FFT-Based Probability Density Imaging of Euler Solutions.

Area of Science:

• Geophysics
• Potential Field Interpretation
• Computational Seismology

Background:

• Traditional Euler deconvolution struggles to differentiate true anomalies from spurious Euler tails using only the structural index.
• Existing methods require manual intervention or complex filtering to remove misplaced Euler solutions, impacting efficiency and accuracy.
• The normalized B-spline probability density (BSS) method offers a data-driven approach to cluster and delineate anomaly sources based on solution similarity and density.

Purpose of the Study:

• To introduce a computationally efficient algorithm for the BSS method, addressing memory and time constraints associated with large datasets.
• To develop and validate a multivariate B-spline probability density estimation method based on the Fast Fourier Transform (BSSFFT) combined with fast linear binning.
• To demonstrate the effectiveness of the BSSFFT algorithm in separating and locating adjacent anomaly sources in geophysical data.

Main Methods:

• A fast linear binning approximation algorithm was integrated into the BSS to accelerate sample projection onto the estimation grid.
• Fast Fourier Transform (FFT) was employed for efficient discrete convolution between the grid and the density function.
• The proposed BSSFFT algorithm was validated using random normal distributions, synthetic models, and real geophysical data (Bishop 5X).

Main Results:

• The BSS and BSSFFT algorithms accurately estimated probability density functions, validated against true pdfs and Gaussian kernel smoothing.
• Analysis of synthetic models using BSS and BSSFFT yielded Euler solutions consistent with theoretical values, confirming algorithm correctness.
• Application to Bishop 5X data demonstrated the BSSFFT's capability to effectively separate and locate adjacent anomaly sources through 3D probability density analysis.

Conclusions:

• The BSSFFT algorithm, incorporating fast linear binning and FFT, provides a robust and efficient solution for Euler deconvolution analysis.
• This method significantly improves the ability to distinguish and delineate multiple, closely spaced anomaly sources in geophysical datasets.
• The BSSFFT algorithm exhibits strong adaptability and practical utility for interpreting complex potential field data.