重力场及重力张量场高效高精度正演问题,这里提出了一种空间波数混合域正演算法,其关键环节包括:①结合新的矩形二度体组合模型波数域表达式和一维Gauss-FFT算法,提出了一种任意密度分布和起伏地形下重力场及重力张量高效、高精度正演算法;②采用新的二维正演算法,计算观测最高点和最低点之间多个不同高度水平网格重力场及重力张量,结合三次样条插值方法,实现了起伏地形上重力场及重力张量场高效、高精度正演。模型算例结果表明,新方法具有高效、高精度的显著特点。

With the development of sensor technology,the measurements of gravity fields and gradient tensor are advancing rapidly,which guarantee the precise inversion for underground density distribution.Forward modelling is the basis of inversion.Calculating the complex gravity fields and gradient tensors rapidly and accurately with arbitrary density distribution is the key to carry out gravity inversion and interpretation with human-computer interaction efficiently.Based on the two-dimensional (2D) forward problem of gravity fields and gradient tensor with arbitrary density distribution and undulating terrain,we present a fast and high-precision two-dimensional forward modeling in wave number domain.The key points include:(1) A 2D forward modeling algorithm,which shows fast and high-precision properties,for gravity fields and gradient tensor of horizontal observation line with arbitrary density distribution is proposed based on wave-number transformation and Gauss-FFT algorithm;(2) The new algorithm is used to calculate the gravity fields and gradient tensor of multiple observation lines with different height.Combined with the cubic spline interpolation method,the 2D forward modelling of gravity fields and gradient tensor with the topography are implemented.The results of the synthetic tests show that the new method has high computational accuracy and efficiency.