Application of Improved Radix-2 FFT Algorithm in Lateral Logging

Array lateral logging technology is currently a hot topic in electrical logging research. How to accurately and quickly extract signal amplitudes from various frequency points of mixed signals is a prerequisite for achieving accurate calculation of formation resistivity. Digital Phase Sensitive Detection (DPSD) and Fast Fourier Transform (FFT) are the two most common digital detection methods in lateral logging tools. A new improved method is proposed to address the issue of long computation time in the reverse order process of the commonly used Reed algorithm in radix-2 FFT. Experimental results have shown that the improved FFT calculation speed is approximately 7 times faster than the conventional radix-2 FFT, and compared to the original method, the improved algorithm has doubled the computation speed; In terms of accuracy, DPSD performs better than traditional FFT in the absence of phase difference. However, as the phase shift increases, the change in dynamic phase difference will significantly increase. However, the improved FFT results are not affected by phase difference. By comparing and analyzing the two methods, it is proven that the resistivity curve obtained by FFT has better consistency and is suitable for measuring high resistivity formations $(100000 \Omega\cdot \mathrm{m})$. Thus, the measurement accuracy of the instrument has been improved, providing more reliable data for the precise identification of oil and gas reservoirs.