This work introduces a new method for simulating facies distribution with two categories based on Fourier analysis of Boolean functions. According to this method, two categories of facies distributed along vertical wells are encoded as Boolean functions taking two values. The subsequent simulation process is divided into three consecutive steps. First, Boolean functions of the well data are decomposed into a binary version of a Fourier series. Decomposition coefficients are then simulated over the two-dimensional area as stationary random fields. Finally, synthetic data in the interwell space are reconstructed from simulated coefficients. The described method was implemented experimentally in software and tested on a case of a real oil field and on a case of a synthetic oil field model. Simulations on the synthetic model were used to test the performance of the method for two different bases in the Fourier expansion (Walsh functions and Haar wavelets). The simulation results were compared to those obtained on the same synthetic model via the classical sequential indicator simulation. It was shown that, for both bases, the new method reproduces statistical parameters of the well data better than sequential indicator simulation.

本文基于布尔函数的傅立叶分析，介绍了一种模拟两类相分布的新方法。根据该方法，沿垂直井分布的两类相被编码为具有两个值的布尔函数。随后的仿真过程分为三个连续的步骤。首先，将井数据的布尔函数分解为傅立叶级数的二进制形式。然后在二维区域上模拟分解系数作为固定随机场。最后，从模拟系数中重建井间空间中的合成数据。所描述的方法在软件中通过实验实现，并且在真实油田的情况下和在合成油田模型的情况下进行了测试。对合成模型进行了仿真，以测试该方法在傅立叶展开中两个不同基础（Walsh函数和Haar小波）的性能。通过经典的顺序指示器模拟，将模拟结果与在相同的合成模型上获得的结果进行比较。结果表明，对于这两个基地，新方法都比顺序指示器模拟更好地再现了井数据的统计参数。