Using relation figures of horizontal and vertical gradient in quantitative interpretation of gravity data

In this paper, it has been shown that there is a special relation between horizontal and vertical gradients of gravity data and the vertical and horizontal components of magnetic data for some of 2-D sources. It has been shown that the Hilbert transform is useful in calculating the vertical gradient of gravity and magnetic anomalies from the horizontal gradient for transformation of gravity and magnetic anomalies and to estimate the parameters of sources.
The plot of horizontal component versus vertical component in Cartesian coordinates is named the relation figure which is introduced by Werner (1953) as the polar plot of the vertical and the horizontal component of the field. The relation figure is used for qualitative interpretation of source parameters.
We have shown the relation figures by plotting the horizontal gradient of gravity versus its Hilbert transform. We have presented here the properties of relation figures of some two- dimensional models of simple geometry such as; thick dike, dip step, vertical step, horizontal step. The relation figures for these models are found to be ellipse or circle with different properties. In the first step, these properties may be used to distinguish whether the source is a dike or other model and then depth, width (for dike), dip, and radius (for horizontal cylinder) of the models. Finally, synthetic and real data is examined. Real data has been measured institute geophysics of Tehran University. There are some differences in the results of the synthetic and real data which are interesting and noticeable. In conclusion these differences and their reasons have been explained.