Calculation of the magnetic gradient tensor from total field gradient measurements and its application to geophysical interpretation

Abstract

The very low inherent noise levels of superconducting quantum interference device (SQUID) sensors have led to proposals for the use of airborne SQUID magnetic gradiometers as geophysical interpretation tools. The quantity measured by such systems will be the gradient tensor, the spatial rate of change of the vector components of the magnetic field. By contrast, existing airborne gradiometers measure the spatial rate of change of the magnitude of the total field. This work describes a technique whereby the gradient tensor can be calculated from measurements of either the vertical or horizontal total field gradients throughout a plane. The signal‐to‐noise ratio of the calculated tensor components is essentially the signal‐to‐noise ratio of the original total field gradient measurements. The resulting tensor components may be upward or downward continued with standard techniques. Two advantages of using the tensor gradients instead of the total field gradients have been determined. Because the tensor components are not a function of the direction of the Earth’s field, contour plots do not suffer the skewing problems that total field or vertical gradient plots do. Thus, tensor gradient contour plots may be easier to interpret or may enhance the information obtained from total field or vertical gradient maps. In addition, the dipole‐tracking algorithm developed by Wynn et al. (1975) has been shown to be quite successful in determining the depth and horizontal location of block‐shaped bodies. The error in depth estimation is a strong inverse function of the ratio of the closest point of approach to largest dimension of the body. However, if the smallest separation is more than twice the largest dimension of the body, errors in depth estimation are less than 10 percent. Because the tensor components are calculated on a horizontal plane, they can be upward continued to meet this condition.