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从第一类积分方程的反演求解入手 ,推导出适合于岩石核磁共振弛豫时间多指数反演的两种算法 :奇异值分解 (singularvaluedecomposition)方法和变换反演算法 .对算法的具体实现过程进行了详细的论述 ,从理论和实例处理两方面分析讨论了两种算法的优缺点 .从解的自由度的角度 ,讨论解的分辨率及最优反演模型的选取原则 :SVD算法适合于信噪比较高的数据反演 ,变换反演算法适应于较低信噪比的数据反演 .在进行岩石核磁共振信号的多指数反演处理时 ,应优先选用变换反演算法 ,只有当原始数据的信噪比SNR≥ 80时 ,可选用SVD反演算法 .为保证T2 反演结果的真实性 ,T2 布点数应在 30～ 50个之间 .研究内容对核磁共振岩心分析和核磁共振测井工作具有重要参考价值
Starting from the inversion of the first kind of integral equation, two algorithms are proposed, which are suitable for the multi-exponential inversion of rock NMR NMR relaxation time: singular value decomposition (STD) method and transform inversion algorithm. The concrete realization of the algorithm The advantages and disadvantages of the two algorithms are analyzed and discussed from two aspects of theory and example processing.From the viewpoint of degree of freedom of solution, the resolution of the solution and the selection principle of the optimal inversion model are discussed: the SVD algorithm is suitable for Inversion of data with high signal-to-noise ratio, inversion inversion algorithm is suitable for data inversion with lower signal-to-noise ratio. In the inversion of multi-exponential inversion of rock nuclear magnetic resonance signals, transform inversion algorithm should be preferred. When the signal-to-noise ratio of the original data is more than or equal to 80, the SVD inversion algorithm can be used.In order to ensure the authenticity of the T2 inversion result, the number of T2 clothings should be between 30 and 50. The research content of NMR analysis and NMR Logging has important reference value