Using fractal crustal magnetization models in magnetic interpretation1

Evidence from borehole susceptibility logs and the spectral analysis of aeromagnetic data suggests that the three-dimensional distribution of magnetization within the crust can be described as fractal. This property can be exploited in magnetic interpretation methods which explicitly require statistical information on the spatial variation of magnetization. Specifically, we address the problem of magnetic source depth estimation through downward continuation and gridding aeromagnetic survey data using the method of kriging. When magnetic data are continued downwards the depth at which the power spectrum flattens out (the ‘white’ depth) can be taken to be an estimate of the top of the source distribution. This procedure assumes that individual sources are uncorrelated with each other. Taking into account the correlation of the magnetization using a fractal description leads to a reduction in this depth estimate. Gridding of randomly distributed magnetic measurements using kriging requires an estimate of the covariance of the data. Compared with the assumption of a white (uncorrelated) magnetization distribution, using fractal covariances for kriging produces gridded estimates which more closely reflect the statistics of the underlying magnetization process and produce maps with a justifiable degree of smoothness.

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