We present a novel methodology for exploring 4D seismic data in the context of monitoring subsurface resources. Data-space exploration is a key activity in scientific research, but it has long been overlooked in favor of model-space investigations. Our methodology performs a data-space exploration that aims to define structures in the covariance matrix of the observational errors. It is based on Bayesian inferences, where the posterior probability distribution is reconstructed through trans-dimensional (trans-D) Markov chain Monte Carlo sampling. The trans-D approach applied to data-structures (termed ”partitions”) of the covariance matrix allows the number of partitions to freely vary in a fixed range during the McMC sampling. Due to the trans-D approach, our methodology retrieves data-structures that are fully data-driven and not imposed by the user. We applied our methodology to 4D seismic data, generally used to extract information about the variations in the subsurface. In our study, we make use of real data that we collected in the laboratory, which allows us to simulate different acquisition geometries and different reservoir conditions. Our approach is able to define and discriminate different sources of noise in 4D seismic data, enabling a data-driven evaluation of the quality (so-called “repeatability”) of the 4D seismic survey. We find that: (a) trans-D sampling can be effective in defining data-driven data-space structures; (b) our methodology can be used to discriminate between different families of data-structures created from different noise sources. Coupling our methodology to standard model-space investigations, we can validate physical hypothesis on the monitored geo-resources.

中文翻译：

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通过跨维采样探索数据空间：以 4D 地震为例

我们提出了一种在监测地下资源的背景下探索 4D 地震数据的新方法。数据空间探索是科学研究中的一项关键活动，但长期以来一直被忽视，有利于模型空间调查。我们的方法执行数据空间探索，旨在定义观测误差的协方差矩阵中的结构。它基于贝叶斯推理，其中后验概率分布通过跨维（trans-D）马尔可夫链蒙特卡罗采样重建。应用于协方差矩阵的数据结构（称为“分区”）的 trans-D 方法允许分区的数量在 McMC 采样期间在固定范围内自由变化。由于 trans-D 方法，我们的方法检索完全由数据驱动且不是由用户强加的数据结构。我们将我们的方法应用于 4D 地震数据，通常用于提取有关地下变化的信息。在我们的研究中，我们利用了我们在实验室收集的真实数据，这使我们能够模拟不同的采集几何形状和不同的储层条件。我们的方法能够定义和区分 4D 地震数据中的不同噪声源，从而能够对 4D 地震勘测的质量（所谓的“可重复性”）进行数据驱动的评估。我们发现： (a) 跨 D 采样可以有效地定义数据驱动的数据空间结构；(b) 我们的方法可用于区分由不同噪声源创建的不同数据结构族。