Interpretation of three‐component borehole magnetometer data

We have made a theoretical study of the problem of locating and defining a magnetized prism in the vicinity of a drillhole. The study shows that a three‐component borehole magnetometer can be very useful in exploration for deep magnetic targets, which are difficult to intersect by drilling. There are nine parameters to be estimated from the data: the x, y, and z positions of the center of the prism; length, width and depth extent; and the three parameters defining the magnetization vector. The parameters are estimated by minimizing the sum of squared differences between the predicted and observed data. Since the problem is nonlinear, it must be solved iteratively. At each iteration a singular value analysis of the sensitivity matrix is performed, and a particular solution is chosen from a set of minimal length solutions; each solution corresponds to a different rank of the sensitivity matrix. The main difficulty is an ambiguity involving the position parameters and the parameters defining the magnetization vector. In order to minimize this obstacle, a parameter scaling matrix is introduced. The effects of noise, wrong model, probe orientation errors, borehole length, and data density are analyzed. We have found that the position and depth extent of the body can be estimated with reasonable accuracy.