In the last two decades, several geostatistical simulation techniques have appeared that allow taking into account complex structural information, by quantifying a multiple-point statistical (MPS) model. The higher-order statistics are typically informed from a training image, sample model, or geological exposure. Such MPS models can represent the subsurface and are then used to simulate subsurface models with high(er) order of realism than is possible using, for example, the widely used 2-point statistical models (such as sequential Gaussian simulation).

All available methods dealing with MPS models are simulation methods, that can be used to generate multiple realizations of the underlying statistical model conditioned to hard and, to some extent, soft data. Such realizations can be very useful but are also computationally expensive to obtain. Here we consider the case when the end-user may not be interested in the set of produced realizations themselves, but rather in parameter-wise marginal statistical properties of a single model parameter derived from the simulated realizations. To obtain these, one would typically generate a larger number of independent realizations, and then compute some marginal statistics of these.

Here we propose an MPS estimation algorithm, a variant of the widely used sequential simulation algorithm, that can be used to directly compute and store parameter-wise conditional statistics. This allows for a potentially faster and more accurate estimation than using sequential simulation. The method is demonstrated on both ENESIM- and SNESIM-type MPS algorithms and results compared using both sequential simulation and estimation. As an example, the method is applied for estimating the existence of near-surface buried valley systems in Kasted, Denmark.

在过去的二十年中，出现了几种地质统计模拟技术，它们通过量化多点统计 (MPS) 模型来考虑复杂的结构信息。高阶统计数据通常来自训练图像、样本模型或地质暴露。此类 MPS 模型可以表示地下，然后用于模拟具有比使用广泛使用的 2 点统计模型（例如连续高斯模拟）可能实现的更高（更高）阶的真实感的地下模型。

处理 MPS 模型的所有可用方法都是模拟方法，可用于生成以硬数据和在某种程度上软数据为条件的底层统计模型的多种实现。这种实现可能非常有用，但获得的计算成本也很高。在这里，我们考虑最终用户可能对生成的实现集本身不感兴趣，而是对从模拟实现导出的单个模型参数的参数方面的边际统计特性感兴趣的情况。为了获得这些，人们通常会生成大量独立的实现，然后计算这些的一些边际统计数据。

在这里，我们提出了一种 MPS 估计算法，它是广泛使用的顺序模拟算法的一种变体，可用于直接计算和存储参数方式的条件统计。这允许比使用顺序模拟更快和更准确的估计。该方法在 ENESIM 和 SNESIM 类型的 MPS 算法上进行了演示，并使用顺序模拟和估计对结果进行了比较。例如，该方法用于估计丹麦卡斯特德近地表埋谷系统的存在。