The Dipping Dike Case: A Computer Curve‐matching Method of Magnetic Interpretation

Abstract

A self‐adjusting curve‐matching computer program for the interpretation of magnetic anomalies produced by dike‐like bodies is described. The method yields an optimum set of dike parameter values by selecting a best‐fit model anomaly curve for a given set of discrete observed data along a profile across a two‐dimensional anomaly. The criterion used by the computer for the selection of a best‐fit curve may be either the linear or least squares condition. Convergence to either of these conditions requires the solution of a nonlinear problem. In the present case, solution is achieved by automatic trial and error modifications of an initial model. Selection of the initial model is based upon the shape of the observed anomaly; the proper choice of an initial model assures convergence of the error of fit to an absolute rather than to a relative minimum. The repeatability of the convergence of the iterative process can be tested by changing the initial model within the allowable ranges of variation of the dike parameters. Interpretations of finite strike length anomalies are achieved through the use of a correction curve. With this method, best‐depth estimates to the top of dike‐like bodies may be determined and for cases of induced magnetization, the effective susceptibility contrast and the dip of the dike may be calculated. Two practical applications of the method are presented.

2D dipping dike magnetic data interpretation using a robust particle swarm optimization

“…The magnetic anomaly by a 2D dipping dike structure is given by (Hood, 1964;McGrath and Hood, 1970):…”

“…First our algorithm is applied on synthetic data created from equation 1 with and without Gaussian noise (Hood, 1964;McGrath and Hood, 1970), the results were given in section 3. Then the proposed algorithm applied to two…”

An Iterative Approach to Depth Determination from Second Moving Average Residual Magnetic Anomalies

“…Figure 3 shows a total magnetic anomaly above an olivine diabase dike, Pishabo Lake, Ontario (McGrath and Hood, 1970). The depth to the outcropping dike (sensor height) is 304 m (Figure 3).…”

Aeromagnetic surveys over Izu-Oshima Volcano before and soon after the 1986 eruption.

“…2) A large-scale trend with a pair of positive and negative anomalies in the NW-SE direction was modeled into the effect of a dyke-like body, by means of an inversion similar to that used by MCGRATH and HOOD (1970).…”