Method for determining elemental concentrations in spectral gamma ray logging

A method for determining the concentrations of elements within a geologic formation includes the use of an inversion algorithm that seeks to minimize a cost function (F). The method includes the use of an iterative process 200 that updates the calculated concentrations of each element at each iteration using the gradient of the cost function (F). If the method returns a negative value for any of the elemental concentrations, the corresponding derivative is set to zero and the iterative process continues. The iteration is terminated if the difference between the model and measurement becomes suitably small or if a predetermined threshold number of iterations have been taken. The results of the determination of the elemental concentrations are displayed on a computer. 种用于确定地质地岩层内的元素的浓度的方法包含设法最小化价值函数（F）的反演算法的使用。该方法包含使用价值函数（F）的斜率更新在每个迭代处的每个元素的所计算的浓度的迭代的过程200的使用。如果该方法对于任何元素浓度返回负值，则对应导数被设置成零并且迭代的过程继续。如果模型和测量之间的差变得适合地小或者如果预定的阈值数量的迭代已经被进行，则迭代被终止。元素浓度的确定的结果被显示在计算机上。