重、磁异常的走向与其振幅谱走向的关系

在文中利用坐标变换的方法,证明了重、磁异常的走向与其振幅谱的走向是垂直的。

THE RELATION BETWEEN THE STRIKE OF THE GRAVITY AND MAGNETIC ANOMALY AND THAT OF ITS AMPLITUDE SPECTRUM

In the space domain, for gravity anomaly （△g） and the reduced to pole magnetic anomaly （or vertical anomaly with vertical magnetization）, the strike of the body causing the anomaly and the strike of the anomaly are the same. In this paper, we will prove that the strike of the anomaly stated above is perpendicular to the strike of its amplitude spectrum.For convenience but without loss of generality, we assume the contours of the anomaly are in the form of ellipse, and for an i contour, it can be expressed byLet x = pix', pi = ai/bi, then eq. （1） becomesFrom this and by use of Hankel's transformation, we get the following equation for the contours of the amplitude spectrum of the anomaly:where u and v are frequency （or wave number） with respect to x and y axis separatly. If ai > bi, then （K2/Pi2） < K2, or if ai < bi, then （K2/Pi2） > K2, i.e, the direction of the long axis of eq. （1） （the strike of the anomaly） is perpendicular to the direction of the long axis of eq.（3） （the strike of the amplitude spectrum of the anomaly）.