The spatial structural characteristics of geological anomaly, including singularity and self-similarity, can be analysed using fractal or multifractal modelling. Here we apply the multifractal methods to potential fields to demonstrate that singularities can characterise geological bodies, including rock density and magnetic susceptibility. In addition to enhancing weak gravity and magnetic anomalies with respect to either strong or weak background levels, the local singularity index (α ≈ 2) can be used to delineate the edges of geological bodies. Two models were established to evaluate the effectiveness of mapping singularities for extracting weak anomalies and delineating edges of buried geological bodies. The Qikou depression of the Dagang oilfield in eastern China has been chosen as a study area for demonstrating the extraction of weak anomalies of volcanic rocks, using the singularity mapping technique to analyse complex magnetic anomalies caused by complex geological background. The results have shown that the singularities of magnetic data mapped in the paper are associated with buried volcanic rocks, which have been verified by both drilling and seismic survey, and the S–N and E–W faults in the region. The targets delineated for deeply seated faults and volcanic rocks in the Qikou depression should be further investigated for the potential application in undiscovered oil and gas reservoirs exploration
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