计算重力异常垂向二阶导数的DCT法——模型实验

DCT Method for Calculating Vertical Second Derivative of Gravity Anomalies——A Modeling Experiment

基于离散余弦变换(DCT,Discrete Cosine Transform)的重力异常垂向二阶导数的计算方法,是笔者提出的新方法。以无限长水平圆柱体为例研究了DCT法的计算规律,模型实验证实,该法计算的无限长水平圆柱体重力异常垂向二阶导数的精度与采样间隔、剩余密度及圆柱体半径大小无关,与圆柱体轴心埋藏深度成正比。通过分析给出了基于DCT的合适的线性滤波方式,滤波后的重力异常垂向二阶导数与理论二阶导数拟合效果好,具有较高的计算精度。

It is a new method that calculates vertical second derivative of gravity anomalies based on discrete cosine transform （DCT）. The paper studies the computing rules of gravity anomalies for infinite cylinder. It is shown in modeling experiments that the calculating precision of gravity anomaly for infinite cylinder is independent of the values of sampling interval, remaining density and cylinder radius and is proportional to imbedded depth of cylinder axes. By analyzing, an adaptive mode of linear filter based on DCT is given out. The curves of the vertical second derivative of gravity anomaly are matched well with those of the academic second derivative, and the calculating precision is much higher.