Creating accurate and geologically realistic reservoir facies based on
limited measurements is crucial for field development and reservoir management,
especially in the oil and gas sector. Traditional two-point geostatistics,
while foundational, often struggle to capture complex geological patterns.
Multi-point statistics offers more flexibility, but comes with its own
challenges. With the rise of Generative Adversarial Networks (GANs) and their
success in various fields, there has been a shift towards using them for facies
generation. However, recent advances in the computer vision domain have shown
the superiority of diffusion models over GANs. Motivated by this, a novel
Latent Diffusion Model is proposed, which is specifically designed for
conditional generation of reservoir facies. The proposed model produces
high-fidelity facies realizations that rigorously preserve conditioning data.
It significantly outperforms a GAN-based alternative.

基于有限测量数据生成准确且地质真实的储层相是油气行业的关键问题之一。本文提出了一种新型潜在扩散模型，用于条件生成储层相，该模型在保持条件数据完整性方面明显优于以 GAN 为基础的备选方案。

条件储层相生成的潜在扩散模型

Latent Diffusion Model for Conditional Reservoir Facies Generation

When modeling geostatistical or areal data, spatial structure is commonly
accommodated via a covariance function for the former and a neighborhood
structure for the latter. In both cases the resulting spatial structure is a
consequence of implicit spatial grouping in that observations near in space are
assumed to behave similarly. It would be desirable to develop spatial methods
that explicitly model the partitioning of spatial locations providing more
control over resulting spatial structures and being able to better balance
global vs local spatial dependence. To this end, we extend product partition
models to a spatial setting so that the partitioning of locations into
spatially dependent clusters is explicitly modeled. We explore the spatial
structures that result from employing a spatial product partition model and
demonstrate its flexibility in accommodating many types of spatial
dependencies. We illustrate the method's utility through simulation studies and
an education application.

本文介绍了使用产品分区模型扩展到空间设置的方法，以明确模型空间位置的划分，提供了更多控制空间结构的方法，能够更好地平衡全局和局部空间依赖性，并通过模拟研究和教育应用示例表明了该方法的实用性。

空间产品分区模型

Spatial Product Partition Models

In this paper we first describe the class of log-Gaussian Cox processes
(LGCPs) as models for spatial and spatio-temporal point process data. We
discuss inference, with a particular focus on the computational challenges of
likelihood-based inference. We then demonstrate the usefulness of the LGCP by
describing four applications: estimating the intensity surface of a spatial
point process; investigating spatial segregation in a multi-type process;
constructing spatially continuous maps of disease risk from spatially discrete
data; and real-time health surveillance. We argue that problems of this kind
fit naturally into the realm of geostatistics, which traditionally is defined
as the study of spatially continuous processes using spatially discrete
observations at a finite number of locations. We suggest that a more useful
definition of geostatistics is by the class of scientific problems that it
addresses, rather than by particular models or data formats.

介绍了基于日志高斯卡克斯过程模型的空间和时空点过程数据，并探讨了推断的方法。同时，通过四个应用程序演示了该模型的实用性。论文认为这类问题自然适用于空间统计学领域，且该领域更适用于科学问题的研究，而非特定的模型或数据格式。