Use of Walsh transforms in estimation of depths of idealized sources from total-field magnetic anomalies

We developed a scheme to compute the depths of four idealized magnetized sources, viz., a monopole, a line of monopoles, a dipole and a line of dipoles from the Walsh spectra of the total-field magnetic anomalies. The sequency numbers, l"m"a"x corresponding to the peaks of the differential energy density spectra over these sources are practically independent of the shape of the observed anomaly and are linearly dependent on the source depths. For each model, we derived a quantitative relation between the depth and the sequency number l"m"a"x. Analyses of simulated data over idealized isolated sources reveal that (i) a profile length of about 8 times the source depth provides accurate value in computed depth; (ii) data spacing of less than one-fourth the source depth has no significant error in depth computation and (iii) the technique is capable of tolerating random error to the tune of 10% of the peak amplitude of the simulated anomaly. We compared the results of depth estimations from Walsh and Fourier spectra. Analysis of total-field magnetic anomalies over a buried water supply pipe has demonstrated the applicability of the proposed method.