Scale invariance, including self-similarity (isotropy), self-affine (stratified structure), generalized self-similarity (anisotropic scale invariance), is the intrinsic property of geological bodies and geological events. Unfortunately, existing scale invariant models and analysis techniques (no matter mono or multi-fractal) are usually assumed self-similarity(hence isotropy). In contrast to these isotropic assumptions and models, geophysical fields are generally highly anisotropic(e.g. atmosphere, earth interior). Now people pay more attention to the anisotropic scale invariance. In order to explain the anisotropic scale invariance system, Lovejoy and Sherzter use Fourier energy spectrum to study the scale invariance, and use rotation and stretch to describe anisotropic scale invariance.With the energy spectral density in frequency domain, the scale invariant generator technique(SIG) is utilized to estimate the parameters of matrix G, the parameters in G and the family of balls, which is calculated from known matrix G and generalized scale invariance to describe the anisotropy between different scales.As we know, the information can be considered to cascades of values of different frequency. The geological anomaly can be thought to be the high energy fluctuation of some frequency in frequency domain.The filter is designed to filter the data of different frequency. Useful information could be extracted from the multi-discipline data of geosciences by using the SIG to reserve regional information, emphasize local abnormal, and restrain the noise of high frequency.The Tongshi gold field as an example in western Shandong Province has been studied. Gravity data were used to distinguish the different geological units and extract the geological anomalous units associated with gold mineralization. The conclusion is that the Tongshi complex unit as a potential source region for gold can display clearly by using the SIG technique based on the gravitational data.
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