The Application Of Fractal Theory In Geophysical Research

The lithology, porosity, permeability and petrophysical of underground rocks possessstrong non-uniformity and anisotropy after the earth undergoing the nonlinear, non-uniform,and multi-stage geological processes which sustained a long geological period. To describethe heterogeneity objects, the corresponding mathematical methods should be used tocharacterize its non-uniformity. Fractal geometry provides an effective tool for the analysis ofnon-uniformity of underground rocks. To combine the two, the geophysical signal representedby the geological and geophysical processes between a variety of scales and scale exhibitself-similarity or scale-independent, called the fractal nature of the geophysical signal.Multiple fractal-the geophysical signal superimposed performance of multi-dimensionalfractal characteristics. The multi-dimensional fractal characteristics of the geophysical signalenergy or energy density, can be time or space the geophysical signal correction, singularity ordifferent geophysical dynamic process of decomposition.In this paper, the geophysical signal in2-D is analyzed by fractal geometry theory. Therelationship between the amplitude of geophysical signal with the area and the powerspectrum of geophysical signal and area is emphasized. The essence of relationshipsmentioned above reflect the heterogeneity of underground media and the abnormallycharacteristics produced by different sizes of target bodies. The signals from different targetbodies can be extracted by the characters of fractal geometry mentioned above, whichprovides an effective tool to study the uniformity and non-uniformity of target bodies. Asimple model and complex model for2-D magnetotelluric numerical simulation are studied.The abnormal characters of target bodies are decomposed by fractal geometry, whichillustrates the applicability of fractal theory in geophysical signal decomposition. For thecomplex model, the decomposition is complex. Whether the fractal geometry can extract thesignal from complex models needs further research and analysis. Finally, the fractal geometry is used for the analysis and processing of metal oreexploration data. The results show that the fractal geometry reflects the known anomalouszone, and new abnormal zone is also found in low abnormal area, which specifies thedirection of further exploration.