The inversion of deep-sea magnetic anomalies using Akaike's Bayesian information criterion

We present a magnetic inversion method in the space domain using Akaike's Bayesian information criterion (ABIC). The horizontal variation of magnetization intensity is represented by a linear combination of bicubic B spline functions, and the problem is set to determine the expansion coefficients. A prior constraint on the roughness of the magnetization variation is incorporated in order to suppress the numerical instability. The ABIC give us the optimal weight of the prior constraint relative to the requirement of fitting the observed data, which is statistically determined from the quality and quantity of the data based on the entropy maximization principle. We applied this method to actual deep‐sea magnetic data collected by using an autonomous underwater vehicle and successfully obtained a magnetization distribution that adequately accounts for the observation. The solution does not suffer from the inevitable smoothing due to high‐cut filtering or an error caused by reducing the data onto a flat surface as sometimes happens in current inversion methods. Our method is especially useful in handling data collected along a surface of extreme topography over a relatively small area. Key Points New inversion method of magnetic data Statistical treatment of prior constraint Advantage in handling deep‐sea data