Research on the inversion method of nuclear magnetic logging data based on improved singular value decomposition method

The inversion of nuclear magnetic logging data is used to obtain nuclear magnetic parameters such as the lateral relaxation time of fluids in reservoir pores by inversion calculation of spin echo strings observed from nuclear magnetic logging. The nuclear magnetic parameters can be used to calculate the porosity, permeability, oil, gas, and water saturation of the rock. The mathematical model for the inversion of nuclear magnetic parameters of pore fluids with spin echo strings is the first type of Fredholm integral equation. In this paper, an extended singular cost decomposition algorithm and the linear truncation algorithm are proposed by analyzing the relationship between the most fulfilling quantity of retained singular values and the signal-to-noise ratio. This algorithm can recognize the spectral inversion shortly and effectively, and it is steadier than the standard singular price decomposition algorithm, i.e., the solution does not change a lot when the signal-to-noise ratio modifies a lot. The linear truncation algorithm can be applied to the spectral inversion with low SNR (SNR>10), and it can maintain the realism of the relaxation spectral distribution at very low SNR.