Improved MAX-MIN method to estimate total magnetization direction using Wiener filtering

Knowledge of the total magnetization direction is useful for forward modeling and reduction-to-the-pole (RTP) of magnetic anomalies. However, remanent magnetization deviates the total magnetization direction from the induced magnetization direction; therefore, it is essential to determine the correct direction of total magnetization. Theoretically, the MAX-MIN method, which searches for the position of the maximum value of the function that comprises the minimum values of the RTP field with different directions, can yield the correct direction of total magnetization. However, such estimations of direction usually indicate large errors in comparison with the results of crosscorrelation methods, which calculate the correlation coefficient between the RTP field and the magnetic magnitude transforms. Our analysis reveals that noise is the primary cause of the inaccuracy in estimation results. We have improved the MAX-MIN method using Wiener filtering based on the principle of least-mean-squares deviation. The k-means clustering algorithm clusters points that are as closely connected as possible, while ensuring that the distances between clusters are as large as possible. Therefore, the k-means clustering algorithm is used to divide the radial logarithmic power spectrum into the effective signal with low wavenumbers and the noisy signal with high wavenumbers. Then, the Wiener filtering RTP operator is constructed using the slope and intercept of the fitted straight line in the corresponding wavenumber bands. The improved MAX-MIN method is tested using magnetic anomalies of spherical and combined cuboid models with different levels of added Gaussian noise and different total magnetization directions. The improved MAX-MIN method is applied to the magnetic anomaly in the Yeshan region (eastern China) and the Taihe region (southwestern China). Results indicate that the improved MAX-MIN method based on the principle of least-mean-squares deviation could obtain reliable estimation of direction from noisy magnetic anomaly data.