Numerical construction method for fault structures based on fourier series

Abstract

The present invention relates to the field of geophysical tomography technology, specifically to a Fourier series-based numerical construction method for fault Structures. Aimed at addressing the non-Nyquist undersampling problem in geophysical exploration, this method first applies gain correction and logarithmic transformation preprocessing to the tomographic scan data. Subsequently, the geological fault model is expressed as a Fourier series, and a mathematical model with Fourier coefficients as optimization variables is established. This model includes a data fidelity term and an adaptive sparse regularization term. In the solution phase, an efficient Alternating Direction Method of Multipliers is employed for iterative optimization, where alternating solving and soft-thresholding shrinkage operations are used to enforce sparsity of the Fourier coefficients in the adaptive dictionary domain. Ultimately, this method effectively suppresses undersampling artifacts and high noise, achieving high-fidelity reconstruction of geological parameter distribution Structures. While preserving the resolution and details of formation structures, the invention significantly improves the quality and efficiency of fault reconstruction, offering substantial value for geological assessment and reservoir modeling.