Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations, which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and must be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles that are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.

中文翻译：

---

地学成像中多维马尔可夫链的收敛性检验

经典的反演方法将具有预定义数量参数的模型调整为观测数据。借助可逆跳马尔可夫链蒙特卡洛（rjMCMC）等多维反演算法，可以在反演过程中更改此数字，并以更灵活的方式解释观测结果。地球科学成像应用程序使用此行为来自动将模型分辨率调整为所研究系统的不均匀性，同时将模型参数保持在最佳水平。结果，rjMCMC算法产生了一个整体，这是一组模型实现，它们共同表示所研究问题的后验概率分布。这些实现是通过从随机选择的初始解中进行顺序更新而演变而来的，并朝着反问题的目标后验分布收敛。直到链中的某个点，实现可能会受到初始模型的强烈偏见，并且必须从最终集成中丢弃。利用收敛评估技术，可以确定链中的这一点。由于参数数量的变化，多维MCMC方法产生的合奏不适用于经典的收敛评估技术。为了克服这一障碍，引入了三种解决方案，以将模型实现转换为通用维，同时保持集合的统计特征。从层析下层调查中推断出模型的标量，向量和矩阵表示，并应用了三种经典的收敛性评估技术。结果表明，作为地质突起创建由光栅化模型的适当选择的标量的转换可以保留类似系综的性质。