Plots of chondrite-normalised rare earth element (REE) patterns often appear as smooth curves. These curves can be decomposed into orthogonal polynomial functions (shape components), each of which captures a feature of the total pattern. The coefficients of these components (known as the lambda coefficients—\(\lambda \)) can be derived using least-squares fitting, allowing quantitative description of REE patterns and dimension reduction of parameters required for this. The tetrad effect is similarly quantified using least-squares fitting of shape components to data, resulting in the tetrad coefficients (\(\tau \)). Our method allows fitting of all four tetrad coefficients together with tetrad-independent \(\lambda \) curvature. We describe the mathematical derivation of the method and two tools to apply the method: the online interactive application BLambdaR, and the Python package pyrolite. We show several case studies that explore aspects of the method, its treatment of redox-anomalous REE, and possible pitfalls and considerations in its use.

球粒陨石归一化稀土元素 (REE) 模式图通常显示为平滑曲线。这些曲线可以分解为正交多项式函数（形状分量），每个函数都捕获总模式的一个特征。这些分量的系数（称为 lambda 系数 - \(\lambda \)）可以使用最小二乘拟合推导出来，从而允许对 REE 模式进行定量描述并降低所需参数的维数。四分体效应类似地使用形状分量对数据的最小二乘拟合进行量化，从而得到四分体系数 ( \(\tau \) )。我们的方法允许将所有四个四分系数与四分无关 \(\lambda \)曲率。我们描述了该方法的数学推导以及应用该方法的两个工具：在线交互式应用程序 BLambdaR 和 Python 包pyrolite。我们展示了几个案例研究，探讨了该方法的各个方面、其对氧化还原异常 REE 的处理以及其使用中可能存在的陷阱和注意事项。